Jean-Pierre Leduc

A new motion parameter estimation algorithm based on the continuous wavelet transform

This paper presents a novel motion parameter estimation (ME) algorithm based on the spatio-temporal continuous wavelet transform (CWT). The multidimensional nature of the CWT allows for the definition of a multitude of energy densities by integrating over a subset of the CWT parameter space. Three energy densities are used to estimate motion parameters by sequentially optimizing a state vector composed of velocity, position, and size parameters. This optimization is performed on a frame-by-frame basis allowing the algorithm to track moving objects. The ME algorithm is designed to address real world challenges encountered in the defense industry and traffic monitoring scenarios, such as attaining robust performance in noise and handling obscuration and crossing object trajectories.

Spatio-temporal wavelet transforms for digital signal analysis

The goal of this paper is to investigate spatio-temporal continuous wavelet transforms. A new wavelet family, called the Galilean wavelet, has been designed to tune to four main parameters, namely, scale, spatio-temporal position, spatial orientation, and velocity. The paper starts with the theory of motion-compensated wavelet filtering in the discrete realm of image processing. As a major difference from multi-dimensional homogeneous spaces, spatio-temporal signal involves motion that warps the signal along the trajectories. Modeling motion with 2-D affine transformations leads to spatio-temporal generalizations. Decomposition into elementary operators leads to developing transformation groups and exploiting the related representation theory. The construction of continuous spatio-temporal wavelets in Rn × R spaces is then handled with classical techniques of calculation. Close connections may then be established among all the spatio-temporal wavelet transforms through different sets of transformations. This approach generates a general framework for the study of future tools. Frames of wavelets are thereafter investigated to revisit discrete wavelet transforms in a more general way. Eventually, illustrations demonstrate the ability of Galilean wavelet transforms to analyze spatio-temporal signals.

Adaptive motion-compensated wavelet filtering for image sequence coding

This paper deals with new advances made in the field of discrete spatio-temporal filters applied to digital image sequences. Within time-varying images, the temporal correlation of the information is folded within the spatio-temporal domain by motions originating from both camera and object displacements. The spatio-temporal video information can be therefore reformulated in terms of motion trajectories and intensity variations along these trajectories. To yield that signal description, the spatio-temporal scenes will be segmented according to motion. Motion-compensated temporal filters have been used as convolutional filters applied along the assumed motion trajectories. Spectral interpretations show the efficiency of motion-compensated filtering for video signals. As a matter of fact, the whole signal analysis performed in this paper also includes a spatial filtering to achieve a complete spatio-temporal (2-D+T) decomposition. Motion-compensated filtering leads to multiresolution applications. It leads to optimum and adaptive signal-to-noise decomposition procedures based on the temporal correlative content. Such properties allow enhancing tasks like temporal interpolation, image sequence smoothing, and restoration. Simulation results are presented in this paper to illustrate the field of image sequence coding.

Spatio-temporal wavelet transforms for motion tracking

This paper addresses the problem of detecting and tracking moving objects in digital image sequences. The main goal is to detect and select mobile objects in a scene, construct the trajectories, and eventually reconstruct the target objects or their signatures. It is assumed that the image sequences are acquired from imaging sensors. The method is based on spatio-temporal continuous wavelet transforms, discretized for digital signal analysis. It turns out that the wavelet transform can be used efficiently in a Kalman filtering framework to perform detection and tracking. Several families of wavelets are considered for motion analysis according to the specific spatio-temporal transformation. Their construction is based on mechanical parameters describing uniform motion, translation, rotation, acceleration, and deformation. The main idea is that each kind of motion generates a specific signal transformation, which is analyzed by a suitable family of continuous wavelets. The analysis is therefore associated with a set of operators that describe the signal transformations at hand. These operators are then associated with a set of selectivity criteria. This leads to a set of filters that are tuned to the moving objects of interest.

Spatio-temporal continuous wavelet transforms for motion-based segmentation in real image sequences

The purpose of this paper is to develop a motion based segmentation for digital image sequences that is based on the continuous wavelet transform. The continuous wavelet transform allows estimating the motion parameters on all the moving discontinuities, edges and boundaries in the image sequence. This technique provides all the information of motion parameter estimates and edge locations at once without going back and forth refining the segmentation and the motion parameter estimation. Also, this is achieved without involving any point/block corresponding techniques in our algorithm. The edges and the motion parameter estimates are calculated locally on small windows or pixels in the image planes by maximizing the square of the modulus of the wavelet transform. A clustering procedure allows separating all the detected edges into clusters of homogeneous motion. Building a ridge skeleton on the reconstructed edges in each cluster provides the ultimate motion-based segments or partition. The algorithm was simulated using real traffic image sequences acquired by a mobile camera and proved to be accurate and robust.

Wavelet based analysis of rotational motion in digital image sequences

This paper addresses the problem of estimating, analyzing and tracking objects moving with spatio-temporal rotational motion (spin or orbit). It is assumed that the digital signals of interest are acquired from a camera and structured as digital image sequences. The trajectories in the signal are two-dimensional spatial projections in time of motion taking place in a three-dimensional space. The purpose of this work is to focus on the rotational motion, i.e. estimate the angular velocity. In natural scenes, rotational motion usually composes with translational or accelerated motion on a trajectory. This paper shows that trajectory parameters and rotational motion can be efficiently estimated and tracked either simultaneously or separately. The final goal of this work is to provide selective reconstructions of moving objects of interest. This paper constructs new continuous wavelet transforms that can be tuned to both translational and rotational motion. The parameters of analysis that are taken into account in these rotational wavelet transforms are space and time position, velocity, spatial scale, angular orientation and angular velocity. The continuous wavelet functions are finally discretized for signal processing. The link between rotational motion, symmetry and critical sampling is also presented. Applications are presented with tracking and estimation.

Analysis of deformational transformations with spatio-temporal continuous wavelet transforms

This paper deals with the estimation of deformational parameters in discrete spatio-temporal signals. The parameters of concern correspond to time-varying scales. As such they can be the coefficients of either a Taylor expansion of the scale or a given deformational transformation. At first sight there are just a few deformational transformations that provide continuous wavelet transforms. The approach presented in this paper associates deformational transformations to motion transformations taking place in higher dimensional spaces and projected on the sensor plane. Then finding continuous wavelet transforms becomes much easier since numerous continuous wavelet transforms have already been defined for motion analysis. It is also known that spatio-temporal continuous wavelet transforms provide minimum-mean-squared-error estimates of motion parameters. Any deformational transformation of features embedded in a spatio-temporal signal may always be related to the projection on the sensor plane of the motion of a rigid object taking place in a higher dimensional space. This reasoning applies conversely. The associated rigid motion may be actual or virtual may take place either on a flat space or on a curved space immersed in higher dimensions. Continuous wavelet transforms for the estimation of deformational parameters may be then deduced from those already existing in motion analysis.

SpatioTemporal Wavelets: A Group-Theoretic Construction for Motion Estimation and Tracking

This paper presents a new group-theoretic perspective for signal and image analysis. It addresses the problem of motion analysis and trajectory determination. The construction exploits the properties of motion parameters to be structured in Lie algebras and Lie groups. The motion models are provided by the group structure which carries an entire theoretical build-up. This theoretical construction is based on a natural association of Lie group representations, minimum-mean-squared-error estimations, and variational principles of optimality. These concepts naturally provide a corresponding association of tools based on continuous wavelet transforms, Kalman filters, and Lagrangians. These tools result in highly parallelizable algorithms based on FFTs, gradients, and dynamic programming. The core of the construction is made of spatiotemporal continuous wavelets that are tuned to the motion parameters to perform motion estimation. The motion parameters consist of scale, orientation, location, velocity, acceler...

Robust object tracking in compressed image sequences

Accurate object tracking is important in defense applications where an interceptor missile must hone into a target and track it through the pursuit until the strike occurs. The expense associated with an interceptor missile can be reduced through a distributed processing arrangement where the computing platform on which the tracking algorithm is run resides on the ground, and the interceptor need only carry the sensor and communications equipment as part of its electronics complement. In this arrangement, the sensor images are compressed, transmitted to the ground, and decompressed to facilitate real-time downloading of the data over available bandlimited channels. The tracking algorithm is run on a ground-based computer while tracking results are transmitted back to the interceptor as soon as they become available. Compression and transmission in this scenario introduce distortion. If severe, these distortions can lead to erroneous tracking results. As a consequence, tracking algorithms employed for this purpose must be robust to compression distortions. In this paper we introduced a robust object tracking algorithm based on the continuous wavelet transform. The algorithm processes image sequence data on a frame-by-frame basis, implicitly taking advantage of temporal history and spatial frame filtering to reduce the impact of compression artifacts. Test results show that tracking performance can be maintained at low transmission bit rates and can be used reliably in conjunction with many well-known image compression algorithms.

Spatiotemporal continuous wavelets applied to missile warhead detection and tracking

This paper addresses the problem of tracking a ballistic missile warhead. In this scenario, the ballistic missile is assumed to be fragmented into many pieces. The goal of the algorithm presented here is to track the warhead that is among the fragments. It is assumed that images are acquired from an optical sensor located in the interceptor nose cone. This imagery is used by the algorithm to steer the course of interception. The algorithm proposed in this paper is based on continuous spatio-temporal wavelet transforms (CWTs). Two different energy densities of the CWT are used to perform velocity detection and filtering. Additional post-processing is applied to discriminate among objects traveling at similar velocities. Particular attention is given to achieving robust performance on noisy sensor data and under conditions of temporary occlusions. First we introduce the spatio-temporal CWT and stress the relationships with classical orientation filters. Then we describe the CWT- based algorithm for target tracking, and present results on synthetically generated sequences.