Characterization of Scenes and Images
In this chapter, we characterize continuous images by discrete parameters. Noting that the input to the camera is a collection of rays of light to which intensity values are attached, we define “scenes” as functions of orientations. Images are perspective projections of these functions onto the image plane. The camera rotation transformation of scenes and images induces representations of SO(3) in the space of functions known as spherical harmonics. We study the geometrical structures of the “scene space” and the “image space” by means of tensor calculus. Then, we analyze invariance properties of “linear functionals” of images, which we call image features, and show how they are used for identification and classification of shapes.
KeywordsImage Plane Irreducible Representation Invariant Measure Spherical Harmonic Invariant Subspace
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