Mercer kernels are used for a wide range of image and signal processing tasks like de-noising, clustering, discriminant analysis etc. These algorithms construct their solutions in terms of the expansions in a high-dimensional feature space F. However, many applications like kernel PCA (principal component analysis) can be used more effectively if a pre-image of the projection in the feature space is available. In this paper, we propose a novel method to reconstruct a unique approximate pre-image of a feature vector and apply it for statistical shape analysis. We provide some experimental results to demonstrate the advantages of kernel PCA over linear PCA for shape learning, which include, but are not limited to, ability to learn and distinguish multiple geometries of shapes and robustness to occlusions.
Segmentation involves separating an object from the background in a given image. The use of image information alone often leads to poor segmentation results due to the presence of noise, clutter, or occlusion. The introduction of shape priors in the geometric active contour (GAC) framework has proven to be an effective way to ameliorate some of these problems. In this work, we propose a novel segmentation method combining image information with prior shape knowledge using level sets. Following the work of Leventon et al., we propose revisiting the use of principal component analysis (PCA) to introduce prior knowledge about shapes in a more robust manner. We utilize kernel PCA (KPCA) and show that this method outperforms linear PCA by allowing only those shapes that are close enough to the training data. In our segmentation framework, shape knowledge and image information are encoded into two energy functionals entirely described in terms of shapes. This consistent description permits us to fully take advantage of the KPCA methodology and leads to promising segmentation results. In particular, our shape-driven segmentation technique allows for the simultaneous encoding of multiple types of shapes and offers a convincing level of robustness with respect to noise, occlusions, or smearing.
In this paper, we propose a particle filtering approach for the problem of registering two point sets that differ by a rigid body transformation. Typically, registration algorithms compute the transformation parameters by maximizing a metric given an estimate of the correspondence between points across the two sets of interest. This can be viewed as a posterior estimation problem, in which the corresponding distribution can naturally be estimated using a particle filter. In this work, we treat motion as a local variation in pose parameters obtained by running a few iterations of a certain local optimizer. Employing this idea, we introduce stochastic motion dynamics to widen the narrow band of convergence often found in local optimizer approaches for registration. Thus, the novelty of our method is threefold: First, we employ a particle filtering scheme to drive the point set registration process. Second, we present a local optimizer that is motivated by the correlation measure. Third, we increase the robustness of the registration performance by introducing a dynamic model of uncertainty for the transformation parameters. In contrast with other techniques, our approach requires no annealing schedule, which results in a reduction in computational complexity (with respect to particle size) as well as maintains the temporal coherency of the state (no loss of information). Also unlike some alternative approaches for point set registration, we make no geometric assumptions on the two data sets. Experimental results are provided that demonstrate the robustness of the algorithm to initialization, noise, missing structures, and/or differing point densities in each set, on several challenging 2D and 3D registration scenarios.
Segmentation involves separating an object from the background. In this work, we propose a novel segmentation method combining image information with prior shape knowledge, within the level-set framework. Following the work of Leventon et al., we revisit the use of principal component analysis (PCA) to introduce prior knowledge about shapes in a more robust manner. To this end, we utilize Kernel PCA and show that this method of learning shapes outperforms linear PCA, by allowing only shapes that are close enough to the training data. In the proposed segmentation algorithm, shape knowledge and image information are encoded into two energy functionals entirely described in terms of shapes. This consistent description allows to fully take advantage of the Kernel PCA methodology and leads to promising segmentation results. In particular, our shape-driven segmentation technique allows for the simultaneous encoding of multiple types of shapes, and offers a convincing level of robustness with respect to noise, clutter, partial occlusions, or smearing.
Abstract. In this work, we present an approach to jointly segment a rigid object in a 2D image and estimate its 3D pose, using the knowledge of a 3D model. We naturally couple the two processes together into a unique energy functional that is minimized through a variational approach. Our methodology differs from the standard monocular 3D pose estimation algorithms since it does not rely on local image features. Instead, we use global image statistics to drive the pose estimation process. This confers a satisfying level of robustness to noise and initialization for our algorithm, and bypasses the need to establish correspondences between image and object features. Moreover, our methodology possesses the typical qualities of region-based active contour techniques with shape priors, such as robustness to occlusions or missing information, without the need to evolve an infinite dimensional curve. Another novelty of the proposed contribution is to use a unique 3D model surface of the object, instead of learning a large collection of 2D shapes to accommodate for the diverse aspects that a 3D object can take when imaged by a camera. Experimental results on both synthetic and real images are provided, which highlight the robust performance of the technique on challenging tracking and segmentation applications. Motivation and Related Work2D image segmentation and 2D-3D pose estimation are ubiquitous tasks in computer vision applications and have received a great deal of attention in the past few years. These two fundamental techniques are usually studied separately in the literature. In this work, we combine both approaches in a variational framework. To appreciate the contribution of this work, we recall some of the results and specifics of both fields.2D-3D pose estimation aims at determining the pose of a 3D object relative to a calibrated camera from one unique or a collection of 2D images. By knowing the mapping between the world coordinates and image coordinates from the camera calibration matrix, and after establishing correspondences between 2D features in the image and their 3D counterparts on the model, it is then possible to solve the pose transformation (from a set of equations that express these correspondences). The literature concerned with 3D pose estimation is very large and a complete survey is beyond the scope of this paper. However, most methods can be distinguished by the type of local image features used to establish correspondences, such as points [1], lines or segments [2, 3], multi-part curve segments [4], or complete contours [5,6].Segmentation consists of separating an object from the background in an image. The geometric active contour (GAC) framework, in which a curve is evolved continuously to 2 Samuel Dambreville, Romeil Sandhu, Anthony Yezzi, and Allen Tannenbaum capture the boundaries of an object, has proven to be quite successful at performing this task. Originally, the method focused on extracting local image features such as edges to perform segmentation; see [7,8] and the references ...
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