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Spherical Regression: Learning Viewpoints, Surface Normals and 3D Rotations on n-Spheres
Many computer vision challenges require continuous outputs, but tend to be
solved by discrete classification. The reason is classification's natural
containment within a probability -simplex, as defined by the popular softmax
activation function. Regular regression lacks such a closed geometry, leading
to unstable training and convergence to suboptimal local minima. Starting from
this insight we revisit regression in convolutional neural networks. We observe
many continuous output problems in computer vision are naturally contained in
closed geometrical manifolds, like the Euler angles in viewpoint estimation or
the normals in surface normal estimation. A natural framework for posing such
continuous output problems are -spheres, which are naturally closed
geometric manifolds defined in the space. By introducing a
spherical exponential mapping on -spheres at the regression output, we
obtain well-behaved gradients, leading to stable training. We show how our
spherical regression can be utilized for several computer vision challenges,
specifically viewpoint estimation, surface normal estimation and 3D rotation
estimation. For all these problems our experiments demonstrate the benefit of
spherical regression. All paper resources are available at
https://github.com/leoshine/Spherical_Regression.Comment: CVPR 2019 camera read
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