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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. Code is available at https://github.com/edomel/BoundaryVT.