Shape-Tailored Deep Neural Networks
This addresses segmentation tasks where object regions have diverse shapes, offering a more efficient and robust alternative to existing CNN-based methods.
The paper tackles the problem of segmentation by extending convolutional networks to compute descriptors on arbitrarily shaped regions using a Poisson PDE formulation, resulting in models that are 3-4 orders of magnitude smaller and exceed state-of-the-art performance with 2-3 orders smaller training sets.
We present Shape-Tailored Deep Neural Networks (ST-DNN). ST-DNN extend convolutional networks (CNN), which aggregate data from fixed shape (square) neighborhoods, to compute descriptors defined on arbitrarily shaped regions. This is natural for segmentation, where descriptors should describe regions (e.g., of objects) that have diverse shape. We formulate these descriptors through the Poisson partial differential equation (PDE), which can be used to generalize convolution to arbitrary regions. We stack multiple PDE layers to generalize a deep CNN to arbitrary regions, and apply it to segmentation. We show that ST-DNN are covariant to translations and rotations and robust to domain deformations, natural for segmentation, which existing CNN based methods lack. ST-DNN are 3-4 orders of magnitude smaller then CNNs used for segmentation. We show that they exceed segmentation performance compared to state-of-the-art CNN-based descriptors using 2-3 orders smaller training sets on the texture segmentation problem.