Pattern Encoding on the Poincare Sphere

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This paper presents a convenient graphical tool for encoding visual patterns (such as image patches and image atoms) as point constellations in a space spanned by perceptual features and with a clear geometrical interpretation. General theory and a practical pattern encoding scheme are presented, inspired by encoding polarization states of a light wave on the Poincare sphere. This new pattern encoding scheme can be useful for many applications in image processing and computer vision. Here, three possible applications are illustrated, in clustering perceptually similar patterns, visualizing properties of learned dictionaries of image atoms and generating new dictionaries of image atoms from spherical codes.