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.

中文翻译：

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用电定位中的多个电子图像表示对象的形状。

弱电鱼通过释放位于尾巴区域的电器官来产生电场。鱼附近的物体会调节自生电场。调制场使鱼类即使在完全黑暗的情况下也能感知物体。鱼的电感应系统提供了感知物体的能力。分布在鱼类皮肤表面上的电感受器可以根据皮肤表面的透皮电压（称为电图像）来感应调制场。鱼可以从电子图像中提取对象的特征，例如横向距离，大小，形状和电特性。尽管先前的研究已经证明了电图像特征与物体的距离和大小之间的关系，但仍不清楚电图像的哪些特征代表物体的 的形状。我们在这里提出一个假设，形状信息不是由单个图像表示，而是由对象旋转或鱼围绕对象运动引起的多个图像表示。为了检验该假设，我们开发了一种计算模型，该模型可以预测由形状不同的物体的旋转产生的电图像。我们使用了五种不同形状的电阻对象：一个圆形，一个正方形，一个等边三角形，一个矩形和一个椭圆形。我们表明，固定形状的不同形状的物体会生成相似的高斯电图像，而不管其形状如何。我们还表明，电子图像的特征（例如峰幅度，半最大宽度和峰位置）表现出与对象旋转有关的角度相关变化特征，具体取决于对象形状和横向距离。此外，我们证明了峰幅度和半最大宽度的积分效应可能是物体形状的不变度量。这些结果表明，通过组合在对象周围的探索行为期间产生的那些图像特征，鱼可以感知对象的形状。