978-1-4244-4547-9/09/$26.00 ©2009 IEEE TENCON 2009 A Fast Image Reconstruction Algorithm using Significant Sample Point Selection and Linear Bivariate Splines Rohit Verma Under-graduate student of Computer Science at Jaypee University of Information Technology Solan, India email4rohit@gmail.com Ruchika Mahrishi Under-graduate student of Computer Science at Jaypee University of Information Technology Solan, India ruchikamahrishi@ieee.org Gaurav Kumar Srivastava Under-graduate student of Computer Science at Jaypee University of Information Technology Solan, India gaurav.srivastava7@gmail.com Siddavatam Rajesh Assistant Professor of Computer Science at Jaypee University of Information Technology Solan, India srajesh@juit.ac.in Abstract— The image reconstruction using linear bivariate splines and delaunay triangulation is addressed in this paper. A novel significant sample point selection is used to get the most significant samples for triangulation. Image reconstruction is done based on the approximation of image regarded as a function, by a linear spline over adapted Delaunay triangulation. The proposed method is compared with some of the existing image reconstruction spline models. Keywords-image processing; delaunay triangulation; linear Bivariate splines. I. INTRODUCTION Image reconstruction using regular and irregular samples have been developed by many researchers recently. *Siddavatam Rajesh et. al. [1] has developed a fast progressive image sampling using B-splines. Eldar et. al [2] has developed image sampling of significant samples using the farthest point strategy. Muthuvel Arigovindan [3] developed Variational image reconstruction from arbitrarily spaced samples giving a fast multiresolution spline solution. Carlos Vazquez et al, [4] has proposed interactive algorithm to reconstruct an image from non-uniform samples obtained as a result of geometric transformation using filters. Cohen and Matei [5] developed edge adapted multiscale transform method to represent the images. Strohmer [7] developed computationally attractive reconstruction of bandlimited images from irregular samples. Eldar and Oppenheim,[8] have developed filter bank reconstruction of bandlimited signals from non-uniform and generalized samples. Aldroubi and Grochenig, [9] have developed nonuniform sampling and reconstruction in shift invariant spaces. Delaunay triangulation [10] has been extensively used for generation of image from irregular data points. The image is reconstructed by either by linear or cubic splines over Delaunay Triangulations of adaptively chosen set of significant points. This paper concerns with triangulation of an image using standard gradient edge detection techniques and reconstruction using bivariate splines from adapted Delaunay triangulation. The reconstruction is done based on the approximation of image regarded as function, by a linear spline over adapted Delaunay triangulation. The reconstruction algorithm deals with generating Delaunay triangulations of scattered image points, obtained by detection of edges using Sobel and Canny edge detection algorithms. Section II describes the significant sample point selection. and in section III the modeling of the 2D images using the Linear Bivariate splines is elaborated. Section IV deals with novel reconstruction algorithm and Significant Performance Measures are presented in section V. The experimental results by using the proposed method are discussed in section VI. II. SIGNIFICANT SAMPLE POINT SELECTION This section provides a generic introduction to the basic features and concepts of novel Significant Sample Point Selection algorithm. Let M be a mXn matrix representing a grayscale image The algorithm involves following steps:- 1) Initialization : initialization of variables 2) Edge Detection: Edge detection using sobel and canny filters. 3) Filtering: Passing the images/matrices through rangefilt. 1