The insideness problem is an image segmentation modality that consists of determining which pixels are inside and outside a region. Deep Neural Networks (DNNs) excel in segmentation benchmarks, but it is unclear that they have the ability to solve the insideness problem as it requires evaluating long-range spatial dependencies. In this paper, the insideness problem is analyzed in isolation, without texture or semantic cues, such that other aspects of segmentation do not interfere in the analysis. We demonstrate that DNNs for segmentation with few units have sufficient complexity to solve insideness for any curve. Yet, such DNNs have severe problems to learn general solutions. Only recurrent networks trained with small images learn solutions that generalize well to almost any curve. Recurrent networks can decompose the evaluation of long-range dependencies into a sequence of local operations, and learning with small images alleviates the common difficulties of training recurrent networks with a large number of unrolling steps.

%8 04/2020 %2https://hdl.handle.net/1721.1/124491

%0 Generic %D 2018 %T Can Deep Neural Networks Do Image Segmentation by Understanding Insideness? %A Kimberly M. Villalobos %A Jamel Dozier %A Vilim Stih %A Andrew Francl %A Frederico Azevedo %A Tomaso Poggio %A Tomotake Sasaki %A Xavier Boix %X**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