Towards a new paradigm for objectively measuring the quantitative similarity of marks: Colour and word marks

^[1]Abstract

Central to many intellectual property disputes is an assessment of the degree of similarity of two contested marks. A determination of similarity is fundamentally a subjective decision, involving a range of relevant tests which include consideration of the perception of the relevant consumer, and recognition of the existence of degrees of similarity within a spectrum (from high to low).

However, a more objective framework could have a number of advantages, including the potential to quantitatively measure the difference between marks, and providing the possibility to define thresholds up to which IP protection could apply, and build a case-law background offering a basis for greater legal consistency.

This study considers the cases of colour and word marks, and outlines some potential methodologies for quantifying the degree of similarity of marks. The analysis suggests that it should be possible to construct objective similarity metrics which could be applied to IP disputes and potentially incorporated into case law.

The proposed algorithm for word marks takes into account both visual (i.e. spelling) and phonetic (i.e. pronunciation) similarity, and also incorporates a number of additional features of an idealised metric such as downweighting the influence of any final 's', putting greater weight on similarity at the start of the strings, and including elements of 'normalisation' relative to the length of the strings - though further 'tuning' is likely to be required. It is, however, worth noting that the suggested model takes no account of conceptual similarity (i.e. meaning) and does not attempt to address similarity of associated goods and services classes.

Other future developments might involve efforts to ascertain the likelihood of confusion of marks (rather than just their similarity). One very simple possible basis for this determination - utilising the numbers of results returned by search engines for the marks in question, as a proxy for their overall commonness or prominence - is also discussed in this study.

Finally, it is important to note that the formulations presented in this study are suggested merely as tools to be incorporated into existing approaches and doctrines - which involve a range of additional manual review processes – rather than being intended to replace (on a wholesale basis) the current nuanced and multi-faceted approach to infringement employed by courts and tribunals.

Introduction

Central to many intellectual property disputes is an assessment of the degree of similarity of two contested marks. This follows from the framework set out in (for example) the UK Trade Marks Act 1994^[2], whereby even a non-identical mark may be considered non-registrable or infringing if it creates a likelihood of confusion (Sections 5(2b) and 10(2b)) with an earlier mark^[3].

A key point to note is that decisions regarding legal similarity are fundamentally subjective, involving a range of relevant tests which include consideration of the perception of the relevant consumer, and recognition of the existence of degrees of similarity within a spectrum (from high to low). 

Whilst trademark comparisons are likely always to retain a degree of subjectivity, there are some areas where objective quantitative formulations can be constructed. A more objective framework could have a number of advantages, including the potential to quantitatively measure the difference between marks. It would be necessary to explicitly incorporate the relevant metrics into comparison tests, but this would offer the potential to define thresholds up to which IP protection could apply, and could provide the basis for new case law to be applied to future analogous disputes, offering the potential for greater legal consistency.

This study considers the cases of colour- and word marks, and outlines some potential methodologies for quantifying the degree of similarity of marks. Any type of quantitative comparison approaches is likely to continue to need to be accompanied by manual review, and the formulations presented in this study are suggested merely as tools to be incorporated into existing approaches and doctrines, rather than being intended to replace (on a wholesale basis) the current nuanced and multi-faceted approach to infringement employed by courts and tribunals.

Part 1: Colour marks

Introduction: colour as a protected characteristic

The history and case-law surrounding trademarks as an indicator of product origin is extremely well established. Trademarks most usually pertain to brand names (word marks) or figurative elements such as logos. There are, however, a number of other characteristics which can have powerful brand associations, including product 'look-and-feel' (trade dress), sound marks and colours.

The legal definition of a trademark was broadened by the World Trade Organization Agreement on Trade-Related Aspects of Intellectual Property Rights, to cover "any sign … capable of distinguishing … goods or services"^[4], and many specific colours have been registered as trademarks by corporations (either as colour marks per se, or as colours included as components of a more complex mark featuring additional elements) (Figure 1) for their particular product classes. The most popular colour groups to be registered as trademarks are shades of blue (18% of registrations), red or pink (18%), yellow or gold (15%), and green (14%). Registration is possible if the colour serves as an indication of source, if it is not purely decorative or functional, and if proof of 'secondary meaning' can be provided (strictly, these definitions relate to US legal tests, which are relevant to various of the brands discussed below). In essence, this requires that the public has come to associate the colour with the associated brand, which can be demonstrated through the use of extensive advertising featuring the colour and/or through consumer surveys^[5].

Figure 1: Examples of colours registered as trademarks by brand owners (either as full marks or as components of a more complex mark) (source: Z. Crockett / The Hustle^[6])

There have been a number of high-profile legal cases involving colour-mark disputes, including actions by Deutsche Telekom regarding the shades of magenta used for their T-Mobile brand^[7,8], efforts to invalidate the registration of the orange shade used by the Veuve Clicquot champagne brand^[9], and other cases involving Cadbury's use of the purple shade Pantone 2685C^[10] and the use by Stihl of a combination of specific shades of orange (RAL 2010) and grey (RAL 7035)^[11,12,13]. 

Frequently, a key element of these types of case is the requirement for the brand owner to be able to demonstrate 'acquired distinctiveness'. One component of this objective is education of the public that the colour can function as a mark - i.e. a distinctive characteristic - in its own right. Initiatives along these lines have recently been employed by both Coca Cola and Mattel (for the Barbie brand), through the use of marketing campaigns incorporating minimalist brand references, where brand colours feature first and foremost^[14] (Figure 2).

Figure 2: Marketing campaigns incorporating prominent display of brand colours for Coca Cola (left) and Barbie (right)

Many of the reported cases raise the question as to the effectiveness of the protection afforded by a registered colour mark, and whether there is (or should be) a threshold of how close a colour needs to be to another, in order to be covered by the umbrella of protection (beyond the vague description that the similarity should be such that the difference between the shades is "barely noticeable"^[15]). Currently, however, there is insufficient case law to provide a definitive answer, and colour-mark protection is not enormously robust. The situation is further complicated by the variability which may exist across the same product in a range of different contexts (e.g. where different product imagery may be displayed on distinct websites, or even just when viewed on different devices, or in the difference between digital displays and physical contexts).

However, the question of colour protection is an important one to be able to answer. Previous work, utilising consumer psychology studies, has shown that colour is one of the primary characteristics (together with packaging shape and style) used by consumers to identify products - with a greater importance than brand name. Colour increases brand recognition by 80%, and accounts for between 62% and 90% of a consumer's initial judgement of a product^[16]. These observations are the reason why the problem of lookalike products is such a concerning issue^[17]. Lookalikes can most effectively be addressed through the registration of packaging as a trademark and a subsequent unfair advantage claim, but the application of colour marks could also be part of the picture.

Removing the subjectivity

In many intellectual property disputes, a central component is the assessment of the degree of similarity (which, in reality, exists as a 'spectrum') between two marks. Whilst this is frequently a subjective determination, colour marks are somewhat different, in that colours can essentially be exactly defined, so that a quantitative measure of difference can be formulated. This being the case, colour marks should be able to lend themselves - through the development of an appropriate landscape of case law - to the formulation of a legal framework whereby similarity can be objectively measured, and thresholds up to which protection may apply, can be defined. 

One simple model for defining colours (as presented in digital format) is the RGB framework, expressing the red, green and blue components (respectively) of any given colour as a number from 0 to 255, and thereby formulating a full ('3D') colour 'space' from [0,0,0] (black) to [255,255,255] (white)^[18], or 16,777,216 (i.e. 256³) colours in total. However, it is worth noting that even this framework does not account for all possibilities, as there will be an infinite number of intermediate shades between any two adjacent RGB colours (if defined using integer numbers), and other characteristics (such as metallicness, reflectivity - i.e. the difference between 'gloss' and 'matt(e)' shades - or fluorescent properties) which are not fully accounted for.

The model is such that any given colour is represented by a point in the colour space, as shown in Figure 3.

Figure 3: 3D representation of a colour ('Colour 1'; [R₁,G₁,B₁]) in RGB space

This framework means that the similarity between two colours (i.e. the geometric distance between them in colour space - 'd' in Figure 3 - with a smaller value of d denoting colours which are more similar) can be exactly defined. Mathematically (according to Pythagoras' theorem):

d = √[(R₁ – R₂)² + (G₁ – G₂)² + (B₁ – B₂)²]

Consequently, the distance (d) between any two colours will be somewhere in the range of 0 to 442 (= √(3 × 255²); the distance between black and white).

It is reasonable that some limited range of colour differences (as defined by a threshold distance d) should be covered under the umbrella of protection provided by a registered colour mark, in order to account for variations in printing and digital display technologies. However, since colour marks have the potential to be so oppressive (in terms of the limitations they may impose on third-party marks), it is likely that this threshold might need to be somewhat smaller than the actual differences which are sometimes currently present across the existing product range for certain brands. 

One implication of the use of a 'threshold' approach would be that it would set an upper limit on the total number of colours within RGB space which could be protected^[19] (much lower than the total 'universe' of 16.8 million colours). 

As an example illustration of the extent of colour variation which exists as a function of distance (d), Figure 4 shows a series of visualisations of the colour space surrounding the point at RGB [50,0,110] (i.e. Cadbury's Pantone 2685C). The circles in the figure show progressively increasing values of d, in steps of 10 units, up to a maximum of 50 (e.g. a protected colour-mark 'bubble' covering up to d = 10 would encompass the colour variations contained within the innermost circle).

Figure 4: Slices through RGB colour space surrounding the point at RGB [50,0,110]:

• (left) slice perpendicular to the red axis, with green and blue increasing to the right and top, respectively
• (middle) slice perpendicular to the green axis, with red and blue increasing to the right and top, respectively
• (right) slice perpendicular to the blue axis, with green and red increasing to the right and top, respectively

Areas where any of the [R,G,B] parameters are less than zero or greater than 255 (i.e. those falling outside the colour space) are shown in black. Circles show progressively increasing values of d, in steps of 10 units, up to a maximum value of 50 units.

It is certainly also possible to formulate modifications to the above approach, such as the use of mathematical weightings to account for the way in which colours are perceived through human vision^[20], or the use of constructs such as the 'normalised inner product'^[21] (essentially, a measure of (just) the differences in 'direction' of each colour from the origin point (i.e. [0,0,0] or black) - as shown by the dashed purple vector arrow in Figure 3). However, regardless of the exact details of the formulation, the key point is that the use of a consistent methodology would allow objective measurements to be applied to the comparison assessment.

As part of this approach, it is also convenient to define a score (expressed as, say, a percentage) to express the degree of similarity between two colours, which aligns well with the familiar terminology of stating marks to be similar to a 'low', 'medium' or 'high' degree (but is, in some ways, more preferable, as it allows an exact value to be quantified). 

One simple approach is to define a difference score (D_col), expressing the distance (d) between two colours as a proportion of the maximum possible distance between two colours in RGB space (i.e. the distance between [0,0,0] and [255,255,255], equal to √(3 × 255²), or approximately 441.7, i.e.:

D_col = d / √(3 × 255²)

From this formulation, D_col will take a value between 0 and 1 (or can be multiplied by 100 to give a percentage). Consequently, the similarity score (S_col) can be defined as:

S_col = 1 – D_col

or, using an equivalent formulation for the full representation:

S_col =  1 – √ { [(R₁ – R₂)² + (G₁ – G₂)² + (B₁ – B₂)²] } / (3 × 255²) }

The relationship between the similarity score (S_col) and the distance (d) for a pair of colours is therefore as shown in Table 1. 

Sim. score (Scol)	Diff. score (Dcol)	Distance (d)
0.00 (0%)	1.00 (100%)	441.7
0.01 (1%)	0.99 (99%)	437.3
0.05 (5%)	0.95 (95%)	419.6
0.10 (10%)	0.90 (90%)	397.5
0.25 (25%)	0.75 (75%)	331.3
0.50 (50%)	0.50 (50%)	220.8
0.75 (75%)	0.25 (25%)	110.4
0.90 (90%)	0.10 (10%)	44.2
0.95 (95%)	0.05 (5%)	22.1
0.99 (99%)	0.01 (1%)	4.4

Table 1: The relationship between colour similarity score (S_col) and distance (d)

Conversely (for example), two colours which are separated by an RGB distance (d) of 10 units can be objectively stated to be 97.7% similar.

Construction of a 'user-friendly' colour-mark database

As part of a colour-mark protection framework, it would make sense to maintain a database of protected colour marks (or, potentially, separate databases for distinct product classes), in which each colour was specified according to its RGB definition. This would allow the distance between each pair of colours to be specified, providing a structure which could easily be expanded to determine whether: (a) a disputed colour fell under the umbrella of protection of an existing mark; and (b) a new mark application was sufficiently far away from an existing protected colour to be registrable (presumably, dependent on any overlap of the associated goods and services classifications).

A mock-up of how this might be presented in practice is outlined in Table 2. The database is constructed using information relating to protected colour marks (or colours featured as components of the definitions of more complex marks) for a number of brands, using either their exact RGB specifications if available, or approximations otherwise. The entries in Table 1 have also sorted into a 'spectral'-style ordering (based on their H (hue) values; see below). The ability to sort colours into a convenient ordering can be highly beneficial in terms of providing ease of manual review of the information. However, in general there is no simple algorithm for translating a 3D colour space into a (1D) linear series of colours, in which all transitions are smooth and continuous.

The ordering used in Table 2 is based on an alternative expression of each colour, using their HSV (rather than RGB) values, where H (hue) is the 'base' colour (on a scale from 0 to 1 in 'spectral' order), S (saturation) is the intensity of the colour, and V ('value') is the darkness of the colour^[22]. Mathematical conversion of the RGB expression of a colour to its HSV equivalent involves a simple algorithm, and a number of pre-written library scripts^[23] are available to implement it.

Table 2: Mock-up of a database of protected colour marks, sorted by their H values (also shown are the L (luminosity) values^[24], a measure of 'lightness' or 'brightness')

Following on from the construction of a colour-mark database, it is then a relatively simple matter to construct (for example) a matrix showing the separation distance (d) (in RGB units) between each pair of colours. This approach could be used to illustrate whether a particular pair of colours were closer than any specific protection 'threshold', as part of the assessment for a dispute, for example.

Case studies and illustrations

1. Stratos v Freia Boble

In February 2025, the Norwegian IP Office rejected (pending appeal) an application by manufacturer Orkla to register the blue shade Pantone 2144 C as a colour mark for 'aerated chocolate' (for its Stratos brand), despite a previous court decision that the company was entitled to protection of the shade through long-term and widespread use^[25]. The earlier case arose when competitor Mondelez launched a similar product (Freia Boble) in 2023 using a "strikingly similar" shade of blue (Pantone 2145 C)^[26] (Figure 5). Orkla's challenge was successful, with Mondelez ordered to change its packaging and pay damages.

Figure 5: Illustrations of the Stratos (redacted) (top) and Freia Boble (bottom) products, taken from the court decision as published^[27]

Considering the RGB representations of the two Pantone shades in question, it is possible to calculate that the distance (d) between the two colours is 30 units, actually making them objectively (‘only’) 93.2% similar. 

2. Heinz

Also in February 2025, Pantone, the global colour standard, released a 'Heinz 57 Red' shade "emblematic of the [ketchup's] enticing appetizing arousing juicy red color [sic]"^[28,29]. This shade is approximately equal to RGB [131,31,31], which is actually significantly different to the 'Heinz Red' values cited by various online colour archives (e.g. [200,41,34] given by schemecolor.com^[30], which is 70 RGB units distinct, or (equivalently) differs by 15.8%). 

Heinz themselves are very defensive of their ketchup colour, as a means of protecting against refills and counterfeit versions, even going so far as to publish a Pantone-based colour 'cheat sheet'^[31] (Figure 6), referencing the 'true' Heinz colour as [211,32,38] (80 units (18.2%) distinct from ‘Pantone Heinz 57 Red’, but only 15 units (3.3%) from Schemecolor's cited value), and containing a guide to non-legitimate product colours (bottom of figure), featuring variants running from 27 units (6.0%) to 110 units (24.9%) distinct.

Figure 6: Heinz's published guide to legitimate and non-legitimate product colours

The lack of consistency between even the various 'official' Heinz colours (which, in some cases are less similar than 'true' Heinz and some of the explicitly-stated non-official shades) raises concerns regarding brand recognition - and, more generally, for the prospect of a robust quantitative framework for colour mark protection which will work well with existing brand collateral. 

Part 3: T-Mobile

T-Mobile (part of the Deutsche Telekom group) is notoriously protective of the magenta colour used in its branding, and has secured a colour trademark registration for 'Pantone Rhodamine Red U' (RGB [228,76,154]), despite actually using a range of different shades in its own marketing. In 2008, the brand (unsuccessfully)^[32] launched a case against rival telecommunications provider Telia for their use of a shade of magenta, followed by a successful case against AT&T subsidiary Aio Wireless in 2014. 

In 2020, T-Mobile targeted insurance provider Lemonade (lemonade.com), despite the reasonable difference between their respective shades of magenta, and the limited overlap between the areas of business of the companies. Lemonade ultimately changed the colour of its marketing materials in Germany, but subsequently launched an action in Europe to invalidate Deutsche Telekom's colour trademark, with an initial successful outcome in France^[33] (Figure 7).

Figure 7: Image (top) (from Twitter / X) of T-Mobile's ex-CEO John Legere showcasing brand colours, and (bottom) a montage of colours from the T-Mobile / Lemonade dispute (courtesy of The Hustle)

These had been just some of the disputes launched by Deutsche Telekom against companies in a range of industry areas, under the justification of the wide portfolio of trademarks held by the organisation in a range of areas, extending to fashion and healthcare.

Lemonade itself has been using shades of pink since its launch in 2015, with a brand association sufficiently strong that the organisation has even commissioned art projects relating to the pink shade #FF0083 (the hexadecimal representation of RGB [255,0,131]), including the creation of an associated portfolio website at ff0083.com.

The difference in colour between T-Mobile's trademark and their own brand colour is actually 85 RGB units (only 80.8% similarity), compared with the distances between their trademark and Lemonade’s three contested colours of 86, 87 and 85 units (and whose distances from T-Mobile's own brand colours are 107, 53, 49 units, respectively). 

Whilst there is perhaps some more reasonable justification for T-Mobile's earlier cases against companies in the same industry area, the Lemonade case highlights a very aggressive approach against an organisation in an area of business a long way from that for which T-Mobile is primarily known. It might be more reasonable to suggest that any formal framework for colour-mark protection should be expected to include a 'trade-off' between the closeness of the colours of competitor brands and the closeness of their (primary) areas of business (insofar as the latter can be quantified).

In the case of T-Mobile, however, the organisation appears to be attempting to protect a 'sphere' of colour variations in RGB space of radius approximately 100 units - covering a visually disparate range of shades - across a wide spectrum of areas of business. This 'sphere' (volume 4,188,790 cubic units) would encompass over one-quarter of the total volume of RGB space (255³, or 16,581,375 cubic units) - i.e. the universe of all possible colours - which would clearly be an unsustainable situation if all brands attempted to do so. 

Conclusions and discussion

Colours can be key distinctive characteristics of particular brands, but currently the framework for protecting specific shades is poorly defined, and the extent of protection is unclear, in part due to a lack of definitive case law. These points mean that many registered colour marks offer protection which is not particularly robust, with the registrations often liable to third-party attempts at invalidation. 

Part of the solution is a programme of consumer education on the distinctiveness of colours as brand identifiers, but it certainly seems to be the case that the legal framework could benefit from the use of rigorous mathematical descriptions, which would remove much of the subjectivity involved in mark comparisons, and allow thresholds for protection to be defined. 

It may also be the case that similar approaches could be formulated for other types of marks whose assessment has traditionally been seen as much more subjective. Certainly, the industry is already seeing evolutions in the protection landscape, with a number of sound marks (including Intel's jingle, MGM's lion roar, and Netflix's 'tu-dum' sound) already registered as brand identifiers, and the abolishment of the requirement in the EU for marks to be represented graphically, with multimedia files now permitted in applications^[34]. From the point of view of potential technological and legislative developments which may allow comparison of marks, sound marks can be 'fingerprinted' through digital analysis techniques, and it may be possible to define algorithms (perhaps incorporating elements of AI-based analysis) to measure degrees of similarity between other types of brand identifiers (such as logos).

For colour marks specifically, it would seem reasonable that the protection afforded by a particular colour-mark registration should also cover very close (but not necessarily identical) colours (for the product class(es) in question). This idea (which has analogies with the concepts of 'identity' and 'similarity' in regular trademarks) would circumvent the possibility of a third party attempting to circumvent the protection by using a variant shade differing by (say) one or two RGB points. The construction of a robust and reproduceable framework would require the definition of the exact degree of difference (i.e. the maximum colour 'distance', d) for which protection should be covered by a colour-mark registration. 

Comments by Lord Clement-Jones, following on from the Influence at Work / Stobbs study 'The Psychology of Lookalikes', highlighted the importance of considering psychological and behavioural analyses in IP disputes, particularly in relation to brand lookalikes^[35]. It is likely that future research concerning the impact of colour variations on subjective perceptions of brand association (or not) will be key to a 'ground-up' approach for defining the thresholds which should be applied in IP protection decisions.

More fundamentally, it may also be appropriate to modify the approach for calculating colour similarity to take account of the way in which colours are perceived by human viewers, rather than simply basing the metric on geometric colour 'distance'. One such approach involves the use of differing weightings^[36] for the differences between the individual red, green and blue components. This type of approach might offer the potential to incorporate ideas relating to the doctrine of imperfect recollection, which states that the similarity of marks must be judged through the eyes of the average consumer of the goods or services in question, who is "deemed to be reasonably well informed and reasonably observant and circumspect, [but who] rarely has the chance to make a direct comparison between the different marks and must place trust in the imperfect picture of them that he or she has kept in mind [and whose] attention is likely to vary according to the category of goods or services in question"^[37]. However, any attempt to quantify concepts along these lines could prove extremely complex, involving considerations of factors such as the existence of cultural associations of colours (which could have impacts on the psychological nature of memories of colour), and the fact that certain medical conditions can create variations in the ways in which different consumers may perceive the same colour.

Also of potential relevance is the fact that colours may be perceived differently depending on the physical context in which they are viewed. This is relevant to the concept of post-sale confusion^[38], where real-life scenarios must be considered when attempting to determine the likelihood of customer confusion. Incorporation of this type of idea might, however, run the risk of creating a framework within which colour-mark protection would be too broad, if it were to encompass the wide range of physical environments in which relevant views of the colour in question might arise.

Additional complications may arise in cases where a combination of colours has been protected (such as considering whether the protection might need to cover slightly greater variations of each of the colours individually, when considered together as a single mark). Furthermore, decisions regarding the degree of overlap of the associated goods and services classes of potentially competing products are likely to continue to add an additional degree of subjectivity.

Part 2: Word marks

Introduction

For word marks - which are less susceptible to exact ‘definition’ in the way that protected colours (Part 1) can be expressed - the situation is even more complex and subject to subjective elements in the assessment process. 

Even with no attempt to consider associated logos or imagery, classes of goods and services, or even the meaning of the words – i.e. ‘lexical’ or ‘semantic’ similarity) there are a number of factors to consider. At the very least, any defined metrics would need to account of the following factors:

• The calculated degree of similarity between two marks differing in a particular way (say, by just one replaced character) should probably be considered to be lower if the marks are shorter (e.g. an appropriate metric should probably determine that (for example) 'LG' and 'LV' are less similar to each other than are (for example) 'Starbucks' and 'Starmucks').

• The degree of similarity may also be dependent on the exact nature of the difference between the marks - for example, two marks differing by just the presence of a final 's' might be considered to be more similar than two marks where a different letter is appended.

• A 'one-size-fits-all' metric might need to take account of a number of different types of similarity, including visual (i.e. spelling, in the case of a word mark), aural (i.e. (phonetic) pronunciation), and conceptual. (Any algorithmic assessment of conceptual similarity would need to take account of misspellings and/or homophones where the meaning is (or may be) preserved, but this point is not considered further in this study.)

• Any metric reflecting the overall level of threat of infringement may need to take account of the degree of commonness or distinctiveness of (elements of) one or both of the marks. Examples to consider might include (say): 'McDonalds' v 'McSweet', where the only overlapping element is the common string 'Mc'; or 'Iceland' and 'Ireland', which are quantitatively very similar (in terms of spelling and pronunciation), but are both very familiar terms with very distinct meanings in their own right.

There are a number of well-established algorithms for quantifying the degree of (visual and phonetic) similarity between two text strings^[39,40,41], and it is informative to consider how effectively these are able to quantify the difference between various pairs of marks involved in previous dispute cases. This study considers the following pairs of marks as case-study examples:

• Starbucks v Charbucks
• Starbucks v Sardarbuksh
• McDonalds v McSweet
• Louboutin v Lubov
• Louis Vuitton v Chewy Vuiton^[42]
• Puma v Coma
• Nike v Nuke
• Lakme v LikeMe
• MDH v MHS
• Mahindra v Mahendra^[43] 
• Magnavox v Multivox
• Hpnotiq v Hopnotic
• Cana v Canya
• Seiko v Seycos^[44]
• Casoria v Castoria
• Trucool v Turcool
• Lucozade v Glucos-Aid
• Bacchus v Cacchus^[45] 
• Simoniz v Permanize
• Zirco v Cozirc
• Cresco v Kresco
• Intelect v Entelec^[46] 
• Bisleri v Bilseri^[47]

Standard algorithms for calculating string similarity^{[48,49,50,51]}

Outlined below are some of the most commonly-used algorithms for quantifying the degree of similarity between two text strings.

A. Spelling-based metrics (for visual similarity) 

(N.B. 'Distance' metrics quantify the degree of difference between the strings (i.e. larger values denote less similarity); 'similarity' metrics quantify the degree of similarity.)

1. Hamming distance - This is an 'edit-based algorithm' (i.e. one which quantifies the number of edits required to transform one string into the other) for strings of equal length, based on comparison of the strings on a character-by-character basis, to determine which are the same and which are distinct. A normalised version of this metric takes the number of non-identical characters and divides it by the length of the string.


2. Levenshtein distance - This metric quantifies the number of edits (character insertion, deletion, or substitution) necessary to transform one string into the other. Conversely, Damerau-Levenshtein distance, a modified version, also permits transpositions (swaps) of adjacent characters.


3. Jaro similarity^[52] - This metric takes consideration of the number of 'matching' characters between the strings (m), the number of 'transpositions' (t), and the string lengths (|s₁| and |s₂|), returning a value of 0 if m = 0, or ⅓[ m/|s₁| + m/|s₂| + (m–t)/m ] otherwise. A modified version, Jaro-Winkler similarity, includes a weighting to take greater account of matching characters occurring at the start of the strings.


4. Jaccard similarity - This is an example of a 'token-based algorithm', which calculate similarity by breaking down strings into smaller sub-strings ('tokens') and quantifying the degree to which the sets of tokens overlap (i.e. are common to both strings). This approach can be implemented by considering the individual words in multi-word strings, or characters or groups of characters ('n-grams') in individual words. Jaccard similarity is defined as the intersection of the two sets of tokens (i.e. the number appearing in both strings) divided by the union of the two sets (i.e. the number of tokens in total). A related metric is Sørensen-Dice similarity, in which the denominator of the metric is instead defined as the average size of the two token sets.


5. Cosine similarity - This metric can be defined for parameters which can be expressed as vectors, and can be applied to strings by expressing them in terms of word frequencies, for example. The metric is expressed as the cosine of the angle between the vectors, thereby falling in a range between -1 (entirely dissimilar - i.e. vectors pointing in entirely opposite directions) and +1 (entirely similar).


6. Ratcliff-Obershelp similarity - This is an example of a 'sequence-based algorithm', which quantify similarity according to the closeness of sequences of characters (or tokens). Ratcliff-Obershelp similarity is one example which considers the longest common subsequence (usually referred to as 'LCS', but referenced in this study as 'LCSSQ') present in both strings - i.e. a set of characters appearing in the same order, though not necessarily in consecutive positions in the strings. It is defined as twice the length of the LCSSQ divided by the sum of the lengths of the two strings, and returns a value between 0 and 1.

B. Pronunciation-based metrics (for aural similarity)

The basic principle behind the comparison of the pronunciation of different strings is the conversion of each string to a phonetic representation, and then comparison of these representations against each other, using one (or more) of the (usually edit-based) algorithms referenced above^[53].

The key component of the analysis is therefore the production of a phonetic representation of each string, for which a number of options are available. Some of the most common techniques involve the use of:

• IPA transcription, involving the conversion of the string to its International Phonetic Alphabet^[54,55,56] representation. The IPA is a means of representing strings phonetically using (mainly) Latin or Greek script, but also utilising other special characters, such as a colon-like character denoting that the preceding sound is long and, in some versions, high or low vertical lines denoting the primary and secondary stressed syllables^[57]. 

• The Soundex algorithm, which encodes a string according to its (English) pronunciation, generating a four-character output comprising a letter and three digits. The initial letter of the encoding is generally the first letter of the string in question, and the subsequent consonants (up to a maximum of three) are encoded with numbers, such that similarly-pronounced consonants (i.e. those articulated by a speaker in a similar way) are assigned the same digit (e.g. b, f, p and v correspond to '1' in American Soundex)^[58].

• The NYSIIS (New York State Identification and Intelligence System) phonetic code^[59], which is similar to Soundex, but also incorporates a number of improvements, including the capability to represent the whole string, and the disregarding of any trailing 's'.

Implementation of the similarity algorithms

This study proposes a calculation of a score (S_wor) representing the overall degree of similarity between two strings which incorporates two elements: one component (S_vis) quantifies the visual (i.e. spelling) similarity between the strings, and one (S_aur) the aural (i.e. pronunciation) similarity. 

The visual (spelling) similarity determination itself makes use of two distinct algorithms (implemented using Python libraries), each of which reflects a different aspect of the similarity (and each of which generates a score which can be expressed as a percentage). The two algorithms are:

• The fuzz.ratio metric (generating an associated score, F_Lev), an algorithm implemented in the Python package 'fuzzywuzzy'^[60], based on the Levenshtein distance metric, but also taking account of other factors (including the length of the strings)

• The Jaro-Winkler similarity algorithm (with an associated score, sim_j) (as implemented in the the Python package 'Levenshtein'^[61], which includes consideration of the proximity of the matching / non-matching characters to the start of the strings. 

From these, the score component reflecting overall visual similarity (S_vis) is expressed just as the simple mean of the above two scores (as below), although it would be possible to apply different weightings if required.

S_vis = (F_Lev + sim_j) / 2

For aural (pronunciation) similarity, the 'Phonemizer' Python algorithm^[62,63] is used to generate phonetic versions of the strings, utilising IPA (International Phonetic Alphabet) encoding^[64], based on a back-end text-to-speech software application named 'espeak-ng'^[65,66,67]. Unlike some other text-to-IPA encoders, this package can handle arbitrary strings, rather than just dictionary terms. It is also worth noting that this particular implementation of IPA is built around American (rather than English) pronunciation - for example, syllables such as 'vox' and 'not' are encoded using a long 'ah' sound (ɑː). This may not always be appropriate for marks targeting an English audience, but is perhaps less of an issue if comparing like with like.

The IPA transcription also in its own right provides a convenient way of visually comparing the degree of aural similarity (according to 'Phonemize') between strings or sub-elements of them; for example, in the case of 'Lucozade' v 'Glucos-Aid', a removal of the initial 'ɡ' from the IPA representation of the latter gives the remaining strings as luːkəzeɪd and luːkoʊzeɪd, showing that they differ only in the middle vowel sound.

In this study, the aural similarity score (S_aur) is calculated just as the output of the fuzz.ratio metric applied to the IPA representations of the strings, or:

S_aur = F_Pho

The overall (word mark) similarity score (S_wor) for the pair of strings can then most simply be expressed as the mean of the two individual components, i.e.:

S_wor = (S_vis + S_aur) / 2

This formulation has a number of advantages over other variations tested previously (which made use of Soundex and NYSIIS representations), including the facts that these alternatives featured much poorer handling of vowel sounds within the strings and, for Soundex, an inability to encode any consonants beyond the first four. Furthermore, the algorithms incorporate elements of 'normalisation' with respect to the length of the strings (i.e. they account for the point that equivalent differences should be considered to be more significant in cases where they arise in shorter strings), and (through the use of Jaro-Winkler similarity) feature a weighting providing an emphasis on characters nearer the start of the strings (where, arguably, consumers may be more likely to notice differences between similar marks).

Additionally, the calculation framework as presented is entirely repeatable (i.e. a particular word-pair will always give the same score) and also allows analyses of the visual and aural similarities separately from each other, if required.

As an illustration of the performance of the algorithm(s), Table 3 shows the analysis of the pairs of marks listed previously, showing what appears (subjectively!) to be a reasonable assignment of scores and overall ranking of the pairs.

Mark 1	Mark 2	Visual sim.  score (Svis)	Mark 1 (IPA)	Mark 2 (IPA)	Aural sim. score (Saur)	Overall sim. score (Swor)
casoria	castoria	95.04	kæsoːɹiə	kæstoːɹiə	95.00	95.02
kresco	cresco	85.94	kɹɛskoʊ	kɹɛskoʊ	100.00	92.97
mahendra	mahindra	91.08	mæhɛndɹə	mæhɪndɹə	89.00	90.04
trucool	turcool	90.86	tɹuːkuːl	tɜːkuːl	82.00	86.43
starbucks	charbucks	81.59	stɑːɹbʌks	tʃɑːɹbʌks	90.00	85.80
bacchus	cacchus	85.46	bækəs	kækəs	83.00	84.23
cana	canya	92.17	kɑːnə	kænjə	67.00	79.58
seiko	seycos	65.50	seɪkoʊ	seɪkoʊz	93.00	79.25
bisleri	bilseri	91.10	baɪslɜːɹi	bɪlsɚɹi	67.00	79.05
lucozade	glucos-aid	72.67	luːkəzeɪd	ɡluːkoʊzeɪd	82.00	77.33
intelect	entelec	77.90	ɪntɛlᵻkt	ɛntɛlɛk	71.00	74.45
starbucks	sardarbuksh	76.21	stɑːɹbʌks	sɑːɹdɑːɹbʌkʃ	70.00	73.11
zirco	cozirc	77.61	zɜːkoʊ	kɑːzɜːk	67.00	72.31
lakme	likeme*	70.32	lækmi	laɪkmiː	71.00	70.66
nike	nuke	80.00	naɪk	nuːk	60.00	70.00
mdh	mhs	61.28	ɛmdiːeɪtʃ	ɛmeɪtʃɛs	74.00	67.64
louis vuitton	chewy vuiton	58.60	luːi vjuːɪʔn̩	tʃuːi vjuːɪtən	76.00	67.30
simoniz	permanize	58.60	sɪmənɪz	pɜːmənaɪz	67.00	62.80
magnavox	multivox	58.33	mæɡnɐvɑːks	mʌltivɑːks	64.00	61.17
puma	coma	58.33	puːmə	koʊmə	50.00	54.17
louboutin	lubov	61.74	laʊbaʊtɪn	luːbɑːv	33.00	47.37
mcdonalds	mcsweet	44.13	məkdɑːnəldz	məkswiːt	48.00	46.07

* rewritten as 'like-me' prior to phonetic analysis, to ensure that the string is interpreted 'correctly'

Table 3: Pairs of marks and their visual similarity scores, IPA representations, and aural and overall similarity scores

The repeatability of the algorithm means it is also possible to produce an illustrative set of representative pairs of marks^[68] which are assigned particular overall word similarity scores (S_wor), to serve as a 'reckoner' to help visualise the meaning of the scores, across a spectrum from high to low:

• Approx. 90%:
• boss / bossi
• billionaire / zillionaire
• thermacare / thermocare
• prinker / prink
• intellicare / intelecare
• chooey / chooee
• mahendra / mahindra

• Approx. 80%:
• zara / zarzar
• rabe / rase
• retaron / retlron
• createme / create.
• spa / spato
• thermomix / termomatrix

• Approx. 70%:
• kelio / kleeo
• terry / terrissa
• tygrys / tigris
• nike / nuke

• Approx. 60%:
• nutella / mixitella
• airbnb / francebnb
• gallo / rampingallo
• iphone / mifon
• joy / bjoie
• jd / jdyaoying

• Approx. 50%:
• zara / zorazone
• quirón / quiromasté

• Approx. 40%:
• book / restaubook
• h10 / motel 10

Possible additions and improvements to the metrics

i. General points

There are a number of possible modifications which could be made to the above framework in order to take account of other characteristics of the marks in question which appear (again, subjectively) potentially to be important. 

As one example, it is instructive to consider a pair of marks such as zirco / cozirc (72.31% similar, according to the proposed algorithm) and ask whether they should perhaps be deemed more similar than the score suggests (since the marks consist just of the same two syllables in a different order). Taking account of these types of characteristics would require the use of some sort of explicit 'token-based' algorithm.

Another factor which may be relevant is the degree of distinctiveness (for the relevant areas of goods and services) of the common element between two marks under comparison (e.g. the 'Mc' in 'McDonalds' v 'McSweet'). 

It is also worth reiterating that the proposed framework takes no account of the meanings of marks, or of associated characteristics such as logos or fonts.

ii. Prominence, distinctiveness or commonness of the mark(s)

The prominence (within bodies of relevant content such as search-engine results), distinctiveness or commonness of the marks in question are additional factors which have not yet been addressed. Realistically, these features are more relevant to the determination of the likelihood of confusion than of the similarity of the marks, and probably should sit within a different analytic model; furthermore, a full assessment of potential (degree of) infringement is a much more complex prospect, involving consideration of a range of factors, including real-world use.

Nevertheless, there are some relatively simple quantitative metrics which might be relevant and are worthy of discussion in this study. One illustration of this point relates to the Iceland / Ireland example. These words are extremely similar, and any simple word-based metric would reflect this point (actually being assigned an overall similarity score, S_wor, of 88.36). However, if this clash arose in an IP dispute, it might be reasonable to argue that these words are simply both just common words, being used with their own meanings - or are both highly established "brands" - rather than being a case of one attempting to pass off as the other. It might therefore be appropriate to construct a modified score (a 'potential infringement threat' score, 'T') which, in this case, should give a lower value. Conversely, if one or both of the marks were more unusual terms, it might be desirable if the threat score (T) were reduced relative to the similarity score by a lesser degree.

One possible way to account for this fact would be to use the number of results returned in response to an Internet search for each mark, as a proxy of its commonness or prominence. Dividing the overall similarity score, S_wor, by some factor, P, which is dependent on the minimum value of the number of results returned for each of the two marks, would be a way of formulating an infringement threat score (T) which is more greatly reduced if both marks are common terms. One option would be to calculate the reduction factor (P) by taking the logarithm of the number of search engine results (N_s) (with an optional additional scaling factor, k), such that:

T = S_wor / P

and

P = log₁₀[min(N_{s_brand1}, N_{s_brand2})] / k

For the Iceland / Ireland case, for example (for which the numbers of results returned in response to a Google search for (an exact match to) the words in question - as of July 2024 - were 828 million and 2.76 billion, respectively), this would give P = 8.9, and therefore (for, say, k = 2) T = 19.82.

iii. Subsequences and substrings

Some similarity metrics (such as Ratcliff-Obershelp similarity) include consideration of features such as the longest common subsequence ('LCSSQ') between the strings (i.e. a set of characters appearing in the same order, though not necessarily in consecutive positions, in the strings). Whilst not incorporated in the similarity score formulation proposed in this study, analysis of this characteristic - together with a related feature, the longest common substring ('LCSST'), in which the characters must appear in both strings in the same order and in consecutive positions (i.e. contiguous characters) - can also yield useful insights in mark comparisons.

These points can be illustrated by considering a dataset comprising a year's worth of data on word mark v. word mark disputes from UK courts^[69], and determining the following characteristics for each pair of marks:

• The LCSSQ and LCSST
• The 'remainder' of each mark, following the removal in each case of the (first instance of^[70]) the common sub-elements
• A 'modified Ratcliff-Obershelp similarity score', defined as the mean of the (true) score (calculated using the LCSSQ) and an analogous score calculated using the LCSST

As an example-set, Table 4 shows the top (i.e. most similar) pairs of marks from the overall dataset, as quantified using the modified Ratcliff-Obershelp similarity score (which itself offers reasonable performance at ranking results by (subjective) similarity).

Table 4: Most similar pairs of marks (by modified Ratcliff-Obershelp similarity score), their LCSSQs and LCSSTs (and 'remainders' in each case)

Overall, the LCSSQ / LCSST analysis provides a framework making it possible to conveniently review the elements which the marks have in common. When assessing overall similarity, it might be reasonable to disregard (or downweight the contribution of) remainders which are extremely generic or non-distinctive (such as 'the', 'my', 'co.', etc.).

However, attempting to quantify the degree of distinctiveness (or non-distinctiveness) of the terms in the remainders is a difficult prospect. Perhaps a more meaningful question to attempt to answer is whether the remainder keywords overlap significantly with the goods and services of the other mark in question.

It is essential that consideration of goods and services - and the degree to which these are likely to be familiar to general consumers for the brand terms in question - should always be incorporated into any overall similarity assessment framework. For example, in 'Honda' v 'Honbike' - objectively not highly similar as words - relevant points to consider might be the extent to which the Honda brand is known to be associated with motorbikes, and whether it is well-known enough that even an abbreviated variant ('Hon') would evoke a brand association in the mind of the average consumer.

In other cases, similarity between the word types in the remainders might imply an overall greater similarity between the marks - such as 'Lemon Perfect' v 'Peach Perfect', where the remainders after the removal of the LCSST are 'lemon' and 'peach' (both fruits), 'Glenfiddich' v 'Inverfiddich', where the remainders are 'Glen' and 'Inver' (both common terms in Scottish place-names), or 'Karmacoin' v 'Karmacash'. 

Another consideration is that if the remainders are very short and/or meaningless (say, single letters), this might also imply a greater degree of similarity between the marks. However, this assertion may also be dependent on their positions within the strings; for example (even disregarding differences in word length), 'Consiglieri' and 'Consigliera' might be deemed to be more similar to each other than are 'Lotus' and 'Motus' (both cases differing by a single character) - particularly when factors such as local-language significance (e.g. just a potential difference in gender) are taken into account. 

For the parts of the marks which are distinct, it might also be worth taking into consideration the degree of similarity between the distinct elements - for example a replacement of one character with another which is phonetically similar (e.g. in the same Soundex ‘group’) might be considered a smaller change than a replacement with a more phonetically contrasting character.

Caveats to the overall approach and further thoughts

One possible risk associated with the adoption of an objective approach to word-mark comparison is that it could reduce the extent to which examiners and hearing officers might tend to apply a context-specific ('common-sense') approach to case assessment in complex mark applications and oppositions, in favour of a reliance on 'black-box' algorithms. There is even also a possibility that bad-faith applicants might deliberately modify their applications so as explicitly to achieve a 'below-threshold' similarity score with a mark against which they are intending to gain an advantage.

Another point to note is that the registration of random strings of letters as trademarks ('nonsense marks') is increasingly gaining popularity as a tactic to achieve success in the registration of the mark (since they more rarely generate 'clashes', and attract oppositions, with pre-existing marks) and achieve preferred-seller status on e-commerce marketplaces (which frequently favour trademark holders)^[71]. Such marks do not operate as brands in the traditional sense, since they are not memorable and therefore do not allow customers to easily carry out repeat transactions, but can be effective on certain platforms where price, rankings and reviews have a greater influence on consumer choice than does brand identity^[72]. The risk is that these types of 'brands' would inevitably produce lower similarity scores with potential competitor marks, a scenario which could be advantageous in securing mark protection within a system they are already 'gaming' (given that the underlying philosophy of trademark law is intended to be the protection of brands for which there is an intention to build and generate good will, and that the administration and management of these types of random marks essentially takes away resource from other legitimate trademark applicants). 

One final point to note is that any algorithmic approach to the assessment of pronunciation will always incorporate some inherent bias. It has been noted above that the IPA conversion process utilised in this study is geared towards American English, but there will additionally be considerations around (say) regional or socio-economic variations in pronunciation, which are not (easily) addressed by this type of approach.

Overall conclusion

The analysis presented in this study has illustrated that - up to a point - it is possible to construct algorithms and associated metrics which objectively quantify the degree of similarity between marks, particularly in the cases of colour and word marks (which are subject to exact 'definition'). The similarity score approach also offers a framework which is repeatable and qualitative, providing the potential for a consistent approach to assessment of these characteristics. It also aligns with the familiar terminological descriptions of 'degrees' of similarity, whilst offering a more granular and continuous scale. The specifics of the algorithms can also be 'tuned' according to specific requirements (though would need to be kept fixed in instances where it is necessary to compare one case against another). 

Realistically, such algorithms should only be considered as tools to be utilised in the overall similarity assessment process, which will inevitably always incorporate significant subjectivity, involving consideration of a range of additional factors. These might typically include (for word marks specifically): conceptual similarity (i.e. meaning) and the distinctiveness of the marks; and (for marks generally) associated imagery, fonts or visual presentation, the associated goods and services, strength and degree of renown, documented evidence of actual confusion, the degree of attention paid by relevant consumers, and the nature of the overall market, all of which contribute to the estimation of the possibility of mark confusion^[73,74].

This point can be illustrated by comparing the 'measured' degree of similarity between pairs of marks, as given by the algorithm, with the point-of-law decisions from trademark disputes concerning those same pairs of marks. This analysis (also using the year's worth of data on UK word mark v. word mark disputes) was carried out in a previous study (using an earlier version of the metric). It essentially found (unsurprisingly) that there is little meaningful correlation between the calculated similarity score and the outcome of the decision (regarding whether the marks were deemed to be similar or different), even if considering only the similarity of the corresponding type (visual or aural). Part of this discrepancy is down to some apparent 'inconsistencies' in the legal decisions (e.g. pairs of marks which differ in analogous ways were sometimes found to be similar, and sometimes different), but really is primarily due to the presence of a significant range of subjective factors (including any consideration of the large number of different languages which may be relevant) contributing to the assessments. 

However, the possibility for the creation of a more objective framework offers the potential to be able to quantitatively measure the difference between marks, to define thresholds up to which IP protection could apply, and to build a case-law background providing a basis for greater legal consistency. 

These types of algorithms also have additional applications in intellectual property and brand protection data analysis, such as the option to be able to 'post-process' results from trademark watching services and obtain a more meaningful ranking of the results (from most similar to least similar pairs of marks), making the manual review process much more efficient.

Acknowledgements

This study was inspired by an initial discussion at Stobbs CaseFest #15 (London, 11-Jul-2024) - with thanks to Jack Wing, Emma Pettipher, Jessica Wolff, Will Haig, Richard Ferguson, John Weston, Geoff Weller, Jacob Larking, Chris Sleep and others for their input.

References

[1] This paper primarily comprises a synopsis of key ideas and case studies presented previously in a series of articles which include:

• https://circleid.com/pdf/similarity_measurement_of_marks_part_1.pdf
  
• https://circleid.com/posts/further-developing-a-colour-mark-similarity-measurement-framework-building-a-database
  
• https://circleid.com/pdf/similarity_measurement_of_marks_part_3.pdf
  
• https://circleid.com/pdf/similarity_measurement_of_marks_part_4.pdf
  
• https://circleid.com/pdf/similarity_measurement_of_marks_part_5.pdf
  
• https://circleid.com/pdf/similarity_measurement_of_marks_part_6.pdf
  
• https://www.linkedin.com/pulse/measuring-similarity-marks-overview-suggested-ideas-david-barnett-zo7fe/
  
• https://www.linkedin.com/pulse/what-degree-variability-might-covered-within-david-barnett-ajyoe/
  
• https://www.linkedin.com/pulse/further-explorations-brand-colour-disputes-t-mobile-david-barnett-uoble/

[2] https://assets.publishing.service.gov.uk/media/63f8963e8fa8f527f110a2e6/Consolidated-Trade-Marks-Act-1994-February23.pdf

[3] Or if the mark "take[s] unfair advantage of, or [is] detrimental to the distinctive character or ... repute" (Sections 5(3) and 10(3)) of, the earlier mark

[4] https://en.wikipedia.org/wiki/Colour_trade_mark

[5] https://ipwatchdog.com/2018/07/14/can-you-trademark-a-color/id=99237/

[6] https://thehustle.co/can-a-corporation-trademark-a-color

[7] https://trademarkblog.kluweriplaw.com/2024/09/24/acquired-distinctiveness-for-non-traditional-trademarks-in-the-benelux-show-your-true-colours/

[8] https://www.colourstudies.com/blog/2022/4/17/trademarking-colours

[9] https://www.tmdn.org/tmview/#/tmview/detail/EM500000000747949

[10] https://www.bailii.org/cgi-bin/format.cgi?doc=/ew/cases/EWHC/Ch/2022/1671.html (referenced at: https://www.pinsentmasons.com/out-law/analysis/cadbury-ruling-guide-registering-colour-trade-marks)

[11] https://www.iam-media.com/article/stihl-successfully-invalidates-infringers-colour-combination-mark

[12] https://curia.europa.eu/juris/document/document.jsf?text=&docid=239252&pageIndex=0&doclang=EN&mode=req&dir=&occ=first&part=1&cid=1772718 (referenced at https://www.fieldfisher.com/en/services/intellectual-property/intellectual-property-blog/cutting-through-the-issues-colour-trade-marks-and and https://www.wiggin.co.uk/insight/general-court-annuls-board-of-appeal-decision-that-colour-combination-mark-was-not-sufficiently-clear-and-precise-to-indicate-origin/)

[13] https://asiaiplaw.com/index.php/article/defending-stihls-orange-and-grey-colour-combination

[14] https://www.linkedin.com/posts/rebecca-newman-267a7756_thinking-of-using-a-non-standard-trade-mark-activity-7216747278231883779-6SH3

[15] 'Infringement of Colour Trademarks', GRUR International, Vol. 70, Iss. 7 (2021), pp. 676 - 680 (https://doi.org/10.1093/grurint/ikab061) (available at: https://academic.oup.com/grurint/article-abstract/70/7/676/6303754)

[16] https://www.semanticscholar.org/paper/The-Psychology-of-Colour-Influences-Consumers%E2%80%99-%E2%80%93-A-Kumar/f7c3b2a780a7a3bf907ef807085b86a63f0d8d0a?p2df

[17] https://www.iamstobbs.com/the-psychology-of-lookalikes

[18] Equivalently, RGB values can be expressed in 'Hex' (hexadecimal, or base-16) format, where each component (R, G, and B) is written as a two-digit hexadecimal number, with each digit in the range from 0 to F (= 15). 255 is would therefore be expressed as FF (i.e. 15 × 16¹ + 15 × 16⁰), and [255,255,255] written as #FFFFFF

[19] This upper limit would be the ratio between the total volume of RGB space (i.e. 255³ cubic units) and the volume of the protected 'bubble' in each case (which would be, for a radius of 20 units, ⁴⁄₃ × π × 20³ = 33,510 cubic units, i.e. 495 colours in total; or, for a radius of 10 units, 3,959 colours)

[20] https://www.baeldung.com/cs/compute-similarity-of-colours

[21] T. Horiuchi and S. Tominaga (2014). Color Similarity. In: 'Computer Vision', K. Ikeuchi, (ed.), Springer, Boston, MA. https://doi.org/10.1007/978-0-387-31439-6_450. (Available at: https://link.springer.com/referenceworkentry/10.1007/978-0-387-31439-6_450)

[22] https://www.alanzucconi.com/2015/09/30/colour-sorting/

[23] e.g. https://github.com/python/cpython/blob/3.13/Lib/colorsys.py

[24] L = √ [ 0.241 × R + 0.691 × G + 0.068 × B ]

[25] https://www.worldtrademarkreview.com/article/the-stratos-saga-continues-uncertain-future-blue-colour-mark-chocolate

[26] https://haavind.no/content/uploads/sites/2/2024/12/Food-beverage-insight-winter-2024.pdf

[27] https://lovdata.no/dokument/TRSIV/avgjorelse/tosl-2023-186489

[28] https://x.com/pantone/status/1262819916928991232

[29] https://www.linkedin.com/posts/carola-seybold-61482613_color-food-design-activity-7293596033001881600-KYJZ/

[30] https://www.schemecolor.com/heinz-red-color.php

[31] https://www.creativemoment.co/heinz-creates-label-with-the-exact-pantone-reference-of-tomato-ketchup-to-fight-ketchup-fraud

[32] https://www.engadget.com/2008-05-28-t-mobile-loses-magenta-suit-against-telia-we-try-not-to-laugh.html

[33] https://www.businesswire.com/news/home/20201216005880/en/%C2%A0Lemonade-Wins-FreeThePink-Case-Against-Deutsche-Telekom-in-France

[34] https://www.iamstobbs.com/opinion/why-brand-owners-should-be-conscious-of-sound-trade-marks

[35] https://www.linkedin.com/posts/geoff-steward-20404015_good-to-know-that-the-psychology-of-lookalikes-activity-7183447412542181377-6omH

[36] http://baeldung.com/cs/compute-similarity-of-colours ('Improved Approach')

[37] https://guidelines.euipo.europa.eu/1922895/1924826/trade-mark-guidelines/3-imperfect-recollection

[38] As per the Iconix v Dream Pairs case regarding the question of similarity between the Umbro diamond trademark and the Dream Pairs logo; see e.g. https://www.schwimmerlegal.com/2024/03/post-purchase-confusion-in-the-uk-iconix-luxembourg-holdings-sarl-v-dream-pairs-europe-inc-anor.html 

[39] https://stackoverflow.com/questions/71822208/how-do-i-calculate-similarity-between-two-words-to-detect-if-they-are-duplicates

[40] https://www.baeldung.com/cs/semantic-similarity-of-two-phrases

[41] https://www.geeksforgeeks.org/python-word-similarity-using-spacy/

[42] https://www.tramatm.com/blog/category/other/sound-alikes-5-high-profile-trademark-disputes-involving-phonetic-similarity

[43] https://www.intepat.com/blog/deceptively-similar-trademarks-examples-case-study/

[44] https://gouchevlaw.com/likelihood-confusion-5-examples-similar-trademarks/

[45] https://banwo-ighodalo.com/grey-matter/trademark-infringement-analyzing-the-concept-of-confusingly-similar-trademarks

[46] https://www.upcounsel.com/similar-trademarks-examples

[47] https://www.forbesindia.com/article/news/belsri-bislleri-bilseri-bisleri-brislei/81445/1

[48] https://www.analyticsvidhya.com/blog/2021/02/a-simple-guide-to-metrics-for-calculating-string-similarity/

[49] https://medium.com/@ahmetmnirkocaman/how-to-measure-text-similarity-a-comprehensive-guide-6c6f24fc01fe

[50] https://yassineelkhal.medium.com/the-complete-guide-to-string-similarity-algorithms-1290ad07c6b7

[51] https://corpustools.readthedocs.io/en/master/string_similarity.html

[52] https://statisticaloddsandends.wordpress.com/2019/09/11/what-is-jaro-jaro-winkler-similarity/

[53] https://ai.stackexchange.com/questions/28556/how-to-measure-the-similarity-the-pronunciation-of-two-words

[54] https://en.wikipedia.org/wiki/International_Phonetic_Alphabet

[55] https://www.internationalphoneticassociation.org/content/ipa-chart

[56] https://www.vocabulary.com/resources/ipa-pronunciation/

[57] https://en.wikipedia.org/wiki/Stress_(linguistics)

[58] https://en.wikipedia.org/wiki/Soundex

[59] https://en.wikipedia.org/wiki/New_York_State_Identification_and_Intelligence_System

[60] https://pypi.org/project/fuzzywuzzy/

[61] https://rapidfuzz.github.io/Levenshtein/levenshtein.html#jaro-winkler

[62] M. Bernard and H. Titeux (2021). Phonemizer: Text to Phones Transcription for Multiple Languages in Python. J. Open Source Software, 6(68), p.3958.

[63] https://pypi.org/project/phonemizer/

[64]   In some cases, data 'cleansing' may be required in order to ensure that the algorithm interprets the string as (apparently) intended - though this will remove some of the objectivity. As examples, taken from the set of strings used in the test analyses (and expressing the IPA representations (as given by the script) instead as 'readable' strings (underlined) where shown in the summary below) :

• Prior to processing, 'OrangeryOS' is re-written as 'orangery-o-s' (to ensure that the pronunciation is rendered as 'oh-es')
• Prior to processing, 'likeme' is re-written as 'like-me' (to ensure that the pronunciation is not rendered as 'lye-keem')
• If not rewritten (according to a subjective interpretation) prior to processing, 'unreadable' strings are often rendered in the IPA representation as individual characters, e.g.:
• 'hpnotic' rendered as 'aitch-pee-notic' (rather than the more likely intended 'h[u]pnotic')
• 'genv3rse' rendered as 'genv-three-rse' (rather than the more likely intended 'genverse')
• 'm4tter' rendered as 'em-four-ter' (rather than the more likely intended 'matter')

[65] https://github.com/bootphon/phonemizer

[66] https://bootphon.github.io/phonemizer/install.html

[67] https://github.com/espeak-ng/espeak-ng#espeak-ng-text-to-speech

[68] These examples are taken from a broader analysis of approximately 200 pairs of marks, most of which were the subjects of trademark disputes from a one-year period ending in late 2024, and (for simplicity) with a particular focus on single-word marks

[69] Taken from the Darts-ip tool (https://app.darts-ip.com/darts-web/login.jsf)

[70] Note that this approach can generate cases where the data might reasonably require some 'cleansing' in order to yield meaningful insights - e.g. the generation of 'te h' as the remainder when the LCSSQ (using the first instance of each character) is removed from 'the holiday people'

[71] https://www.linkedin.com/posts/robert-reading-500b4b1a_trademarks-activity-7264990820607389697-qe2J/

[72] https://harvardlawreview.org/print/vol-134/fanciful-failures-keeping-nonsense-marks-off-the-trademark-register/

[73] https://bowmanslaw.com/insights/degrees-of-similarity-put-to-the-test/

[74] https://www.taylorwessing.com/en/insights-and-events/insights/2021/03/were-confused-how-the-general-court-decides-when-trade-marks-are-confusingly-similar

This article was first published on 23 May 2025 at:

https://www.linkedin.com/posts/dnbarnett2001_measuring-the-similarity-of-marks-activity-7331669662260224000-rh-R/