Graph Spectral Image Processing

Recent advent of graph signal processing (GSP) has spurred intensive studies of signals that live naturally on irregular data kernels described by graphs (e.g., social networks, wireless sensor networks). Though a digital image contains pixels that reside on a regularly sampled 2D grid, if one can design an appropriate underlying graph connecting pixels with weights that reflect the image structure, then one can interpret the image (or image patch) as a signal on a graph, and apply GSP tools for processing and analysis of the signal in graph spectral domain. In this article, we overview recent graph spectral techniques in GSP specifically for image / video processing. The topics covered include image compression, image restoration, image filtering and image segmentation

A graph-based mathematical morphology reader

This survey paper aims at providing a "literary" anthology of mathematical morphology on graphs. It describes in the English language many ideas stemming from a large number of different papers, hence providing a unified view of an active and diverse field of research

A gradient-like Variational Bayesian approach for inverse scattering problems

[1]: L. Gharsalli, H. Ayasso, B. Duchêne, and A. Mohammad-Djafari, "A gradient-like variational Bayesian approach: application to microwave imaging for breast tumor detection'', submitted in IEEE International Conference on Image Processing (ICIP). Paris, france 2014.In this document, we present computations of updating shaping parameters for a new method based on the variational Bayesian approach (VBA) allowing to solve a nonlinear inverse scattering problem. The objective is to detect an unknown object from measurements of the scattered field at different frequencies and for several illuminations. This inverse problem is known to be non-linear and ill-posed. So it needs to be regularized by introducing an a priori information. This is tackled in a Bayesian framework where the particular prior information we account for is that the object is composed of a finite known number of different materials distributed in compact regions. Then we propose the approximate the true joint posterior by a separable law by mean of a gradient-like Variational Bayesian technique. This latter is applied to compute the posterior estimators by allowing a joint update of the shape parameters of the approximating marginals and reconstruct the sought object. The main work is given in [1], while technical details of the variational calculations are presented in the current paper

An Universal Image Attractiveness Ranking Framework

We propose a new framework to rank image attractiveness using a novel pairwise deep network trained with a large set of side-by-side multi-labeled image pairs from a web image index. The judges only provide relative ranking between two images without the need to directly assign an absolute score, or rate any predefined image attribute, thus making the rating more intuitive and accurate. We investigate a deep attractiveness rank net (DARN), a combination of deep convolutional neural network and rank net, to directly learn an attractiveness score mean and variance for each image and the underlying criteria the judges use to label each pair. The extension of this model (DARN-V2) is able to adapt to individual judge's personal preference. We also show the attractiveness of search results are significantly improved by using this attractiveness information in a real commercial search engine. We evaluate our model against other state-of-the-art models on our side-by-side web test data and another public aesthetic data set. With much less judgments (1M vs 50M), our model outperforms on side-by-side labeled data, and is comparable on data labeled by absolute score.Comment: Accepted by 2019 Winter Conference on Application of Computer Vision (WACV

Bayesian Lower Bounds for Dense or Sparse (Outlier) Noise in the RMT Framework

Robust estimation is an important and timely research subject. In this paper, we investigate performance lower bounds on the mean-square-error (MSE) of any estimator for the Bayesian linear model, corrupted by a noise distributed according to an i.i.d. Student's t-distribution. This class of prior parametrized by its degree of freedom is relevant to modelize either dense or sparse (accounting for outliers) noise. Using the hierarchical Normal-Gamma representation of the Student's t-distribution, the Van Trees' Bayesian Cram\'er-Rao bound (BCRB) on the amplitude parameters is derived. Furthermore, the random matrix theory (RMT) framework is assumed, i.e., the number of measurements and the number of unknown parameters grow jointly to infinity with an asymptotic finite ratio. Using some powerful results from the RMT, closed-form expressions of the BCRB are derived and studied. Finally, we propose a framework to fairly compare two models corrupted by noises with different degrees of freedom for a fixed common target signal-to-noise ratio (SNR). In particular, we focus our effort on the comparison of the BCRBs associated with two models corrupted by a sparse noise promoting outliers and a dense (Gaussian) noise, respectively