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Boundaries are among the primary visual cues used by human and computervision systems. One of the key problems in boundary detection is the labelrepresentation, which typically leads to class imbalance and, as a consequence,to thick boundaries that require non-differential post-processing steps to bethinned. In this paper, we re-interpret boundaries as 1-D surfaces andformulate a one-to-one vector transform function that allows for training ofboundary prediction completely avoiding the class imbalance issue.Specifically, we define the boundary representation at any point as the unitvector pointing to the closest boundary surface. Our problem formulation leadsto the estimation of direction as well as richer contextual information of theboundary, and, if desired, the availability of zero-pixel thin boundaries alsoat training time. Our method uses no hyper-parameter in the training loss and afixed stable hyper-parameter at inference. We provide theoreticaljustification/discussions of the vector transform representation. We evaluatethe proposed loss method using a standard architecture and show the excellentperformance over other losses and representations on several datasets. Code isavailable at https://github.com/edomel/BoundaryVT.

Zero Pixel Directional Boundary by Vector Transform