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

Analysis of Optimization Methods in Multisteerable Filter Design

The purpose of this thesis is to study and investigate a practical and efficient implementation of corner orientation detection using multisteerable filters. First, practical theory involved in applying multisteerable filters for corner orientation estimation is presented. Methods to improve the efficiency with which multisteerable corner filters are applied to images are investigated and presented. Prior research in this area presented an optimization equation for determining the best match of corner orientations in images; however, little research has been done on optimization techniques to solve this equation. Optimization techniques to find the maximum response of a similarity function to determine how similar a corner feature is to a multioriented corner template are also explored and compared in this research

Seismic Fault Preserving Diffusion

This paper focuses on the denoising and enhancing of 3-D reflection seismic data. We propose a pre-processing step based on a non linear diffusion filtering leading to a better detection of seismic faults. The non linear diffusion approaches are based on the definition of a partial differential equation that allows us to simplify the images without blurring relevant details or discontinuities. Computing the structure tensor which provides information on the local orientation of the geological layers, we propose to drive the diffusion along these layers using a new approach called SFPD (Seismic Fault Preserving Diffusion). In SFPD, the eigenvalues of the tensor are fixed according to a confidence measure that takes into account the regularity of the local seismic structure. Results on both synthesized and real 3-D blocks show the efficiency of the proposed approach.Comment: 10 page

Lv volume quantification via spatiotemporal analysis of real-time 3-d echocardiography

Abstract—This paper presents a method of four-dimensional (4-D) (3-D + Time) space–frequency analysis for directional denoising and enhancement of real-time three-dimensional (RT3D) ultrasound and quantitative measures in diagnostic cardiac ultrasound. Expansion of echocardiographic volumes is performed with complex exponential wavelet-like basis functions called brushlets. These functions offer good localization in time and frequency and decompose a signal into distinct patterns of oriented harmonics, which are invariant to intensity and contrast range. Deformable-model segmentation is carried out on denoised data after thresholding of transform coefficients. This process attenuates speckle noise while preserving cardiac structure location. The superiority of 4-D over 3-D analysis for decorrelating additive white noise and multiplicative speckle noise on a 4-D phantom volume expanding in time is demonstrated. Quantitative validation, computed for contours and volumes, is performed on in vitro balloon phantoms. Clinical applications of this spaciotemporal analysis tool are reported for six patient cases providing measures of left ventricular volumes and ejection fraction. Index Terms—Echocardiography, LV volume, spaciotemporal analysis, speckle denoising. I

LV Volume Quantification via Spatiotemporal Analysis of Real-Time 3-D Echocardiography

This paper presents a method of four-dimensional (4-D) (3-D+Time) space-frequency analysis for directional denoising and enhancement of real-time three-dimensional (RT3D) ultrasound and quantitative measures in diagnostic cardiac ultrasound. Expansion of echocardiographic volumes is performed with complex exponential wavelet-like basis functions called brushlets. These functions offer good localization in time and frequency and decompose a signal into distinct patterns of oriented harmonics, which are invariant to intensity and contrast range. Deformable-model segmentation is carried out on denoised data after thresholding of transform coefficients. This process attenuates speckle noise while preserving cardiac structure location. The superiority of 4-D over 3-D analysis for decorrelating additive white noise and multiplicative speckle noise on a 4-D phantom volume expanding in time is demonstrated. Quantitative validation, computed for contours and volumes, is performed on in vitro balloon phantoms. Clinical applications of this spatiotemporal analysis tool are reported for six patient cases providing measures of left ventricular volumes and ejection fraction

Geophysical data registration using modified plane-wave destruction filters

I propose a method to efficiently measure local shifts, slopes, and scaling functions between seismic traces using modified plane-wave destruction filters. Plane-wave destruction can efficiently measure shifts of less than a few samples, making this algorithm particularly effective for detecting small shifts. When shifts are large, amplitude-adjusted plane-wave destruction can also be used to refine shift estimates obtained by other methods. Amplitude-adjusted plane-wave destruction separates estimation of local shifts and amplitude weights, allowing the time-shift to be measured more accurately. This algorithm has clear applications to geophysical data registration problems, including time-lapse image registration, multicomponent image registration, automatic gather flattening, automatic seismic-well ties, and image merging. The effectiveness of this algorithm in predicting shifts associated with fluid migration, wave mode conversions, and anisotropy and amplitude gradients associated with amplitude variations with offset or angle is demonstrated by applying the algorithm to a synthetic trace, a time-lapse field data example from the Cranfield CO₂ sequestration project, a multicomponent field data example from West Texas, and the Mobil AVO prestack seismic data. Finding correspondence between different parts of the same dataset falls into the same category of problems as local shift estimation. Computation of structure-oriented amplitude gradients for attribute-assisted interpretation requires the estimation of local slopes by correlating reflections between neighboring seismic traces in an image. One of the major challenges of interpreting seismic images is the delineation of reflection discontinuities that are related to geologic features, such as faults, channels, salt boundaries, and unconformities. Visually prominent reflection features often overshadow these subtle discontinuous features which are critical to understanding the structural and depositional environment of the subsurface. For this reason, precise manual interpretation of these reflection discontinuities in seismic images can be tedious and time-consuming, especially when data quality is poor. Discontinuity enhancement attributes are commonly used to facilitate the interpretation process by enhancing edges in seismic images and providing a quantitative measure of the significance of discontinuous features. These attributes require careful pre-processing to maintain geologic features and suppress acquisition and processing artifacts which may be artificially detected as a geologic edge. The plane-wave Sobel filter cascades plane-wave destruction filters with plane-wave shaping in the transverse direction to compute an enhanced discontinuity attribute. The plane-wave Sobel attribute can be applied directly to a seismic image to efficiently and effectively enhance discontinuous features, or to a coherence image to create a sharper and more detailed image. I demonstrate the effectiveness of this method by applying it to two field data sets from offshore New Zealand and offshore Nova Scotia with several faults and channel features and compare the results to other coherence attributes.Geological Science

Image-Based Approaches to Hair Modeling

Hair is a relevant characteristic of virtual characters, therefore the modeling of plausible facial hair and hairstyles is an essential step in the generation of computer generated (CG) avatars. However, the inherent geometric complexity of hair together with the huge number of filaments of an average human head make the task of modeling hairstyles a very challenging one. To date this is commonly a manual process which requires artist skills or very specialized and costly acquisition software. In this work we present an image-based approach to model facial hair (beard and eyebrows) and (head) hairstyles. Since facial hair is usually much shorter than the average head hair two different methods are resented, adapted to the characteristics of the hair to be modeled. Facial hair is modeled using data extracted from facial texture images and missing information is inferred by means of a database-driven prior model. Our hairstyle reconstruction technique employs images of the hair to be modeled taken with a thermal camera. The major advantage of our thermal image-based method over conventional image-based techniques lies on the fact that during data capture the hairstyle is "lit from the inside": the thermal camera captures heat irradiated by the head and actively re-emitted by the hair filaments almost isotropically. Following this approach we can avoid several issues of conventional image-based techniques, like shadowing or anisotropy in reflectance. The presented technique requires minimal user interaction and a simple acquisition setup. Several challenging examples demonstrate the potential of the proposed approach

Modulation Domain Image Processing

The classical Fourier transform is the cornerstone of traditional linearsignal and image processing. The discrete Fourier transform (DFT) and thefast Fourier transform (FFT) in particular led toprofound changes during the later decades of the last century in howwe analyze and process 1D and multi-dimensional signals.The Fourier transform represents a signal as an infinite superpositionof stationary sinusoids each of which has constant amplitude and constantfrequency. However, many important practical signals such as radar returnsand seismic waves are inherently nonstationary. Hence, more complextechniques such as the windowed Fourier transform and the wavelet transformwere invented to better capture nonstationary properties of these signals.In this dissertation, I studied an alternative nonstationary representationfor images, the 2D AM-FM model. In contrast to thestationary nature of the classical Fourier representation, the AM-FM modelrepresents an image as a finite sum of smoothly varying amplitudesand smoothly varying frequencies. The model has been applied successfullyin image processing applications such as image segmentation, texture analysis,and target tracking. However, these applications are limitedto \emph{analysis}, meaning that the computed AM and FM functionsare used as features for signal processing tasks such as classificationand recognition. For synthesis applications, few attempts have been madeto synthesize the original image from the AM and FM components. Nevertheless,these attempts were unstable and the synthesized results contained artifacts.The main reason is that the perfect reconstruction AM-FM image model waseither unavailable or unstable. Here, I constructed the first functionalperfect reconstruction AM-FM image transform that paves the way for AM-FMimage synthesis applications. The transform enables intuitive nonlinearimage filter designs in the modulation domain. I showed that these filtersprovide important advantages relative to traditional linear translation invariant filters.This dissertation addresses image processing operations in the nonlinearnonstationary modulation domain. In the modulation domain, an image is modeledas a sum of nonstationary amplitude modulation (AM) functions andnonstationary frequency modulation (FM) functions. I developeda theoretical framework for high fidelity signal and image modeling in themodulation domain, constructed an invertible multi-dimensional AM-FMtransform (xAMFM), and investigated practical signal processing applicationsof the transform. After developing the xAMFM, I investigated new imageprocessing operations that apply directly to the transformed AM and FMfunctions in the modulation domain. In addition, I introduced twoclasses of modulation domain image filters. These filters produceperceptually motivated signal processing results that are difficult orimpossible to obtain with traditional linear processing or spatial domainnonlinear approaches. Finally, I proposed three extensions of the AM-FMtransform and applied them in image analysis applications.The main original contributions of this dissertation include the following.- I proposed a perfect reconstruction FM algorithm. I used aleast-squares approach to recover the phase signal from itsgradient. In order to allow perfect reconstruction of the phase function, Ienforced an initial condition on the reconstructed phase. The perfectreconstruction FM algorithm plays a critical role in theoverall AM-FM transform.- I constructed a perfect reconstruction multi-dimensional filterbankby modifying the classical steerable pyramid. This modified filterbankensures a true multi-scale multi-orientation signal decomposition. Such adecomposition is required for a perceptually meaningful AM-FM imagerepresentation.- I rotated the partial Hilbert transform to alleviate ripplingartifacts in the computed AM and FM functions. This adjustment results inartifact free filtering results in the modulation domain.- I proposed the modulation domain image filtering framework. Iconstructed two classes of modulation domain filters. I showed that themodulation domain filters outperform traditional linear shiftinvariant (LSI) filters qualitatively and quantitatively in applicationssuch as selective orientation filtering, selective frequency filtering,and fundamental geometric image transformations.- I provided extensions of the AM-FM transform for image decompositionproblems. I illustrated that the AM-FM approach can successfullydecompose an image into coherent components such as textureand structural components.- I investigated the relationship between the two prominentAM-FM computational models, namely the partial Hilbert transformapproach (pHT) and the monogenic signal. The established relationshiphelps unify these two AM-FM algorithms.This dissertation lays a theoretical foundation for future nonlinearmodulation domain image processing applications. For the first time, onecan apply modulation domain filters to images to obtain predictableresults. The design of modulation domain filters is intuitive and simple,yet these filters produce superior results compared to those of pixeldomain LSI filters. Moreover, this dissertation opens up other research problems.For instance, classical image applications such as image segmentation andedge detection can be re-formulated in the modulation domain setting.Modulation domain based perceptual image and video quality assessment andimage compression are important future application areas for the fundamentalrepresentation results developed in this dissertation