Color Sparse Representations for Image Processing: Review, Models, and Prospects

International audienceSparse representations have been extended to deal with color images composed of three channels. A review of dictionary-learning-based sparse representations for color images is made here, detailing the differences between the models, and comparing their results on real data and simulated data. These models are considered in a unifying framework that is based on the degrees of freedom of the linear filtering/transformation of the color channels. Moreover, this allows it to be shown that the scalar quaternionic linear model is equivalent to constrained matrix-based color filtering, which highlights the filtering implicitly applied through this model. Based on this reformulation, the new color filtering model is introduced, using unconstrained filters. In this model, spatial morphologies of color images are encoded by atoms, and colors are encoded by color filters. Color variability is no longer captured in increasing the dictionary size, but with color filters, this gives an efficient color representation

Connected Attribute Filtering Based on Contour Smoothness

A new attribute measuring the contour smoothness of 2-D objects is presented in the context of morphological attribute filtering. The attribute is based on the ratio of the circularity and non-compactness, and has a maximum of 1 for a perfect circle. It decreases as the object boundary becomes irregular. Computation on hierarchical image representation structures relies on five auxiliary data members and is rapid. Contour smoothness is a suitable descriptor for detecting and discriminating man-made structures from other image features. An example is demonstrated on a very-high-resolution satellite image using connected pattern spectra and the switchboard platform

Bifurcation analysis of the Topp model

In this paper, we study the 3-dimensional Topp model for the dynamicsof diabetes. We show that for suitable parameter values an equilibrium of this modelbifurcates through a Hopf-saddle-node bifurcation. Numerical analysis suggests thatnear this point Shilnikov homoclinic orbits exist. In addition, chaotic attractors arisethrough period doubling cascades of limit cycles.Keywords Dynamics of diabetes · Topp model · Reduced planar quartic Toppsystem · Singular point · Limit cycle · Hopf-saddle-node bifurcation · Perioddoubling bifurcation · Shilnikov homoclinic orbit · Chao

Frequency Domain Decomposition of Digital Video Containing Multiple Moving Objects

Motion estimation has been dominated by time domain methods such as block matching and optical flow. However, these methods have problems with multiple moving objects in the video scene, moving backgrounds, noise, and fractional pixel/frame motion. This dissertation proposes a frequency domain method (FDM) that solves these problems. The methodology introduced here addresses multiple moving objects, with or without a moving background, 3-D frequency domain decomposition of digital video as the sum of locally translational (or, in the case of background, a globally translational motion), with high noise rejection. Additionally, via a version of the chirp-Z, fractional pixel/frame motion detection and quantification is accomplished. Furthermore, images of particular moving objects can be extracted and reconstructed from the frequency domain. Finally, this method can be integrated into a larger system to support motion analysis. The method presented here has been tested with synthetic data, realistic, high fidelity simulations, and actual data from established video archives to verify the claims made for the method, all presented here. In addition, a convincing comparison with an up-and-coming spatial domain method, incremental principal component pursuit (iPCP), is presented, where the FDM performs markedly better than its competition

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

A review of image fusion algorithms based on the Super-Resolution paradigm

A critical analysis of remote sensing image fusion methods based on the super-resolution (SR) paradigm is presented in this paper. Very recent algorithms have been selected among the pioneering studies adopting a new methodology and the most promising solutions. After introducing the concept of super-resolution and modeling the approach as a constrained optimization problem, different SR solutions for spatio-temporal fusion and pan-sharpening are reviewed and critically discussed. Concerning pan-sharpening, the well-known, simple, yet effective, proportional additive wavelet in the luminance component (AWLP) is adopted as a benchmark to assess the performance of the new SR-based pan-sharpening methods. The widespread quality indexes computed at degraded resolution, with the original multispectral image used as the reference, i.e., SAM (Spectral Angle Mapper) and ERGAS (Erreur Relative Globale Adimensionnelle de Synthèse), are finally presented. Considering these results, sparse representation and Bayesian approaches seem far from being mature to be adopted in operational pan-sharpening scenarios