Pose detection of 3-D objects using S²-correlated images and discrete spherical harmonic transforms

Abstract

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 2 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 2 . 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.

An Analysis of Sphere Tessellations for Pose Estimation of 3-D Objects Using Spherically Correlated Images

“…In [11] the authors propose a method for 3-D pose estimation using spherical sampling and the Spherical Har- Figure 4. Quality measures outlined in Section 2 computed for all three tessellations and averaged over all objects in Fig.…”

“…In this section, we briefly give an overview of the SHT algorithm developed in [11]. For this analysis, we are using CAD generated ray-traced images, examples of which are shown in Fig.…”

“…This drawback has been addressed using several different approaches [5][6][7][8][9][10][11]. In [10], Chang et al showed that if the image data set was correlated in one dimension, then the FFT may be used to approximate the desired subspace dimension, as well as the principal eigenimages.…”

“…In [10], Chang et al showed that if the image data set was correlated in one dimension, then the FFT may be used to approximate the desired subspace dimension, as well as the principal eigenimages. In [11] the authors extended this concept to correlation in twodimensions by using the Spherical Harmonic Transform (SHT) in place of the FFT to capture the frequency information of this data set. The issue is then in deciding the "best" tessellation of the sphere such that a representative set of samples is achieved.…”

Eigendecomposition of Images Correlated on $S^{1}$, $S^{2}$, and $SO(3)$ Using Spectral Theory

“…Over the last decade, spherical harmonics have been gaining popularity in the computer vision and computer graphics arena. Spherical harmonics have been applied to several computer vision applications with unknown lighting [34]- [37], as well as 3-D model retrieval [38], [39], 3-D shape descriptors [40], and pose estimation [17], [18], [20]. Spherical harmonics have also been applied to rotation estimation and convolution of spherical images [41].…”