Nudged Elastic Band in Topological Data Analysis

We use the nudged elastic band method from computational chemistry to analyze high-dimensional data. Our approach is inspired by Morse theory, and as output we produce an increasing sequence of small cell complexes modeling the dense regions of the data. We test the method on data sets arising in social networks and in image processing. Furthermore, we apply the method to identify new topological structure in a data set of optical flow patches

Motion estimation using optical flow field

Over the last decade, many low-level vision algorithms have been devised for extracting depth from intensity images. Most of them are based on motion of the rigid observer. Translation and rotation are constants with respect to space coordinates. When multi-objects move and/or the objects change shape, the algorithms cannot be used. In this dissertation, we develop a new robust framework for the determination of dense 3-D position and motion fields from a stereo image sequence. The framework is based on unified optical flow field (UOFF). In the UOFF approach, a four frame mode is used to compute six dense 3-D position and velocity fields. Their accuracy depends on the accuracy of optical flow field computation. The approach can estimate rigid and/or nonrigid motion as well as observer and/or object(s) motion. Here, a novel approach to optical flow field computation is developed. The approach is named as correlation-feedback approach. It has three different features from any other existing approaches. They are feedback, rubber window, and special refinement. With those three features, error is reduced, boundary is conserved, subpixel estimation accuracy is increased, and the system is robust. Convergence of the algorithm is proved in general. Since the UOFF is based on each pixel, it is sensitive to noise or uncertainty at each pixel. In order to improve its performance, we applied two Kalman filters. Our analysis indicates that different image areas need different convergence rates, for instance. the areas along boundaries have faster convergence rate than an interior area. The first Kalman filter is developed to conserve moving boundary in optical How determination by applying needed nonhomogeneous iterations. The second Kalman filter is devised to compute 3-D motion and structure based on a stereo image sequence. Since multi-object motion is allowed, newly visible areas may be exposed in images. How to detect and handle the newly visible areas is addressed. The system and measurement noise covariance matrices, Q and R, in the two Kalman filters are analyzed in detail. Numerous experiments demonstrate the efficiency of our approach

Intrinsic Dynamic Shape Prior for Fast, Sequential and Dense Non-Rigid Structure from Motion with Detection of Temporally-Disjoint Rigidity

While dense non-rigid structure from motion (NRSfM) has been extensively studied from the perspective of the reconstructability problem over the recent years, almost no attempts have been undertaken to bring it into the practical realm. The reasons for the slow dissemination are the severe ill-posedness, high sensitivity to motion and deformation cues and the difficulty to obtain reliable point tracks in the vast majority of practical scenarios. To fill this gap, we propose a hybrid approach that extracts prior shape knowledge from an input sequence with NRSfM and uses it as a dynamic shape prior for sequential surface recovery in scenarios with recurrence. Our Dynamic Shape Prior Reconstruction (DSPR) method can be combined with existing dense NRSfM techniques while its energy functional is optimised with stochastic gradient descent at real-time rates for new incoming point tracks. The proposed versatile framework with a new core NRSfM approach outperforms several other methods in the ability to handle inaccurate and noisy point tracks, provided we have access to a representative (in terms of the deformation variety) image sequence. Comprehensive experiments highlight convergence properties and the accuracy of DSPR under different disturbing effects. We also perform a joint study of tracking and reconstruction and show applications to shape compression and heart reconstruction under occlusions. We achieve state-of-the-art metrics (accuracy and compression ratios) in different scenarios

Video Interpolation using Optical Flow and Laplacian Smoothness

Non-rigid video interpolation is a common computer vision task. In this paper we present an optical flow approach which adopts a Laplacian Cotangent Mesh constraint to enhance the local smoothness. Similar to Li et al., our approach adopts a mesh to the image with a resolution up to one vertex per pixel and uses angle constraints to ensure sensible local deformations between image pairs. The Laplacian Mesh constraints are expressed wholly inside the optical flow optimization, and can be applied in a straightforward manner to a wide range of image tracking and registration problems. We evaluate our approach by testing on several benchmark datasets, including the Middlebury and Garg et al. datasets. In addition, we show application of our method for constructing 3D Morphable Facial Models from dynamic 3D data

Multi-Scale 3D Scene Flow from Binocular Stereo Sequences

Scene flow methods estimate the three-dimensional motion field for points in the world, using multi-camera video data. Such methods combine multi-view reconstruction with motion estimation. This paper describes an alternative formulation for dense scene flow estimation that provides reliable results using only two cameras by fusing stereo and optical flow estimation into a single coherent framework. Internally, the proposed algorithm generates probability distributions for optical flow and disparity. Taking into account the uncertainty in the intermediate stages allows for more reliable estimation of the 3D scene flow than previous methods allow. To handle the aperture problems inherent in the estimation of optical flow and disparity, a multi-scale method along with a novel region-based technique is used within a regularized solution. This combined approach both preserves discontinuities and prevents over-regularization – two problems commonly associated with the basic multi-scale approaches. Experiments with synthetic and real test data demonstrate the strength of the proposed approach.National Science Foundation (CNS-0202067, IIS-0208876); Office of Naval Research (N00014-03-1-0108

General Dynamic Scene Reconstruction from Multiple View Video

This paper introduces a general approach to dynamic scene reconstruction from multiple moving cameras without prior knowledge or limiting constraints on the scene structure, appearance, or illumination. Existing techniques for dynamic scene reconstruction from multiple wide-baseline camera views primarily focus on accurate reconstruction in controlled environments, where the cameras are fixed and calibrated and background is known. These approaches are not robust for general dynamic scenes captured with sparse moving cameras. Previous approaches for outdoor dynamic scene reconstruction assume prior knowledge of the static background appearance and structure. The primary contributions of this paper are twofold: an automatic method for initial coarse dynamic scene segmentation and reconstruction without prior knowledge of background appearance or structure; and a general robust approach for joint segmentation refinement and dense reconstruction of dynamic scenes from multiple wide-baseline static or moving cameras. Evaluation is performed on a variety of indoor and outdoor scenes with cluttered backgrounds and multiple dynamic non-rigid objects such as people. Comparison with state-of-the-art approaches demonstrates improved accuracy in both multiple view segmentation and dense reconstruction. The proposed approach also eliminates the requirement for prior knowledge of scene structure and appearance

Deep Optical Flow Estimation Via Multi-Scale Correspondence Structure Learning

As an important and challenging problem in computer vision, learning based optical flow estimation aims to discover the intrinsic correspondence structure between two adjacent video frames through statistical learning. Therefore, a key issue to solve in this area is how to effectively model the multi-scale correspondence structure properties in an adaptive end-to-end learning fashion. Motivated by this observation, we propose an end-to-end multi-scale correspondence structure learning (MSCSL) approach for optical flow estimation. In principle, the proposed MSCSL approach is capable of effectively capturing the multi-scale inter-image-correlation correspondence structures within a multi-level feature space from deep learning. Moreover, the proposed MSCSL approach builds a spatial Conv-GRU neural network model to adaptively model the intrinsic dependency relationships among these multi-scale correspondence structures. Finally, the above procedures for correspondence structure learning and multi-scale dependency modeling are implemented in a unified end-to-end deep learning framework. Experimental results on several benchmark datasets demonstrate the effectiveness of the proposed approach.Comment: 7 pages, 3 figures, 2 table