Contour shape alignment is a fundamental but challenging problem in computer\nvision, especially when the observations are partial, noisy, and largely\nmisaligned. Recent ConvNet-based architectures that were proposed to align\nimage structures tend to fail with contour representation of shapes, mostly due\nto the use of proximity-insensitive pixel-wise similarity measures as loss\nfunctions in their training processes. This work presents a novel ConvNet,\n"ProAlignNet" that accounts for large scale misalignments and complex\ntransformations between the contour shapes. It infers the warp parameters in a\nmulti-scale fashion with progressively increasing complex transformations over\nincreasing scales. It learns --without supervision-- to align contours,\nagnostic to noise and missing parts, by training with a novel loss function\nwhich is derived an upperbound of a proximity-sensitive and local\nshape-dependent similarity metric that uses classical Morphological Chamfer\nDistance Transform. We evaluate the reliability of these proposals on a\nsimulated MNIST noisy contours dataset via some basic sanity check experiments.\nNext, we demonstrate the effectiveness of the proposed models in two real-world\napplications of (i) aligning geo-parcel data to aerial image maps and (ii)\nrefining coarsely annotated segmentation labels. In both applications, the\nproposed models consistently perform superior to state-of-the-art methods.\n
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