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Manifold learning and applications to shape and image processing

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Academic year: 2021

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Figure 1.1: A set of points in R 3 lying on a manifold sampled from a 2-
Figure 1.2: Each image is a vector in R 4096 , but we observe only three degrees of freedom: 2 rotation angles and 1 illumination parameter
Figure 1.3: The Face data lies on a 3-dimensional curved submanifold X embedded in R 4096
Figure 2.1: Travel length for the bird is shorter as the travel length of the ant. The ant is constrained to move in a different metric space than the bird.
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