Grid smoothing: a graph-based approach

Authors:
Guillaume Noel;Karim Djouani;Yskandar Hamam
Affiliations:
French South African Institute of Technology, Tshwane University of Techology, Pretoria, South Africa;French South African Institute of Technology, Tshwane University of Techology, Pretoria, South Africa;French South African Institute of Technology, Tshwane University of Techology, Pretoria, South Africa
Venue:
CIARP'10 Proceedings of the 15th Iberoamerican congress conference on Progress in pattern recognition, image analysis, computer vision, and applications
Year:
2010

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Abstract

In the past few years, mesh representation of images has attracted a lot of research interest due to its wide area of applications in image processing. In the mesh framework, an image is represented by a graph in which the nodes represent the pixels and the edges reflect the connectivity. The definition of the most adapted mesh for a given image is a challenge in terms of computation cost and information representation. In this paper, a new method for content adaptive mesh representation of gray scale images, called grid smoothing, is presented. A cost function is defined using the spatial coordinates of the nodes and the gray levels present in the image. The minimisation of the cost function leads to new spatial coordinates for each node. Using an adequate cost function, the grid is compressed in the regions with large gradient values and relaxed in the other regions. The result is a grid which better fits the objects in the image. The mathematical framework of the method is introduced in the paper. An in-depth study of the convergence is presented as well as results on real gray scale images.