Optical Flow Constraint Research Articles

Estimation du champ de déplacement dense sur une séquence échocardiographique

Dense motion field estimation on a echocardiographic sequence. The estimation of the dense motion field is a first stage treatment often encountered in echocardiographic sequence diagnosis systems. Due to the low time sampling rate and the significant noise of such images, the usual methods based on the first order approximation of the optical flow constraint are inefficient. In this paper we propose a new method capable of dealing with these two problems by using the discrete form of this constraint. However, with this approach we are confronted with a non-convex minimization problem, dealt with by means of a continuation process. Finally, we present the results obtained on different echocardiographic sequences.

Mode based hierarchical optical flow estimation

In this paper, a robust estimation of the optical flow field that preserves the boundaries of the movement is shown. Arising from the techniques based on the Optical Flow Constraint (OFC), an estim...

ON THE STUDY OF VLSI DERIVATION FOR OPTICAL FLOW ESTIMATION

In this paper we propose studying several ways to implement a realistic and efficient VLSI design for a gradient-based dense motion estimator. The kind of estimator we focus on belongs to the class of differential methods. It is classically based on the optical flow constraint equation in association with a smoothness regularization term and also incorporates robust cost functions to alleviate the influence of large residuals. This estimator is expressed as the minimization of a global energy function defined within the framework of an incremental formulation associated with a multiresolution setup. In order to make possible the conception of efficient hardware, we consider a modified minimization strategy. This new minimization strategy is not only well suited to VLSI derivation, it is also very efficient in terms of quality of the result. The complete VLSI derivation is realized using high-level specifications.

Detection of obstacles on runways using ego-motion compensation and tracking of significant features

This paper describes a method for obstacle detection on a runway for autonomous navigation and landing of an aircraft, in presence of extraneous features, such as tire-marks. An obstacle is defined as an object, which has a significant motion or height relative to the runway. Suitable features are extracted from the image and warping is performed, using approximately known camera and plane parameters, to compensate the ego-motion as far as possible. Residual disparity after warping is estimated using an optical flow algorithm. Features are tracked from frame to frame to obtain more reliable estimates of their motion. The residual disparities are used to correct the motion parameters with a robust method, where features having large residual disparities are signaled as obstacles. Nelson's optical flow constraint is proposed to separate moving obstacles from stationary ones. A Bayesian framework is used at every stage so that the confidence in the estimates can be determined.

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 f...

Bandpass optical flow for tagged MRI.

MR tagging has shown great promise for detailed noninvasive cardiac motion imaging. Our research uses low-frequency tags coupled with gradient-based optical flow estimation to compute cardiac motion. We develop here a novel, fast, fully automated optical flow method for tagged MRI by exploiting the Fourier content of the tagged images. This new method, called bandpass optical flow, works by extracting various subband images from tagged cardiac data, and then formulating multiple optical flow constraints for each subband. The resulting system is solved by least squares pseudo-inversion. The proposed method is validated on simulated and real tagged data.

An Accurate and Fast Pattern Localization Algorithm for Automated Visual Inspection

Accurate and efficient localization of patterns from noisy images is very crucial in automated visual inspection. In this paper we present an accurate, efficient and robust algorithm for 2D pattern localization based on a modified optical flow constraint, which is derived from the first-order Taylor series approximation of the generalized brightness assumption. Our algorithm allows for large global illumination changes since this factor is explicitly modeled on the generalized brightness assumption. The proposed pattern localization algorithm is based on an energy minimization approach, with the energy function being defined as a weighted sum of the modified optical flow constraints at selected locations with reliable constraints. This location selection is facilitated by a reliability measure given in this paper. The energy minimization is accomplished via an efficient Newton-like iterative algorithm, which has been proved to be reliable for precise localization problems with a rough initial guess from our experiments. Experimental results on some real images and the corresponding simulated images are given to demonstrate the accuracy, efficiency and robustness of our algorithm.

Digital watermarking of MPEG-4 facial animation parameters

The enforcement of intellectual property rights is difficult for digital data. One possibility of supporting enforcement is the embedding of digital watermarks containing information about copyright owner and/or receiver of the data. Watermarking methods have already been presented for audio, images, video, and polygonal 3D models. In this paper, we present a method for digital watermarking of MPEG-4 facial animation parameter data sets. The watermarks are additively embedded into the parameter values and can be retrieved either from the watermarked parameters or from video sequences rendered using the watermarked animation parameters for head animation. For retrieval from rendered sequences, the facial animation parameters have to be estimated first. We use a model-based approach for the estimation of the facial parameters that combines a motion model of an explicit 3D textured wireframe with the optical flow constraint from the video data. This leads to a linear algorithm that is robustly solved in a hierarchical framework with low computational complexity. Experimental results confirm the applicability of the presented watermarking technique.

Dense estimation and object-based segmentation of the optical flow with robust techniques

In this paper, we address the issue of recovering and segmenting the apparent velocity field in sequences of images. As for motion estimation, we minimize an objective function involving two robust terms. The first one cautiously captures the optical flow constraint, while the second (a priori) term incorporates a discontinuity-preserving smoothness constraint. To cope with the nonconvex minimization problem thus defined, we design an efficient deterministic multigrid procedure. It converges fast toward estimates of good quality, while revealing the large discontinuity structures of flow fields. We then propose an extension of the model by attaching to it a flexible object-based segmentation device based on deformable closed curves (different families of curve equipped with different kinds of prior can be easily supported). Experimental results on synthetic and natural sequences are presented, including an analysis of sensitivity to parameter tuning.

Estimation of three-dimensional cardiac velocity fields: assessment of a differential method and application to three-dimensional CT data

We have investigated an optical flow method for the estimation of the three-dimensional endocardial wall motion from high-resolution X-ray CT data. This method was originally proposed by Song and Leahy. It is based on the optical flow, the divergence-free and the smoothness constraints. Due to the characteristics of the imaging modality, we studied the restriction of this approach to the boundary of the left ventricular (LV) cavity. The behaviour of the method is quantified through simulations approximating the overall motion of the LV cavity through an affine transform involving a dilation and a rotation. The method implies the choice of three parameters weighting the constraints. The results show a weak dependence of the velocity field on the weighting of the optical flow constraint. The accuracy of the method relies more heavily on the relative weighting of the smoothness and divergence-free constraints. In our experiments, the best results were obtained for a largely predominant divergence-free constraint. The results also show that the accuracy of the method is reasonable for low values of the rotation angle (minimum mean error of 1.1 voxel for 5°). This is compatible with values reported in other studies for the overall rotation of the LV. We provide a qualitative description of the results obtained in vivo on a canine heart by visualizing the distribution of the estimated velocity vector magnitudes over the endocardial surface. These results (evolution of the field over time, maximum velocities) are in agreement with the known physiological behaviour of the heart.

Optical flow computation using extended constraints

Several approaches for optical flow estimation use partial differential equations to model changes in image brightness throughout time. A commonly used equation is the so-called optical flow constraint (OFC), which assumes that the image brightness is stationary with respect to time. More recently, a different constraint referred to as the extended optical flow constraint (EOFC) has been introduced, which also contains the divergence of the flow field of image brightness. There is no agreement in the literature about which of these constraints provides the best estimation of the velocity field. Two new solutions for optical flow computation are proposed, which are based on an approximation of the constraint equations. The two techniques have been used with both EOFC and OFC constraint equations. Results achieved by using these solutions have been compared with several well-known computational methods for optical flow estimation in different motion conditions. Estimation errors have also been measured and compared for different types of motion.

Optical flow estimation and the interaction between measurement errors at adjacent pixel positions

In order to estimate both components of optical flow as well as their first spatio-temporal derivatives, it is postulated that the Optical Flow Constraint Equation (OFCE) is valid in a spatio-temporal neighborhood of pixels. So far, it has been tacitly assumed that the partial derivatives of the gray value distribution—which are required for this approach at the pixel positions involved—are independent from each other. It is shown how dropping this assumption affects the estimation procedure, based on well established approaches of estimation theory. The insight gained thereby is used to develop an approach towards merging image regions based on the compatibility of optical flow estimates obtained within the regions considered for merger.

Analysis of optical flow constraints

Different constraint equations have been proposed in the literature for the derivation of optical flow. Despite of the large number of papers dealing with computational techniques to estimate optical flow, only a few authors have investigated conditions under which these constraints exactly model the velocity field, that is, the perspective projection on the image plane of the true 3-D velocity. These conditions are analyzed under different hypotheses, and the departures of the constraint equations in modeling the velocity field are derived for different motion conditions. Experiments are also presented giving measures of these departures and of the induced errors in the estimation of the velocity field.

Motion estimation methods and noisy phenomena

In an infrared surveillance system (which must detect remote sources and thus has a very low resolution) in an aerospace environment, the estimation of the cloudy sky velocity should lower the false alarm rate in discriminating the motion between various moving shapes by means of a background velocity map. The optical flow constraint equation, based on a Taylor expansion of the intensity function, is often used to estimate the motion for each pixel. One of the main problems in motion estimation is that, for one pixel, the real velocity cannot be found because of the aperture problem. Another kinematic estimation method is based on a matched filter [generalized Hough transform (GHT)]: it gives a global velocity estimation for a set of pixels. On the one hand we obtain a local velocity estimation for each pixel with little credibility because the optical flow is so sensitivity to noise; on the other hand, we obtain a robust global kinematic estimation, the same for all selected pixels. This paper aims to adapt and improve the GHT in our typical application in which one must discern the global movement of objects (clouds), whatever their form may be (clouds with hazy edges or distorted shapes or even clouds that have very little structure). We propose an improvement of the GHT algorithm by segmentation images with polar constraints on spatial gradients. One pixel, at timet, is matched with another one at timet + ΔT, only if the direction and modulus of the gradient are similar. This technique, which is very efficient, sharpens the peak and improves the motion resolution. Each of these estimations is calculated within windows belonging to the image, these windows being selected by means of an entropy criterion. The kinematic vector is computed accurately by means of the optical flow constraint equation applied on the displaced window. We showed that, for small displacements, the optical flow constraint equation sharpens the results of the GHT. Thus a semi-dense velocity field is obtained for cloud edges. A velocity map computed on real sequences with these methods is shown. In this way, a kinematic parameter discriminates between a target and the cloudy background.

Optical flow from constraint lines parametrization

Optical flow is a measure of the change of image brightness in a frame sequence and is commonly used as an approximation of the velocity field, which is the perspective projection of the three-dimensional (3D) real velocity on the image plane. One method for evaluating optical flow is based on the Optical Flow Constraint (OFC) equation. Such an equation is associated with each image pixel. Under the assumption that in the immediate neighbourhood of a pixel the optical flow field is smooth, the constraint equations in that neighbourhood should have a common solution. Least-squares techniques are commonly used to derive the solution, which typically is very sensitive to discontinuities. A new method of evaluating the optical flow from the OFC equation is presented, which performs well in the presence of discontinuities. The method proposes to accumulate evidence from the solution of all pairs of constraints in each image segment to provide the most probable value for optical flow, rather than adopting least-squares techniques. The proposed accumulation of evidence is performed using a variant of the Hough transform, the Combinatorial Hough transform. Experimental results under different types of motion are presented. An efficient implementation of the algorithm is discussed on a highly parallel architecture.

The estimation of velocity vector fields from time-varying image sequences

Changes in successive images from a time-varying image sequence of a scene can be characterized by velocity vector fields. The estimate of the velocity vector field is determined as a compromise between optical flow and directional smoothness constraints. The optical flow constraints relate the values of the time-varying image function at the corresponding points of the successive images of the sequence. The directional smoothness constraints relate the values of neighboring velocity vectors. To achieve the compromise, we introduce a system of nonlinear equations of the unknown estimate of the velocity vector field using a novel variational principle applied to the weighted average of the optical flow and the directional smoothness constraints. A stable iterative method for solving this system is developed. The optical flow and the directional smoothness constraints are selectively suppressed in the neighborhoods of the occluding boundaries by implicitly adjusting their weights. These adjustments are based on the spatial variations of the estimates of the velocity vectors and the spatial variations of the time-varying image function. The system of nonlinear equations is defined in terms of the time-varying image function and its derivatives. The initial image functions are in general discontinuous and cannot be directly differentiated. These difficulties are overcome by treating the initial image functions as generalized functions and their derivatives as generalized derivatives. These generalized functions are evaluated (observed) on the parametric family of testing (smoothing) functions to obtain parametric families of secondary images, which are used in the system of nonlinear equations. The parameter specifies the degree of smoothness of each secondary image. The secondary images with progressively higher degrees of smoothness are sampled with progressively lower resolutions. Then coarse-to-fine control strategies are used to obtain the estimate.

Review of motion analysis techniques

Motion analysis is an important component of computer vision, dealing with the measurement of motion information from a time varying image sequence. The analysis of dynamic image sequences finds a wide range of applications, including robot navigation, target tracking, traffic monitoring, motion of biological cells, cloud and weather systems tracking, image coding, etc. The paper reviews the various techniques used in motion analysis from image sequences. The approaches are classified according to the methodology in two main groups: methods based on the optical flow constraint equation, and matching. The advantages and disadvantages of both methodologies are also discussed.