Following the Mandelbrot's theory of fractals, many shapes and phenomena in nature have been suggested to be fractal. Even animal behavior and human physiological responses can also be represented as fractal. Here, we show the evidence that it is possible to apply the concept of fractals even to the facial expression recognition, which is one of the most important parts of human recognition. Rating data derived from judging morphed facial images were represented in the two-dimensional psychological space by multidimensional scaling of four different scales. The resultant perimeter of the structure of the emotion circumplex was fluctuated and was judged to have a fractal dimension of 1.18. The smaller the unit of measurement, the longer the length of the perimeter of the circumplex. In this study, we provide interdisciplinarily important evidence of fractality through its application to facial expression recognition.
Nonlinear transduction of emotional facial expression
