An improved method to estimate the fractal dimension of colour images

Fractals in Neuropsychology and Cognitive Neuroscience

The fractal dimension of cognition refers to the idea that the cognitive processes of the human brain exhibit fractal properties. This means that certain patterns of cognitive activity, such as visual perception, memory, language, or problem-solving, can be described using the mathematical concept of fractal dimension.The idea that cognition is fractal has been proposed by some researchers as a way to understand the complex, self-similar nature of the human brain. However, it's a relatively new idea and is still under investigation, so it's not yet clear to what extent cognitive processes exhibit fractal properties or what implications this might have for our understanding of the brain and clinical practice. Indeed, the mission of the "fractal neuroscience" field is to define the characteristics of fractality in human cognition in order to differently characterize the emergence of brain disorders.

The art of pain: A quantitative color analysis of the self-portraits of Frida Kahlo

Frida Kahlo (1907–1954) was a Mexican artist who is remembered for her self-portraits, pain and passion, and bold, vibrant colors. This work aims to use her life story and her artistic production in a longitudinal study to examine with quantitative tools the effects of physical and emotional pain (rage) on artistic expression. Kahlo suffered from polio as a child, was involved in a bus accident as a teenager where she suffered multiple fractures of her spine and had 30 operations throughout her lifetime. She also had a tempestuous relationship with her painter husband, Diego Rivera. Her physical and personal troubles however became the texture of her vivid visual vocabulary—usually expressed through the depiction of Mexican and indigenous culture or the female experience and form. We applied color analysis to a series of Frida's self-portraits and revealed a very strong association of physical pain and emotional rage with low wavelength colors (red and yellow), indicating that the expression of her ailments was, consciously or not, achieved by increasing the perceived luminance of the canvas. Further quantitative analysis that used the fractal dimension identified “The broken column” as the portrait with higher compositional complexity, which matches previous critical acclaim of this portrait as the climax of her art. These results confirm the ability of color analysis to extract emotional and cognitive features from artistic work. We suggest that these tools could be used as markers to support artistic and creative interventions in mental health.

Color Image Complexity versus Over-Segmentation: A Preliminary Study on the Correlation between Complexity Measures and Number of Segments

It is said that image segmentation is a very difficult or complex task. First of all, we emphasize the subtle difference between the notions of difficulty and complexity. Then, in this article, we focus on the question of how two widely used color image complexity measures correlate with the number of segments resulting in over-segmentation. We study the evolution of both the image complexity measures and number of segments as the image complexity is gradually decreased by means of low-pass filtering. In this way, we tackle the possibility of predicting the difficulty of color image segmentation based on image complexity measures. We analyze the complexity of images from the point of view of color entropy and color fractal dimension and for color fractal images and the Berkeley data set we correlate these two metrics with the segmentation results, more specifically the number of quasi-flat zones and the number of JSEG regions in the resulting segmentation map. We report on our experimental results and draw conclusions.

Signature identification by Minkowski dimension

In this article, we propose and investigate the possibility of signature identification based on its fractal Minkowski dimension. We consider a signature as a trajectory of a pen tip that obeys the Langevin equations, for which we calculate the fractal Minkowski dimension. This parameter is different for original and intentionally falsified signatures, thus allowing one to reliably distinguish between the signatures left by different persons. The proposed approach together with machine learning techniques is a potentially powerful tool for identification and verification of signatures and any other kind of notations.

Novel digital image analysis using fractal dimension for assessment of skin radiance

BACKGROUND

Despite a strong desire to quantify skin radiance in the field of cosmetics, there does not exist a robust method to characterize it. Classical shine that quantifies the specular reflection from skin has been commonly used as the metric to characterize radiance. However, it does not always correlate with the perceived radiance as there are many other parameters that inform radiance perception including spatial distribution of shine and color homogeneity.

MATERIALS AND METHODS

In this work, we propose a novel method using fractal analysis to better characterize radiance by considering the spatial heterogeneity of pixel intensities as well as color evenness. A simulated image library (nine images) from very dull to very bright was created using bare face images of 20 panelists. Product images taken post-product usage were ranked along this library by finding the image in the library that most resembles the product image by our algorithm as well as experts. Additionally, classical shine and color measurements were made as benchmarks.

RESULTS

Our results confirm a strong correlation (R²  = 0.99) between the expert radiance rankings and the rankings by fractal dimension algorithm. The new algorithm offers an improved product differentiation compared with classical shine or color measurements.

CONCLUSION

Fractal dimension calculation offers higher sensitivity and resolution compared with other descriptors such as classical shine or color heterogeneity. In cases where the image rank is dominated by pixel intensities rather than color evenness, the image ranks resulting from calculating the fractal dimension is comparable with use of classical shine as the ranking parameter.