﻿ Tansei 11 - Invitation to Science - From mathematical research of visual illusions to their application in science and technology: The world of mathematical vision science

# From mathematical research of visual illusions to their application in science and technology: The world of mathematical vision science

The human eye is susceptible to visual illusions.
Mathematical vision science is a new discipline that approaches the mechanisms of visual perception using advanced mathematical methods.
This approach has given birth to innovative image processing technology and art.
Today, we are witnessing an ongoing fusion of vision, illusion, computer vision, art and advanced mathematics.

Figure 1: Floating hearts visual illusion. © Hitoshi Arai and Shinobu Arai

Illusions produced by the human visual sense are known as visual illusions. Visual illusions represent an important theme in the research of visual perception, and up until now have been explored from the perspective of psychology and brain science. Mathematical vision science is a new discipline proposed by the author for the purpose of exploring visual illusions, human visual perception, and various applied technologies based thereon, using the capabilities of advanced mathematics.

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Figure 2: Control of the magnitude of visual illusion. © Hitoshi Arai and Shinobu Arai.

First, let's take a look at some examples of visual illusions. Around 2005, the creation of seemingly tilted character strings for fun gained popularity on Internet bulletin boards in Japan. With my research associate Shinobu Arai, we named such strings "Mojiretsu Keisha illusions," which means tilt illusions constructed by character strings, and subjected them to mathematical analysis as part of our research on visual illusions. Figure 2 (1) shows an example of a Mojiretsu Keisha illusion that we identified using mathematical methods. So why do these strings, which are aligned in parallel, appear tilted? It happens as a result of information processing by relevant neurons in the brain. We created mathematical models of visual information processing in the brain, and used them to identify neuronal information processing activities related to visual illusions. This research produced the world's first successful method for exercising free control over the magnitude of visual illusions. Figure 2 (2) and (3) present examples of practical application of this method. It is possible to observe how the magnitude of the visual illusion gradually decreases.

We advanced further research on visual information processing in the brain, and discovered an algorithm that can convert any image into a floating illusion (fuyuu illusion) by triggering a specific neural response in the brain. (The algorithm has been patented.) Figure 1 shows an example of this process. Slowly move the image diagonally, and you will see the hearts sway gently. Next, slowly move your face closer to the image, then pull back, and repeat the action. The image gives the illusion that the heart is beating.

Furthermore, we has successfully applied mathematical vision science research in the development of numerous inventions, such as a new image processing system, an original filter design method, and a color-perception analyzer. We have several patents pending approval.

Currently, the practical application of research with a focus on the mathematics of vision is expanding into the fields of science and technology, as well as industry and medicine.