Encoding cognitive processes through geometric transformations
In nature and in art, geometric symmetry is everywhere. It has also progressively found its way into the basic ideas and techniques of mathematics, such as the continuous and discrete groups of transformations and their uses. The impression of beauty and aesthetic pleasure, which are linked to symmetric patterns, is another significant function of symmetry in our lives.
Geometric symmetry is defined mathematically as being invariant to several types of geometric changes. For example, a circle would stay a circle (be invariant/symmetric) under a translation, rotation, and dilation combination, but not a skew transformation. Numerous studies have shown evidence of geometric invariance in the motor, perceptual, and underlying brain activity of primates.
Cognitive geometric transformations also include topic such as how the human brain perceives the image and how it recognizes objects despite of transformation in the image, does it uses some kind of transformation to recognize or it use some other mechanism. This is an active area of research in the field of cognitive science and computer vision.
The representation of cognitive processes in the brain, according to Felix Polyakov of Bar-Ilan University, is based on geometric variables and transformations that are crucial for bridging the gap between cognitive and mechanistic components of behavior, for integrating information from various sensory modalities, for sensory-motor integration, and for compactly representing learned skills.
Encoding cognitive processes through geometric transformations