A Metric Approach to nD Images Edge Detection with Clifford Algebras

Authors:
Thomas Batard;Christophe Saint-Jean;Michel Berthier
Affiliations:
Laboratoire Mathématiques, Image et Applications, Université de La Rochelle, La Rochelle Cedex, France 17042;Laboratoire Mathématiques, Image et Applications, Université de La Rochelle, La Rochelle Cedex, France 17042;Laboratoire Mathématiques, Image et Applications, Université de La Rochelle, La Rochelle Cedex, France 17042
Venue:
Journal of Mathematical Imaging and Vision
Year:
2009

Citing 6
Cited 4

A note on the gradient of a multi-image

Computer Vision, Graphics, and Image Processing - Lectures notes in computer science, Vol. 201 (G. Goos and J. Hartmanis, Eds.)
Edge detection in multispectral images

CVGIP: Graphical Models and Image Processing
Color snakes

Computer Vision and Image Understanding
Geometric computing with Clifford algebras: theoretical foundations and applications in computer vision and robotics

Geometric computing with Clifford algebras: theoretical foundations and applications in computer vision and robotics
A general framework for low level vision

IEEE Transactions on Image Processing
Modified curvature motion for image smoothing and enhancement

IEEE Transactions on Image Processing

Clifford Bundles: A Common Framework for Image, Vector Field, and Orthonormal Frame Field Regularization

SIAM Journal on Imaging Sciences
Heat Equations on Vector Bundles--Application to Color Image Regularization

Journal of Mathematical Imaging and Vision
Hypercomplex Mathematical Morphology

Journal of Mathematical Imaging and Vision
Polyakov action on (ρ,g)-equivariant functions application to color image regularization

SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision

Quantified Score

Hi-index	0.00

Visualization

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 some constraints on colors and to edge detection in color-infrared images with constraints on both colors and temperature. Other applications related to different choices of connections, sections and embedding spaces for nD images may be considered from this general theoretical framework.