Multiscale optical flow computation from the monogenic signal

National audienceWe have developed an algorithm for the estimation of cardiac motion from medical images. The algorithm exploits monogenic signal theory, recently introduced as an N-dimensional generalization of the analytic signal. The displacement is computed locally by assuming the conservation of the monogenic phase over time. A local affine displacement model replaces the standard translation model to account for more complex motions as contraction/expansion and shear. A coarse-to-fine B-spline scheme allows a robust and effective computation of the models parameters and a pyramidal refinement scheme helps handle large motions. Robustness against noise is increased by replacing the standard pointwise computation of the monogenic orientation with a more robust least-squares orientation estimate. This paper reviews the results obtained on simulated cardiac images from different modalities, namely 2D and 3D cardiac ultrasound and tagged magnetic resonance. We also show how the proposed algorithm represents a valuable alternative to state-of-the-art algorithms in the respective fields

04251 -- Imaging Beyond the Pinhole Camera

From 13.06.04 to 18.06.04, the Dagstuhl Seminar 04251 ``Imaging Beyond the Pin-hole Camera. 12th Seminar on Theoretical Foundations of Computer Vision\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

A Panorama on Multiscale Geometric Representations, Intertwining Spatial, Directional and Frequency Selectivity

The richness of natural images makes the quest for optimal representations in image processing and computer vision challenging. The latter observation has not prevented the design of image representations, which trade off between efficiency and complexity, while achieving accurate rendering of smooth regions as well as reproducing faithful contours and textures. The most recent ones, proposed in the past decade, share an hybrid heritage highlighting the multiscale and oriented nature of edges and patterns in images. This paper presents a panorama of the aforementioned literature on decompositions in multiscale, multi-orientation bases or dictionaries. They typically exhibit redundancy to improve sparsity in the transformed domain and sometimes its invariance with respect to simple geometric deformations (translation, rotation). Oriented multiscale dictionaries extend traditional wavelet processing and may offer rotation invariance. Highly redundant dictionaries require specific algorithms to simplify the search for an efficient (sparse) representation. We also discuss the extension of multiscale geometric decompositions to non-Euclidean domains such as the sphere or arbitrary meshed surfaces. The etymology of panorama suggests an overview, based on a choice of partially overlapping "pictures". We hope that this paper will contribute to the appreciation and apprehension of a stream of current research directions in image understanding.Comment: 65 pages, 33 figures, 303 reference

Velocity field computation in vibrated granular media using an optical flow based multiscale image analysis method

International audienceAn image analysis method has been developed in order to compute the velocity field of a granular medium (sand grains, mean diameter 600 µm) submitted to different kinds of mechanical stresses. The differential method based on optical flow conservation consists in describing a dense motion field with vectors associated to each pixel. A multiscale, coarse-to-fine, analytical approach through tailor sized windows yields the best compromise between accuracy and robustness of the results, while enabling an acceptable computation time. The corresponding algorithmis presented and its validation discussed through different tests. The results of the validation tests of the proposed approach show that the method is satisfactory when attributing specific values to parameters in association with the size of the image analysis window. An application in the case of vibrated sand has been studied. An instrumented laboratory device provides sinusoidal vibrations and enables external optical observations of sand motion in 3D transparent boxes. At 50 Hz, by increasing the relative acceleration , the onset and development of two convective rolls can be observed. An ultra fast camera records the grain avalanches, and several pairs of images are analysed by the proposed method. The vertical velocity profiles are deduced and allow to precisely quantify the dimensions of the fluidized region as a function of

Dynamic Multivariate Simplex Splines For Volume Representation And Modeling

Volume representation and modeling of heterogeneous objects acquired from real world are very challenging research tasks and playing fundamental roles in many potential applications, e.g., volume reconstruction, volume simulation and volume registration. In order to accurately and efficiently represent and model the real-world objects, this dissertation proposes an integrated computational framework based on dynamic multivariate simplex splines (DMSS) that can greatly improve the accuracy and efficacy of modeling and simulation of heterogenous objects. The framework can not only reconstruct with high accuracy geometric, material, and other quantities associated with heterogeneous real-world models, but also simulate the complicated dynamics precisely by tightly coupling these physical properties into simulation. The integration of geometric modeling and material modeling is the key to the success of representation and modeling of real-world objects. The proposed framework has been successfully applied to multiple research areas, such as volume reconstruction and visualization, nonrigid volume registration, and physically based modeling and simulation

Smooth representation of thin shells and volume structures for isogeometric analysis

The purpose of this study is to develop self-contained methods for obtaining smooth meshes which are compatible with isogeometric analysis (IGA). The study contains three main parts. We start by developing a better understanding of shapes and splines through the study of an image-related problem. Then we proceed towards obtaining smooth volumetric meshes of the given voxel-based images. Finally, we treat the smoothness issue on the multi-patch domains with C1 coupling. Following are the highlights of each part. First, we present a B-spline convolution method for boundary representation of voxel-based images. We adopt the filtering technique to compute the B-spline coefficients and gradients of the images effectively. We then implement the B-spline convolution for developing a non-rigid images registration method. The proposed method is in some sense of “isoparametric”, for which all the computation is done within the B-splines framework. Particularly, updating the images by using B-spline composition promote smooth transformation map between the images. We show the possible medical applications of our method by applying it for registration of brain images. Secondly, we develop a self-contained volumetric parametrization method based on the B-splines boundary representation. We aim to convert a given voxel-based data to a matching C1 representation with hierarchical cubic splines. The concept of the osculating circle is employed to enhance the geometric approximation, where it is done by a single template and linear transformations (scaling, translations, and rotations) without the need for solving an optimization problem. Moreover, we use the Laplacian smoothing and refinement techniques to avoid irregular meshes and to improve mesh quality. We show with several examples that the method is capable of handling complex 2D and 3D configurations. In particular, we parametrize the 3D Stanford bunny which contains irregular shapes and voids. Finally, we propose the B´ezier ordinates approach and splines approach for C1 coupling. In the first approach, the new basis functions are defined in terms of the B´ezier Bernstein polynomials. For the second approach, the new basis is defined as a linear combination of C0 basis functions. The methods are not limited to planar or bilinear mappings. They allow the modeling of solutions to fourth order partial differential equations (PDEs) on complex geometric domains, provided that the given patches are G1 continuous. Both methods have their advantages. In particular, the B´ezier approach offer more degree of freedoms, while the spline approach is more computationally efficient. In addition, we proposed partial degree elevation to overcome the C1-locking issue caused by the over constraining of the solution space. We demonstrate the potential of the resulting C1 basis functions for application in IGA which involve fourth order PDEs such as those appearing in Kirchhoff-Love shell models, Cahn-Hilliard phase field application, and biharmonic problems

Motion representation using composite energy features

This work tackles the segmentation of apparent-motion from a bottom-up perspective. When no information is available to build prior high-level models, the only alternative are bottom-up techniques. Hence, the whole segmentation process relies on the suitability of the low-level features selected to describe motion. A wide variety of low-level spatio-temporal features have been proposed so far. However, all of them suffer from diverse drawbacks. Here, we propose the use of composite energy features in bottom-up motion segmentation to solve several of these problems. Composite energy features are clusters of energy filters—pairs of band-pass filters in quadrature—each one sensitive to a different set of scale, orientation, direction of motion and speed. They are grouped in order to reconstruct independent motion patterns in a video sequence. A composite energy feature, this is, the response of one of these clusters of filters, can be built as a combination of the responses of the individual filters. Therefore, it inherits the desirable properties of energy filters but providing a more complete representation of motion patterns. In this paper, we will present our approach for integration of composite features based on the concept of Phase Congruence. We will show some results that illustrate the capabilities of this low-level motion representation and its usefulness in bottom-up motion segmentation and tracking.This work has been financially supported by the Ministry of Education and Science of the Spanish Government, through the Research Project TIN2006-08447.S

Riesz pyramids for fast phase-based video magnification

We present a new compact image pyramid representation, the Riesz pyramid, that can be used for real-time phase-based motion magnification. Our new representation is less overcomplete than even the smallest two orientation, octave-bandwidth complex steerable pyramid, and can be implemented using compact, efficient linear filters in the spatial domain. Motion-magnified videos produced with this new representation are of comparable quality to those produced with the complex steerable pyramid. When used with phase-based video magnification, the Riesz pyramid phase-shifts image features along only their dominant orientation rather than every orientation like the complex steerable pyramid.Quanta Computer (Firm)Shell ResearchNational Science Foundation (U.S.) (CGV-1111415)Microsoft Research (PhD Fellowship)Massachusetts Institute of Technology. Department of MathematicsNational Science Foundation (U.S.). Graduate Research Fellowship (Grant 1122374

Multiresolution Moment Filters: Theory and Applications

We introduce local weighted geometric moments that are computed from an image within a sliding window at multiple scales. When the window function satisfies a two-scale relation, we prove that lower order moments can be computed efficiently at dyadic scales by using a multiresolution wavelet-like algorithm. We show that B-splines are well-suited window functions because, in addition to being refinable, they are positive, symmetric, separable, and very nearly isotropic (Gaussian shape). We present three applications of these multiscale local moments. The first is a feature-extraction method for detecting and characterizing elongated structures in images. The second is a noise-reduction method which can be viewed as a multiscale extension of Savitzky-Golay filtering. The third is a multiscale optical-flow algorithm that uses a local affine model for the motion field, extending the Lucas-Kanade optical-flow method. The results obtained in all cases are promising