Visual Elements in Logo Design

Many mid-level visual features have been proposed to characterize the aesthetic prop-erties of visual arts. Since we are restricting ourselves to the study of logo, we will consider three mid-level visual attributes that are deemed important in the composi-tion of logo. We have deliberately left out one essential attribute: color in this study as we believe that this topic deserves further investigation to arrive at some concrete conclusions. In the following, we will introduce balance, complexity and repetition and define proper formula for computing these quantities from input images.

3.1 Balance

Balance is often associated with symmetry. Indeed, the simplest form of balance is symmetry. However, balance can be achieved when the visual forces of asymmetri-cally arranged elements compensate for each other. It is therefore a more general concept than the notion of symmetry. The balance score defined by Wilson et al. is calculated using Eqs. 1-4, and the partition styles are depicted in Fig. 1.

ܵ_ଵൌ  σ_{௪௜ௗ௧௛}σ_{௛௘௜௚௛௧}ͳ݂݅ሺݔǡ ݕሻ  א  ܣ_ଵ (1)

ܵ_ଶൌ  σ_{௪௜ௗ௧௛}σ_{௛௘௜௚௛௧}ͳ݂݅ሺݔǡ ݕሻ  א  ܣ_ଶ (2)

ܴ_௜ൌ^ȁௌ_ௌ^{భିௌమȁ}

భାௌమሺ݅ ൌ ͳǡ ǤǤͺ…‘””‡•’‘†•–‘†‹ˆˆ‡”‡–’ƒ”–‹–‹‘•–›Ž‡•） (3)

ܤ݈ܽܽ݊ܿ݁ ൌ^ଵ_଼σ^଻_௜ୀ଴ܴ_௜ (4)

The original formula defined above can only cope with black-and-white images.

We propose the following modifications shown in Eqs. 5-6 to compute balance score from grayscale images.

76 W.-H. Liao and P.-M. Chen

Fig. 1. Eight region partitions for computing the balance score (white: A1, black: A2)

ܵ_ଵൌ  σ_{௪௜ௗ௧௛}σ_{௛௘௜௚௛௧}݃ሺݔǡ ݕሻതതതതതതതതത݂݅ሺݔǡ ݕሻאܣ_ଵ(5)

ܵ_ଶൌ  σ_{௪௜ௗ௧௛}σ_{௛௘௜௚௛௧}݃ሺݔǡ ݕሻതതതതതതതതത݂݅ሺݔǡ ݕሻ אܣ_ଶ (6)

™Š‡”‡݃ሺݔǡ ݕሻതതതതതതതതതത ൌ ʹͷͷ െ ݃ݎܽݕሺݔǡ ݕሻ For color images, we can utilize RGB color space and compute the balance of individual channel using the above formula. However, we will get three different balance scores in this manner. It is challenging to interpret the combined effect of these scores as the role of ‘color’ is coming into play. To exclude the color factor, we will adopt the HSV representation and define the balance score using only the S (Saturation) and V (Value) components in this research. The newly modified balance measure becomes: ܴ_௜ൌ^ȁௌ_ௌ^{భିௌమȁ} భାௌమ כ ߱ ൅^ȁ௏_௏^{భି௏మȁ} భା௏మ כ ሺͳ െ ߱ሻ (7)

where ܵ_ଵൌ  σ σ ݏሺݔǡ ݕሻ݂݅ሺݔǡ ݕሻ א  ܣ_{௪ ௛ ଵ} (8)

ܵ_ଶൌ  σ σ ݏሺݔǡ ݕሻ݂݅ሺݔǡ ݕሻ  א  ܣ_{௪ ௛ ଶ} (9)

ܸ_ଵൌ  σ σ ݒሺݔǡ ݕሻ_{௪ ௛}തതതതതതതതത݂݅ሺݔǡ ݕሻ߳ܣ_ଵ (10)

ܸ_ଶൌ  σ σ ݒሺݔǡ ݕሻ_{௪ ௛}തതതതതതതതത݂݅ሺݔǡ ݕሻ߳ܣ_ଶ (11)

Analysis of Visual Elements in Logo Design 77

The symbol ω in Eq. 7 denotes the weight assigned to the saturation component. In all our experiments, we set ω to 0.5. Fig. 2 shows two logos and their corresponding balance score. Notice that the balance score thus defined indicates more balance when the value is closer to 0, and signifies imbalance when the value is approaching 1.

”‹‰‹ƒŽ ƒ–—”ƒ–‹‘ ƒŽ—‡

 

 

Fig. 2. Top logo: R={0.005,0.13,0,112,0.106,0.06,0.106,0.135,0.163}, Balance=0.102, Bottom logo R={0.154,0.416,0.181,0.370,0.048,0.081,0.064,0.12}, Balance=0.180

3.2 Complexity

Complexity measure is directly related to entropy using information-theoretic modeling. Higher entropy corresponds to more complex configuration in an image.

The discrete version of entropy can be expressed as Eq. 12:

ܪ ൌ  െ σ ݌_{௜ ௜}Ž‘‰_ଶ݌_௜ (12) In this study, we employ a top-down image partition algorithm to segment the logo into homogeneous regions with similar brightness value. A low complexity image will contain only a few large homogeneous blocks, and vice versa for a high complexity image. The partition can be applied vertically or horizontally. We will iterate through all columns are rows and compute the corresponding entropies, as shown in Eq. 13-14. The entropy H is used to determine whether the partition should continue. If the minimum of the sum of the entropies of two partitioned re-gions is smaller than a threshold ߠ, the segmentation process stops. Otherwise the partition proceeds according to Eq. 15. The flowchart of the proposed image partition algorithm is depicted in Fig. 3.

ܧ_ଵ௜ ൌ ߣ_ଵ௜ȉ ܪ൫ܫሺͲǡ ݅ሻ൯ ൅ ሺͳ െ ߣ_ଵ௜ሻ ȉ ܪ൫ܫሺ݅ ൅ ͳǡ ܹሻ൯

78 W.-H. Liao and P.-M. Chen

ߣ_ଵ௜ൌ ሺ݅ ൅ ͳሻȀܹ (13) ܧ_ଶ௝ൌ ߣ_ଶ௝ȉ ܪ൫ܫሺͲǡ ݆ሻ൯ ൅ ሺͳ െ ߣ_ଵ௜ሻ ȉ ܪ൫ܫሺ݆ ൅ ͳǡ ܪሻ൯ ߣ_ଶ௝ൌ ሺ݆ ൅ ͳሻȀܪ (14)

ܲ ൌ ”‰‹൫ܪ כ ܧ_ଵ௜ǡ ܹ כ ܧ_ଶ௝൯݅ ൌ Ͳ̱ܹ െ ͳǡ ݆ ൌ Ͳ̱ܪ െ ͳ (15)

Fig. 3. Flowchart of the proposed image partition algorithm

Once the partition is done, the complexity score can be computed accordingly.

However, we notice that there exist several possible interpretations of the partitioned result. The first complexity measure, denoted as partition-based complexity, is direct-ly related to the distribution of the area of the partitioned segments and can be com-puted using Eq. 16. If the sizes of the partitioned regions are diverse, the image is thought to possess higher complexity.

ܥ_௣ൌ ܪሺܵ݅ݖ݁ሺܣݎ݁ܽ_௜ሻሻ (16) Secondly, since the direction of partition is either vertical or horizontal, a homo-genous yet irregularly shaped region may be divided into smaller segments. It would be unfair to calculate the complexity using only the partitioned area. Instead, we can examine the distribution of the entropy of the segments and defined another com-plexity measure, denoted as homogeneity-based comcom-plexity, based on the homogenei-ty of the entropy of segmented regions as shown in Eq. (17).

Finally, the total numbe the complexity of a logo. T complexity which can be co ܥ_௥ൌ^ோ_ே™Š‡”‡ܴ

Fig. 4 illustrates the nec metric may not effectively r

’—–‘‰‘

Fig. 4. Co

3.3 Repetition

The repetition score can be tours in a logo. We propose and perform subsequent sim be extracted from the image

1. Apply Gaussian smo 2. Employ Canny edge 3. Use topological stru

Analysis of Visual Elements in Logo Design

ܥ_௙ ൌ ܪሺܪሺܣݎ݁ܽ_௜ሻሻ ( er of partitions with respect to the image size also refle Therefore, we define the third metric denoted as area-ra omputed using Eq. 18.

ܴ ൌ ‘–ƒŽ—„‡”‘ˆƒ”–‹–‹‘•ǡ ܰ ൌ ܹ כ ܪ ( essity of having different complexity measures as a sin reveal the structure of the logo image.

ƒ”–‹–‹‘ ‡•—Ž– ‘’Ž‡š‹–›

omplexity measures based on different criteria

e computed by comparing the constitution of principal c e to use Fourier descriptor to represent the major conto milarity analysis. However, topological structures have es first. This is done using the following three steps:

oothing to eliminate boundaries that are too close e detector to candidate boundary pixels

uctural analysis to find the contours [14]

79

80 W.-H. Liao and P.-M

Since the number of con duce the number to a max 0.5% of the total area, and retained. Fig. 5 depicts th changes in the boundary.

Fig. 5. Bou The 2-D boundary is co where the centroid of the bo and the boundary is encode into frequency domain usin and the similarity between distance [15]. The proper c will enhance robustness aga Finally, to derive a scor some basis of comparison.

standard deviation of the E mean is less than half of th ܥ_௜ǡ ܥ_௝are considered to be c into four levels according to

ܵܮ ൌ ەۖ

۔

ۖۓ



The repetition score is d cording to Eq. 21. Fig. 7 gi above procedure.

ܴሺܫሻ ൌ  σ^ସ_௜ୀଵ‘—–ሺܵܮ M. Chen

ntours thus extracted can be large, we use two criteria to ximum of 16: (1) the area enclosed has to be greater t (2) only the top 16 contours with largest enclosed area he final contours extracted from a logo image with grad

undary extraction using the proposed approach

onverted into a 1-D representation using shape signatu oundary is calculated and the distance between the centr ed, as illustrated in Fig. 6. The 1-D signal is then conver ng Fourier transform. These coefficients will be normali

two shape contours will be calculated using earth move combination of representation scheme and distance me ainst rotation, translation and scaling.

re that quantify the degree of repetition, we need to h . The statistics are obtained by computing the mean MD of all samples in the dataset. If the deviation from he standard deviation (shown in Eq. 19), the two conto comparatively similar. The degree of similarity is quanti

o Eq. 20.

defined as the weighted summation of similarity levels ives two examples of computing repetition scores using

ܮ_௜ሻ כ߱_௜ǡ ߱＝ሼͳǡ ͳ ͶΤ ǡ ͳ ͻΤ ǡ ͳ ͳ͸Τ ሽ (

Fig. 6. Use centroid

F

4 Experimental R

We have collected 26000 lo that no artifact will be gene used in our study. Three

Analysis of Visual Elements in Logo Design

distance to covert 2-D boundary into 1-D representation

Contour count =4 Repetition score=1.972

Contour count =16 Repetition score=108.75 Fig. 7. Repetition scores of two logos