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Warping patch on sphere

Consider the following image with denoted region of interest (ROI). Assuming the helmet in the image is a perfect sphere, how to warp the ROI so that it simulates rotation of the sphere? The goal is to generate "training" patterns that are likely to happen when the head rotates.

image description

Warping patch on sphere

Consider the following image with denoted region of interest (ROI). Assuming the helmet in the image is a perfect sphere, how to warp the ROI so that it simulates rotation of the sphere? The goal is to generate "training" training patterns that are likely to happen when the head rotates.

image description