Deformable kernels for early vision

Early vision algorithms often have a first stage of linear-filtering that `extracts' from the image information at multiple scales of resolution and multiple orientations. A common difficulty in the design and implementation of such schemes is that one feels compelled to discretize coarsely the space of scales and orientations in order to reduce computation and storage costs. A technique is presented that allows: 1) computing the best approximation of a given family using linear combinations of a small number of `basis' functions; and 2) describing all finite-dimensional families, i.e., the families of filters for which a finite dimensional representation is possible with no error. The technique is based on singular value decomposition and may be applied to generating filters in arbitrary dimensions and subject to arbitrary deformations. The relevant functional analysis results are reviewed and precise conditions for the decomposition to be feasible are stated. Experimental results are presented that demonstrate the applicability of the technique to generating multiorientation multi-scale 2D edge-detection kernels. The implementation issues are also discussed

Elliptical Monogenic Wavelets for the analysis and processing of color images

International audienceThis paper studies and gives new algorithms for image processing based on monogenic wavelets. Existing greyscale monogenic filterbanks are reviewed and we reveal a lack of discussion about the synthesis part. The monogenic synthesis is therefore defined from the idea of wavelet modulation, and an innovative filterbank is constructed by using the Radon transform. The color extension is then investigated. First, the elliptical Fourier atom model is proposed to generalize theanalytic signal representation for vector-valued signals. Then a color Riesz-transform is defined so as to construct color elliptical monogenic wavelets. Our Radon-based monogenic filterbank can be easily extended to color according to this definition. The proposed wavelet representation provides efficient analysis of local features in terms of shape and color, thanks to the concepts of amplitude, phase, orientation, and ellipse parameters. The synthesis from local features is deeply studied. We conclude the article by defining the color local frequency, proposing an estimation algorithm

An experimental study of the feasibility of phase‐based video magnification for damage detection and localisation in operational deflection shapes

Optical measurements from high‐speed, high‐definition video recordings can be used to define the full‐field dynamics of a structure. By comparing the dynamic responses resulting from both damaged and undamaged elements, structural health monitoring can be carried out, similarly as with mounted transducers. Unlike the physical sensors, which provide point‐wise measurements and a limited number of output channels, high‐quality video recording allows very spatially dense information. Moreover, video acquisition is a noncontact technique. This guarantees that any anomaly in the dynamic behaviour can be more easily correlated to damage and not to added mass or stiffness due to the installed sensors. However, in real‐life scenarios, the vibrations due to environmental input are often so small that they are indistinguishable from measurement noise if conventional image‐based techniques are applied. In order to improve the signal‐to‐noise ratio in low‐amplitude measurements, phase‐based motion magnification has been recently proposed. This study intends to show that model‐based structural health monitoring can be performed on modal data and time histories processed with phase‐based motion magnification, whereas unamplified vibrations would be too small for being successfully exploited. All the experiments were performed on a multidamaged box beam with different damage sizes and angles

Local Geometric Transformations in Image Analysis

The characterization of images by geometric features facilitates the precise analysis of the structures found in biological micrographs such as cells, proteins, or tissues. In this thesis, we study image representations that are adapted to local geometric transformations such as rotation, translation, and scaling, with a special emphasis on wavelet representations. In the first part of the thesis, our main interest is in the analysis of directional patterns and the estimation of their location and orientation. We explore steerable representations that correspond to the notion of rotation. Contrarily to classical pattern matching techniques, they have no need for an a priori discretization of the angle and for matching the filter to the image at each discretized direction. Instead, it is sufficient to apply the filtering only once. Then, the rotated filter for any arbitrary angle can be determined by a systematic and linear transformation of the initial filter. We derive the Cramér-Rao bounds for steerable filters. They allow us to select the best harmonics for the design of steerable detectors and to identify their optimal radial profile. We propose several ways to construct optimal representations and to build powerful and effective detector schemes; in particular, junctions of coinciding branches with local orientations. The basic idea of local transformability and the general principles that we utilize to design steerable wavelets can be applied to other geometric transformations. Accordingly, in the second part, we extend our framework to other transformation groups, with a particular interest in scaling. To construct representations in tune with a notion of local scale, we identify the possible solutions for scalable functions and give specific criteria for their applicability to wavelet schemes. Finally, we propose discrete wavelet frames that approximate a continuous wavelet transform. Based on these results, we present a novel wavelet-based image-analysis software that provides a fast and automatic detection of circular patterns, combined with a precise estimation of their size

Modelling the dynamics of motion integration with a new luminance-gated diffusion mechanism

The dynamics of motion integration show striking similarities when observed at neuronal, psychophysical, and oculomotor levels. Based on the inter-relation and complementary insights given by those dynamics, our goal was to test how basic mechanisms of dynamical cortical processing can be incorporated in a dynamical model to solve several aspects of 2D motion integration and segmentation. Our model is inspired by the hierarchical processing stages of the primate visual cortex: we describe the interactions between several layers processing local motion and form information through feedforward, feedback, and inhibitive lateral connections. Also, following perceptual studies concerning contour integration and physiological studies of receptive fields, we postulate that motion estimation takes advantage of another low level cue, which is luminance smoothness along edges or surfaces, in order to gate recurrent motion diffusion. With such a model, we successfully reproduced the temporal dynamics of motion integration on a wide range of simple motion stimuli: line segments, rotating ellipses, plaids, and barber poles. Furthermore, we showed that the proposed computational rule of luminance-gated diffusion of motion information is sufficient to explain a large set of contextual modulations of motion integration and segmentation in more elaborated stimuli such as chopstick illusions, simulated aperture problems, or rotating diamonds. As a whole, in this paper we proposed a new basal luminance-driven motion integration mechanism as an alternative to less parsimonious models, we carefully investigated the dynamics of motion integration, and we established a distinction between simple and complex stimuli according to the kind of information required to solve their ambiguities

Video Magnification for Structural Analysis Testing

The goal of this thesis is to allow a user to see minute motion of an object at different frequencies, using a computer program, to aid in vibration testing analysis without the use of complex setups of accelerometers or expensive laser vibrometers. MIT’s phase-based video motion processing ­was modified to enable modal determination of structures in the field using a cell phone camera. The algorithm was modified by implementing a stabilization algorithm and permitting the magnification filter to operate on multiple frequency ranges to enable visualization of the natural frequencies of structures in the field. To implement multiple frequency ranges a new function was developed to implement the magnification filter at each relevant frequency range within the original video. The stabilization algorithm would allow for a camera to be hand-held instead of requiring a tripod mount. The following methods for stabilization were tested: fixed point video stabilization and image registration. Neither method removed the global motion from the hand-held video, even after masking was implemented, which resulted in poor results. Specifically, fixed point did not remove much motion or created sharp motions and image registration introduced a pulsing effect. The best results occurred when the object being observed had contrast from the background, was the largest feature in the video frame, and the video was captured from a tripod at an appropriate angle. The final program can amplify the motion in user selected frequency bands and can be used as an aid in structural analysis testing