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Differential Geometric Aspects in Image Processing

Dr. Marcelo C´ ardenas

Classroom exercises: November 7, 2019

Problem C1.1

Show that a simple closed curve is strictly convex if and only if the turning angleν is strictly monotone.

Problem C1.2

i) Show that the affine metricgis invariant under special affine transformations.

ii) Let ˜c(s) = Ac(s) + b be an affine transformation of c. Show that d˜dss = (detA)1/3.

Problem C1.3

Show thatGL(d,R) with the usual multiplication of matrices is a Lie group.

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Differential Geometric Aspects of Image Processing

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Differential Geometric Aspects in Image Processing

Differential Geometric Aspects in Image

Differential Geometric Aspects in Image Processing

Differential Geometric Aspects in Image

Differential Geometric Aspects in Image Processing

Differential Geometric Aspects in Image

Differential Geometric Aspects in Image Processing

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