978-1-4244-2794-9/09/$25.00 ©2009 IEEE SMC 2009 Depth Map Estimation Using Exponentially Decaying Focus Measure Based on Susan Operator Pankajkumar Mendapara, Rashid Minhas, Q.M. Jonathan Wu Department of Electrical Engineering University of Windsor Windsor, Canada {mendapa, minhasr, jwu}@ uwindsor.ca Abstract— This paper presents a novel technique for depth map estimation using a sequence of images acquired at varying focus. In depth map estimation noise, illumination variations and types of extracted features significantly affect the performance of a focus measure. This paper proposes the use of SUSAN operator, to extract features, because of its structure preserving noise filtering which plays a pivotal role in depth estimation of a scene. We introduce a new focus measure based on exponentially decaying function to use neighborhood information of an extracted feature point that assigns more weight to the closer pixel points. Experiments validate superior performance of our proposed algorithm in comparison to other well-documented methods. Keywords—focus measure, 3D shape recovery, shape from focus, exponentially decaying function, multi-focus imaging. I. INTRODUCTION The technique utilized to retrieve spatial information from a sequence of images with varying focus plane is termed as shape from focus (SFF). In SFF, a sequence of images (SI) is acquired at varying relative distance between a camera lens and a scene object. Such a sequence captures well focused partial information of a scene in different images. To reconstruct a well focused image, SI acquired with varying distances is processed to extract focused points from individual image frames. Traditional SFF techniques assume convex shaped objects for accurate depth map estimation. SFF removes the inherent limitation of traditional image acquisition for its inability to capture details of a scene with a considerably large depth. The objective of depth map estimation is to determine the depth of every object point with respect to the camera. For scenes with considerably large depth, object points present on a focus plane appear sharp in an acquired image whereas blur of imaged points increases as they move away from the focus plane. Basic image formation geometry when camera parameters are known is shown in Fig. 1. Distance of an object from camera lens i.e. u is required for exact 3D reconstruction of a scene. Depth of a scene, distance of an object from lens, illumination conditions, camera movement, aberration effects in lens and movement in a scene can severely affect the depth map estimation. Computing distance of an object from a camera lens is simple if blur circle radius R is equal to zero. If image detector (ID) is placed at an exact distance v; sharp focused image P of an object point P is formed. Relationship between object distance u, focal distance of lens f and ID distance v is given by Gaussian lens law. v u f 1 1 1 Figure 1. Image formation geometry of a 3D object In literature [1-6,14,15] commonly used operators in SFF are sum of modified Laplacian (FM SML ), Tenengrade focus measure (FM T ), gray level variance focus measure (FM GLV ), curvature focus measure (FM C ), M2 focus measure (FM M2 ), point focus measure (FM P ) and steerable filters based focus measure (FM SF ). Approximation and learning based focus measures have also been proposed [7-9] that utilize neural network, neuro fuzzy systems and dynamic programming based approaches for accurate depth map estimation. Approximation based techniques use any of the conventional aforementioned focus measures for pre-processing whereas comprehensive rule base and appropriate selection of training data restrict their application to specific domains. In this paper a new scheme is proposed to estimate depth map by searching the frame number for the best focused object points. Most of the established focus measure operators for SFF work well for regions with dense texture only. Hence their degraded performance is observed in presence of noise, poor texture and singularities along curves. Proceedings of the 2009 IEEE International Conference on Systems, Man, and Cybernetics San Antonio, TX, USA - October 2009 978-1-4244-2794-9/09/$25.00 ©2009 IEEE 3805