Pose detection of 3-D objects using S<sup>2</sup>-correlated images and discrete spherical harmonic transforms

Abstract

The pose detection of three-dimensional (3-D) objects from two-dimensional (2-D) images is an important issue in computer vision and robotics applications. Specific examples include automated assembly, automated part inspection, robotic welding, and human robot interaction, as well as a host of others. Eigendecomposition is a common technique for dealing with this issue and has been applied to sets of correlated images for this purpose. Unfortunately, for the pose detection of 3-D objects, a very large number of correlated images must be captured from many different orientations. As a result, the eigendecomposition of this large set of images is very computationally expensive. In this work, we present a method for capturing images of objects from many locations by sampling S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> appropriately. Using this spherical sampling pattern, the computational burden of computing the eigendecomposition can be reduced by using the spherical harmonic transform to "condense" information due to the correlation in S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . We propose a computationally efficient algorithm for approximating the eigendecomposition based on the spherical harmonic transform analysis. Experimental results are presented to compare and contrast the algorithm against the true eigendecomposition, as well as quantify the computational savings.