Construction of Appearance Manifold with Embedded View-Dependent Covariance Matrix for 3D Object Recognition

We propose the construction of an appearance manifold with embedded view-dependent covariance matrix to recognize 3D objects which are influenced by geometric distortions and quality degradation effects. The appearance manifold is used to capture the pose variability, while the covariance matrix is used to learn the distribution of samples for gaining noise-invariance. However, since the appearance of an object in the captured image is different for every different pose, the covariance matrix value is also different for every pose position. Therefore, it is important to embed view-dependent covariance matrices in the manifold of an object. We propose two models of constructing an appearance manifold with view-dependent covariance matrix, called the View-dependent Covariance matrix by training-Point Interpolation (VCPI) and View-dependent Covariance matrix by Eigenvector Interpolation (VCEI) methods. Here, the embedded view-dependent covariance matrix of the VCPI method is obtained by interpolating every training-points from one pose to other trainingpoints in a consecutive pose. Meanwhile, in the VCEI method, the embedded view-dependent covariance matrix is obtained by interpolating only the eigenvectors and eigenvalues without considering the correspondences of each training image. As it embeds the covariance matrix in manifold, our view-dependent covariance matrix methods are robust to any pose changes and are also noise invariant. Our main goal is to construct a robust and efficient manifold with embedded view-dependent covariance matrix for recognizing objects from images which are influenced with various degradation effects. key words: 3D object recognition, appearance manifold, view-dependent covariance matrix, eigenvector interpolation, eigenvalue interpolation, eigenspace