Zero Pixel Directional Boundary by Vector Transform

Boundaries are among the primary visual cues used by human and computer vision systems. One of the key problems in boundary detection is the label representation, which typically leads to class imbalance and, as a consequence, to thick boundaries that require non-differential post-processing steps to be thinned. In this paper, we re-interpret boundaries as 1-D surfaces and formulate a one-to-one vector transform function that allows for training of boundary prediction completely avoiding the class imbalance issue. Specifically, we define the boundary representation at any point as the unit vector pointing to the closest boundary surface. Our problem formulation leads to the estimation of direction as well as richer contextual information of the boundary, and, if desired, the availability of zero-pixel thin boundaries also at training time. Our method uses no hyper-parameter in the training loss and a fixed stable hyper-parameter at inference. We provide theoretical justification/discussions of the vector transform representation. We evaluate the proposed loss method using a standard architecture and show the excellent performance over other losses and representations on several datasets. Boundaries are important interpretable visual cues that can describe both the low-level image characteristics as well as high-level semantics in an image. Human vision uses occluding contours and boundaries to interpret unseen or seen objects and classes. In several vision tasks, they are exploited as priors (Zhu et al., 2020; Kim et al., 2021; Hatamizadeh et al., 2019; Revaud et al., 2015; Cashman & Fitzgibbon, 2012). Some key works on contours (Cootes et al., 2001; Matthews & Baker, 2004; Kass et al., 1988) have greatly impacted early research in computer vision. Although the advent of end-to-end deep learning has somewhat shifted the focus away from interpretable visual cues, boundary discovery still remains important in computer vision tasks. Boundary detection, however, has seen a rather modest share of such progress. Although, modern deeply learned methods (Xie & Tu, 2015; Liu et al., 2017; Maninis et al., 2017) provide better accuracy and the possibility to learn only the high-level boundaries, a particularly elusive goal in learned boundary detection has been the so-called crisp boundaries (Isola et al., 2014; Wang et al., 2018; Deng et al., 2018).