Dynamic occlusion analysis in optical flow fields

Optical flow can be used to locate dynamic occlusion boundaries in an image sequence. We derive an edge detection algorithm sensitive to changes in flow fields likely to be associated with occlusion. The algorithm is patterned after the Marr-Hildreth zero-crossing detectors currently used to locate boundaries in scalar fields. Zero-crossing detectors are extended to identify changes in direction and/or magnitude in a vector-valued flow field. As a result, the detector works for flow boundaries generated due to the relative motion of two overlapping surfaces, as well as the simpler case of motion parallax due to a sensor moving through an otherwise stationary environment. We then show how the approach can be extended to identify which side of a dynamic occlusion boundary corresponds to the occluding surface. The fundamental principal involved is that at an occlusion boundary, the image of the surface boundary moves with the image of the occluding surface. Such information is important in interpreting dynamic scenes. Results are demonstrated on optical flow fields automatically computed from real image sequences.     

On robust optical flow estimation on image sequences with differently exposed frames using primal–dual optimization

Optical flow methods are used to estimate pixelwise motion information based on consecutive frames in image sequences. The image sequences traditionally contain frames that are similarly exposed. However, many real-world scenes contain high dynamic range content that cannot be captured well with a single exposure setting. Such scenes result in certain image regions being over- or underexposed, which can negatively impact the quality of motion estimates in those regions. Motivated by this, we propose to capture high dynamic range scenes using different exposure settings every other frame. A framework for OF estimation on such image sequences is presented, that can straightforwardly integrate techniques from the state-of-the-art in conventional OF methods. Different aspects of robustness of OF methods are discussed, including estimation of large displacements and robustness to natural illumination changes that occur between the frames, and we demonstrate experimentally how to handle such challenging flow estimation scenarios. The flow estimation is formulated as an optimization problem whose solution is obtained using an efficient primal–dual method.     

Volumetric Deformation Analysis Using Mechanics-Based Data Fusion: Applications in Cardiac Motion Recovery

Non-rigid motion estimation from image sequences is essential in analyzing and understanding the dynamic behavior of physical objects. One important example is the dense field motion analysis of the cardiac wall, which could potentially help to better understand the physiological processes associated with heart disease and to provide improvement in patient diagnosis and treatment. In this paper, we present a new method of estimating volumetric deformation by integrating intrinsic instantaneous velocity data with geometrical token displacement information, based upon continuum mechanics principles. This object-dependent approach allows the incorporation of physically meaningful constraints into the ill-posed motion recovery problem, and the integration of the two disparate but complementary data sources overcomes some of the limitations of the single-image-source-based motion estimation approaches.     

Accurate optical flow computation under non-uniform brightness variations

In this paper, we present a very accurate algorithm for computing optical flow with non-uniform brightness variations. The proposed algorithm is based on a generalized dynamic image model (GDIM) in conjunction with a regularization framework to cope with the problem of non-uniform brightness variations. To alleviate flow constraint errors due to image aliasing and noise, we employ a reweighted least-squares method to suppress unreliable flow constraints, thus leading to robust estimation of optical flow. In addition, a dynamic smoothness adjustment scheme is proposed to efficiently suppress the smoothness constraint in the vicinity of the motion and brightness variation discontinuities, thereby preserving motion boundaries. We also employ a constraint refinement scheme, which aims at reducing the approximation errors in the first-order differential flow equation, to refine the optical flow estimation especially for large image motions. To efficiently minimize the resulting energy function for optical flow computation, we utilize an incomplete Cholesky preconditioned conjugate gradient algorithm to solve the large linear system. Experimental results on some synthetic and real image sequences show that the proposed algorithm compares favorably to most existing techniques reported in literature in terms of accuracy in optical flow computation with 100% density.     

Multi-body Factorization with Uncertainty: Revisiting Motion Consistency

Dynamic analysis of video sequences often relies on the segmentation of the sequence into regions of consistent motions. Approaching this problem requires a definition of which motions are regarded as consistent. Common approaches to motion segmentation usually group together points or image regions that have the same motion between successive frames (where the same motion can be 2D, 3D, or non-rigid). In this paper we define a new type of motion consistency, which is based on temporal consistency of behaviors across multiple frames in the video sequence. Our definition of consistent “temporal behavior” is expressed in terms of multi-frame linear subspace constraints. This definition applies to 2D, 3D, and some non-rigid motions without requiring prior model selection. We further show that our definition of motion consistency extends to data with directional uncertainty, thus leading to a dense segmentation of the entire image. Such segmentation is obtained by applying the new motion consistency constraints directly to covariance-weighted image brightness measurements. This is done without requiring prior correspondence estimation nor feature tracking.     

Exploiting Discontinuities in Optical Flow

Most optical flow estimation techniques have substantial difficulties dealing with flow discontinuities. Methods which simultaneously detect flow boundaries and use the detected boundaries to aid in flow estimation can produce significantly improved results. Current approaches to implementing these methods still have important limitations, however. We demonstrate three such problems: errors due to the mixture of image properties across boundaries, an intrinsic ambiguity in boundary location when only short sequences are considered, and difficulties insuring that the motion of a boundary aids in flow estimation for the surface to which it is attached without corrupting the flow estimates for the occluded surface on the other side. The first problem can be fixed by basing flow estimation only on image changes at edges. The second requires an analysis of longer time intervals. The third can be aided by using a boundary detection mechanism which classifies the sides of boundaries as occluding and occluded at the same time as the boundaries are detected.     

Motion estimation and segmentation

In the general structure-from-motion (SFM) problem involving several moving objects in a scene, the essential first step is to segment moving objects independently. We attempt to deal with the problem of optical flow estimation and motion segmentation over a pair of images. We apply a mean field technique to determine optical flow and motion boundaries and present a deterministic algorithm. Since motion discontinuities represented by line process are embedded in the estimation of the optical flow, our algorithm provides accurate estimates of optical flow especially along motion boundaries and handles occlusion and multiple motions. We show that the proposed algorithm outperforms other well-known algorithms in terms of estimation accuracy and timing.     

On the Geometry of Visual Correspondence

Image displacement fields—optical flow fields, stereo disparity fields, normal flow fields—due to rigid motion possess a global geometric structure which is independent of the scene in view. Motion vectors of certain lengths and directions are constrained to lie on the imaging surface at particular loci whose location and form depends solely on the 3D motion parameters. If optical flow fields or stereo disparity fields are considered, then equal vectors are shown to lie on conic sections. Similarly, for normal motion fields, equal vectors lie within regions whose boundaries also constitute conics. By studying various properties of these curves and regions and their relationships, a characterization of the structure of rigid motion fields is given. The goal of this paper is to introduce a concept underlying the global structure of image displacement fields. This concept gives rise to various constraints that could form the basis of algorithms for the recovery of visual information from multiple views.     

On 3-D scene flow and structure recovery from multiview image sequences

Two novel systems computing dense three-dimensional (3-D) scene flow and structure from multiview image sequences are described in this paper. We do not assume rigidity of the scene motion, thus allowing for nonrigid motion in the scene. The first system, integrated model-based system (IMS), assumes that each small local image region is undergoing 3-D affine motion. Non-linear motion model fitting based on both optical flow constraints and stereo constraints is then carried out on each local region in order to simultaneously estimate 3-D motion correspondences and structure. The second system is based on extended gradient-based system (EGS), a natural extension of two-dimensional (2-D) optical flow computation. In this method, a new hierarchical rule-based stereo matching algorithm is first developed to estimate the initial disparity map. Different available constraints under a multiview camera setup are further investigated and utilized in the proposed motion estimation. We use image segmentation information to adopt and maintain the motion and depth discontinuities. Within the framework for EGS, we present two different formulations for 3-D scene flow and structure computation. One formulation assumes that initial disparity map is accurate, while the other does not. Experimental results on both synthetic and real imagery demonstrate the effectiveness of our 3-D motion and structure recovery schemes. Empirical comparison between IMS and EGS is also reported.     

Structure from Motion: Beyond the Epipolar Constraint

The classic approach to structure from motion entails a clear separation between motion estimation and structure estimation and between two-dimensional (2D) and three-dimensional (3D) information. For the recovery of the rigid transformation between different views only 2D image measurements are used. To have available enough information, most existing techniques are based on the intermediate computation of optical flow which, however, poses a problem at the locations of depth discontinuities. If we knew where depth discontinuities were, we could (using a multitude of approaches based on smoothness constraints) accurately estimate flow values for image patches corresponding to smooth scene patches; but to know the discontinuities requires solving the structure from motion problem first. This paper introduces a novel approach to structure from motion which addresses the processes of smoothing, 3D motion and structure estimation in a synergistic manner. It provides an algorithm for estimating the transformation between two views obtained by either a calibrated or uncalibrated camera. The results of the estimation are then utilized to perform a reconstruction of the scene from a short sequence of images.The technique is based on constraints on image derivatives which involve the 3D motion and shape of the scene, leading to a geometric and statistical estimation problem. The interaction between 3D motion and shape allows us to estimate the 3D motion while at the same time segmenting the scene. If we use a wrong 3D motion estimate to compute depth, we obtain a distorted version of the depth function. The distortion, however, is such that the worse the motion estimate, the more likely we are to obtain depth estimates that vary locally more than the correct ones. Since local variability of depth is due either to the existence of a discontinuity or to a wrong 3D motion estimate, being able to differentiate between these two cases provides the correct motion, which yields the least varying estimated depth as well as the image locations of scene discontinuities. We analyze the new constraints, show their relationship to the minimization of the epipolar constraint, and present experimental results using real image sequences that indicate the robustness of the method.     

Dense estimation of fluid flows

In this paper, we address the problem of estimating and analyzing the motion of fluids in image sequences. Due to the great deal of spatial and temporal distortions that intensity patterns exhibit in images of fluids, the standard techniques from computer vision, originally designed for quasi-rigid motions with stable salient features, are not well adapted in this context. We thus investigate a dedicated minimization-based motion estimator. The cost function to be minimized includes a novel data term relying on an integrated version of the continuity equation of fluid mechanics, which is compatible with large displacements. This term is associated with an original second-order div-curl regularization which prevents the washing out of the salient vorticity and divergence structures. The performance of the resulting fluid flow estimator is demonstrated on meteorological satellite images. In addition, we show how the sequences of dense motion fields we estimate can be reliably used to reconstruct trajectories and to extract the regions of high vorticity and divergence     

Optical flow approximation based motion object extraction for MPEG-2 video stream

This paper presents a compressed-domain motion object extraction algorithm based on optical flow approximation for MPEG-2 video stream. The discrete cosine transform (DCT) coefficients of P and B frames are estimated to reconstruct DC + 2AC image using their motion vectors and the DCT coefficients in I frames, which can be directly extracted from MPEG-2 compressed domain. Initial optical flow is estimated with Black’s optical flow estimation framework, in which DC image is substituted by DC + 2AC image to provide more intensity information. A high confidence measure is exploited to generate dense and accurate motion vector field by removing noisy and false motion vectors. Global motion estimation and iterative rejection are further utilized to separate foreground and background motion vectors. Region growing with automatic seed selection is performed to extract accurate object boundary by motion consistency model. The object boundary is further refined by partially decoding the boundary blocks to improve the accuracy. Experimental results on several test sequences demonstrate that the proposed approach can achieve compressed-domain video object extraction for MPEG-2 video stream in CIF format with real-time performance.     

Moving object detection using region tracking

For many vision-based systems, it is important to detect a moving object automatically. The region-based motion estimation method is popular for automatic moving object detection. The region-based method has several advantages in that it is robust to noise and variations in illumination. However, there is a critical problem in that there exists an occlusion problem which is caused by the movement of the object. The occlusion problem results in an incorrect motion estimation and faulty detection of moving objects. When there are occlusion regions, the motion vector is not correctly estimated. That is, a stationary background in the occluded region can be classified as a moving object.In order to overcome this occlusion problem, a new occlusion detection algorithm is proposed. The proposed occlusion detection algorithm is motivated by the assumption that the distribution of the error histogram of the occlusion region is different from that of the nonocclusion region. The proposed algorithm uses the mean and variance values to decide whether an occlusion has occurred in the region. Therefore, the proposed occlusion detection and motion estimation scheme detects the moving regions and estimates the new motion vector, while avoiding misdetection caused by the occlusion problem. The experimental results for several video sequences demonstrate the robustness of the proposed approach to the occlusion problem.This work was presented in part at the 8th International Symposium on Artificial Life and Robotics, Oita, Japan, January 24–26, 2003     

Stereoscopic Scene Flow Computation for 3D Motion Understanding

Building upon recent developments in optical flow and stereo matching estimation, we propose a variational framework for the estimation of stereoscopic scene flow, i.e., the motion of points in the three-dimensional world from stereo image sequences. The proposed algorithm takes into account image pairs from two consecutive times and computes both depth and a 3D motion vector associated with each point in the image. In contrast to previous works, we partially decouple the depth estimation from the motion estimation, which has many practical advantages. The variational formulation is quite flexible and can handle both sparse or dense disparity maps. The proposed method is very efficient; with the depth map being computed on an FPGA, and the scene flow computed on the GPU, the proposed algorithm runs at frame rates of 20 frames per second on QVGA images (320×240 pixels). Furthermore, we present solutions to two important problems in scene flow estimation: violations of intensity consistency between input images, and the uncertainty measures for the scene flow result.     

Learned Models for Estimation of Rigid and Articulated Human Motion from Stationary or Moving Camera

We propose an approach for modeling, measurement and tracking of rigid and articulated motion as viewed from a stationary or moving camera. We first propose an approach for learning temporal-flow models from exemplar image sequences. The temporal-flow models are represented as a set of orthogonal temporal-flow bases that are learned using principal component analysis of instantaneous flow measurements. Spatial constraints on the temporal-flow are then incorporated to model the movement of regions of rigid or articulated objects. These spatio-temporal flow models are subsequently used as the basis for simultaneous measurement and tracking of brightness motion in image sequences. Then we address the problem of estimating composite independent object and camera image motions. We employ the spatio-temporal flow models learned through observing typical movements of the object from a stationary camera to decompose image motion into independent object and camera motions. The performance of the algorithms is demonstrated on several long image sequences of rigid and articulated bodies in motion.     

Optical Flow Constraints on Deformable Models with Applications to Face Tracking

Optical flow provides a constraint on the motion of a deformable model. We derive and solve a dynamic system incorporating flow as a hard constraint, producing a model-based least-squares optical flow solution. Our solution also ensures the constraint remains satisfied when combined with edge information, which helps combat tracking error accumulation. Constraint enforcement can be relaxed using a Kalman filter, which permits controlled constraint violations based on the noise present in the optical flow information, and enables optical flow and edge information to be combined more robustly and efficiently. We apply this framework to the estimation of face shape and motion using a 3D deformable face model. This model uses a small number of parameters to describe a rich variety of face shapes and facial expressions. We present experiments in extracting the shape and motion of a face from image sequences which validate the accuracy of the method. They also demonstrate that our treatment of optical flow as a hard constraint, as well as our use of a Kalman filter to reconcile these constraints with the uncertainty in the optical flow, are vital for improving the performance of our system.     

Motion Competition: A Variational Approach to Piecewise Parametric Motion Segmentation

We present a novel variational approach for segmenting the image plane into a set of regions of parametric motion on the basis of two consecutive frames from an image sequence. Our model is based on a conditional probability for the spatio-temporal image gradient, given a particular velocity model, and on a geometric prior on the estimated motion field favoring motion boundaries of minimal length.Exploiting the Bayesian framework, we derive a cost functional which depends on parametric motion models for each of a set of regions and on the boundary separating these regions. The resulting functional can be interpreted as an extension of the Mumford-Shah functional from intensity segmentation to motion segmentation. In contrast to most alternative approaches, the problems of segmentation and motion estimation are jointly solved by continuous minimization of a single functional. Minimizing this functional with respect to its dynamic variables results in an eigenvalue problem for the motion parameters and in a gradient descent evolution for the motion discontinuity set.We propose two different representations of this motion boundary: an explicit spline-based implementation which can be applied to the motion-based tracking of a single moving object, and an implicit multiphase level set implementation which allows for the segmentation of an arbitrary number of multiply connected moving objects.Numerical results both for simulated ground truth experiments and for real-world sequences demonstrate the capacity of our approach to segment objects based exclusively on their relative motion.     

Piecewise-Smooth Dense Optical Flow via Level Sets

We propose a new algorithm for dense optical flow computation. Dense optical flow schemes are challenged by the presence of motion discontinuities. In state of the art optical flow methods, over-smoothing of flow discontinuities accounts for most of the error. A breakthrough in the performance of optical flow computation has recently been achieved by Brox et~al. Our algorithm embeds their functional within a two phase active contour segmentation framework. Piecewise-smooth flow fields are accommodated and flow boundaries are crisp. Experimental results show the superiority of our algorithm with respect to alternative techniques. We also study a special case of optical flow computation, in which the camera is static. In this case we utilize a known background image to separate the moving elements in the sequence from the static elements. Tests with challenging real world sequences demonstrate the performance gains made possible by incorporating the static camera assumption in our algorithm.     

Regularization of optical flow with M-band wavelet transform

The optical flow is an important tool for problems arising in the analysis of image sequences. Flow fields generated by various existing solving techniques are often noisy and partially incorrect, especially near occlusions or motion boundaries. Therefore, the additional information on the scene gained from a sequence of images is usually worse. In this paper, discrete wavelet transform has been adopted in order to enhance the reliability of optical flow estimation. A generalization of the well-known dyadic orthonormal wavelets to the case of the dilation scale factor M > 2 with N vanishing moments has been used, and it has proved to be a useful regularizing tool. The advantages in the computations have been shown by experimental results performed on real image sequences.