**THIS MEMO IS REPLACED BY CBMM MEMO 105**

A key component of visual cognition is the understanding of spatial relationships among objects. Albeit effortless to our visual system, state-of-the-art artificial neural networks struggle to distinguish basic spatial relationships among elements in an image. As shown here, deep neural networks (DNNs) trained with hundreds of thousands of labeled examples cannot accurately distinguish whether pixels lie inside or outside 2D shapes, a problem that seems much simpler than image segmentation. In this paper, we sought to analyze the capability of ANN to solve such inside/outside problems using an analytical approach. We demonstrate that it is a mathematically tractable problem and that two previously proposed algorithms, namely the Ray-Intersection Method and the Coloring Method, achieve perfect accuracy when implemented in the form of DNNs.

%8 12/2018