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Journal Articles Journal of Mathematical Imaging and Vision Year : 2009

A Metric Approach to nD Images Edge Detection With Clifford Algebras

Abstract

The aim of this paper is to perform edge detection in color-infrared images from the point of view of Clifford algebras. The main idea is that such an image can be seen as a section of a Clifford bundle associated to the RGBT-space (Red, Green, Blue, Temperature) of acquisition. Dealing with geometric calculus and covariant derivatives of appropriate sections with respect to well-chosen connections allows to get various color and temperature information needed for the segmentation. We show in particular how to recover the first fundamental form of the image embedded in a LSHT-space (Luminance, Saturation , Hue, Temperature) equipped with a metric tensor. We propose applications to color edge detection with respect to a given hue interval and to edge detection in color-infrared images with constraints on temperature. Others applications related to different choices of connections, sections and embedding spaces for nD images may be considered from this general theorical framework.
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Dates and versions

hal-00267629 , version 1 (28-03-2008)
hal-00267629 , version 2 (17-09-2008)

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Thomas Batard, Christophe Saint-Jean, Michel Berthier. A Metric Approach to nD Images Edge Detection With Clifford Algebras. Journal of Mathematical Imaging and Vision, 2009, 33 (3), pp.296-312. ⟨10.1007/s10851-008-0115-0⟩. ⟨hal-00267629v2⟩

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