Representation of object's shape by multiple electric images in electrolocation

Weakly electric fish generate an electric field by discharging an electric organ located on the tail region. An object near the fish modulates the self-generated electric field. The modulated field enables the fish to perceive objects even in complete darkness. The ability to perceive objects is provided by the electrosensory system of the fish. Electroreceptors distributed on the fish's skin surface can sense the modulated field, on the basis of transdermal voltage across the skin surface, called electric images. The fish can extract object's features such as lateral distance, size, shape, and electric property from an electric image. Although previous studies have demonstrated the relationship between electric-image features and object's distance and size, it remains unclear what features of an electric image represent the object's shape. We make here a hypothesis that shape information is not represented by a single image but by multiple images caused by the object's rotation or fish movement around the object. To test the hypothesis, we develop a computational model that can predict electric images produced by the rotation of differently shaped objects. We used five different shapes of resistive objects: a circle, a square, an equilateral triangle, a rectangle, and an ellipsoid. We show that differently shaped objects of a fixed arrangement generate similar Gaussian electric images, irrespective of their shapes. We also show that the features of an electric image such as the peak amplitude, half-maximum width, and peak position exhibit the angle-dependent variations characteristic to object rotation, depending on object shapes and lateral distances. Furthermore, we demonstrate that an integration effect of the peak amplitude and half-maximum width could be an invariant measure of object shape. These results suggest that the fish could perceive an object shape by combining those image features produced during exploratory behaviors around the object.