Face recognition in 2D and 2.5D using ridgelets and photometric stereo

A new technique for face recognition - Ridgefaces - is presented. The method combines the well-known Fisherface method with the ridgelet transform and high-speed Photometric Stereo (PS). The paper first derives ridgelet projections for 2D/2.5D face images before the Fisherface approach is used to reduce the dimensionality and increase the spread of the resulting feature vectors. The ridgelet transform is attractive because it is efficient at extracting highly discriminating low-frequency directional features. Best recognition is obtained when Ridgefaces is performed on surface normals acquired from PS, although good results are also found using standard 2D images and PS-derived albedo maps. © 2012 Elsevier Ltd. All rights reserved

Détection de bateaux dans les images de radar à ouverture synthétique

Le but principal de cette thèse est de développer des algorithmes efficaces et de concevoir un système pour la détection de bateaux dans les images Radar à Ouverture Synthetique (ROS.) Dans notre cas, la détection de bateaux implique en premier lieu la détection de cibles de points dans les images ROS. Ensuite, la détection d'un bateau proprement dit dépend des propriétés physiques du bateau lui-même, tel que sa taille, sa forme, sa structure, son orientation relative a la direction de regard du radar et les conditions générales de l'état de la mer. Notre stratégie est de détecter toutes les cibles de bateaux possibles dans les images de ROS, et ensuite de chercher autour de chaque candidat des évidences telle que les sillons. Les objectifs de notre recherche sont (1) d'améliorer 1'estimation des paramètres dans Ie modèle de distribution-K et de déterminer les conditions dans lesquelles un modèle alternatif (Ie Gamma, par exemple) devrait être utilise plutôt; (2) d'explorer Ie modèle PNN (Probabilistic Neural Network) comme une alternative aux modèles paramétriques actuellement utilises; (3) de concevoir un modèle de regroupement flou (FC : Fuzzy Clustering) capable de détecter les petites et grandes cibles de bateaux dans les images a un seul canal ou les images a multi-canaux; (4) de combiner la détection de sillons avec la détection de cibles de bateaux; (5) de concevoir un modèle de détection qui peut être utilisé aussi pour la détection des cibles de bateaux en zones costières.Abstract: The main purpose of this thesis is to develop efficient algorithms and design a system for ship detection from Synthetic Aperture Radar (SAR) imagery. Ship detection usually involves through detection of point targets on a radar clutter background.The detection of a ship depends on the physical properties of the ship itself, such as size, shape, and structure; its orientation relative to the radar look-direction; and the general condition of the sea state. Our strategy is to detect all possible ship targets in SAR images, and then search around each candidate for the wake as further evidence.The objectives of our research are (1) to improve estimation of the parameters in the K-distribution model and to determine the conditions in which an alternative model (Gamma, for example) should be used instead; (2) to explore a PNN (Probabilistic Neural Networks) model as an alternative to the commonly used parameteric models; (3) to design a FC (Fuzzy Clustering) model capable of detecting both small and large ship targets from single-channel images or multi-channel images; (4) to combine wake detection with ship target detection; (5) to design a detection model that can also be used to detect ship targets in coastal areas. We have developed algorithms for each of these objectives and integrated them into a system comprising six models.The system has been tested on a number of SAR images (SEASAT, ERS and RADARSAT-1, for example) and its performance has been assessed

Asymptotic Hyperfunctions, Tempered Hyperfunctions, and Asymptotic Expansions

We introduce new subclasses of Fourier hyperfunctions of mixed type, satisfying polynomial growth conditions at infinity, and develop their sheaf and duality theory. We use Fourier transformation and duality to examine relations of these 'asymptotic' and 'tempered' hyperfunctions to known classes of test functions and distributions, especially the Gelfand-Shilov-Spaces. Further it is shown that the asymptotic hyperfunctions, which decay faster than any negative power, are precisely the class that allow asymptotic expansions at infinity. These asymptotic expansions are carried over to the higher-dimensional case by applying the Radon transformation for hyperfunctions.Comment: 31 pages, 1 figure, typos corrected, references adde

New Algorithms in Computational Microscopy

Microscopy plays an important role in providing tools to microscopically observe objects and their surrounding areas with much higher resolution ranging from the scale between molecular machineries (angstrom) and individual cells (micrometer). Under microscopes, illumination, such as visible light and electron-magnetic radiation/electron beam, interacts with samples, then they are scattered to a plane and are recorded. Computational microscopy corresponds to image reconstruction from these measurements as well as improving quality of the images. Along with the evolution of microscopy, new studies are discovered and algorithms need development not only to provide high-resolution imaging but also to decipher new and advanced research. In this dissertation, we focus on algorithm development for inverse problems in microscopy, specifically phase retrieval and tomography, and the application of these techniques to machine learning. The four studies in this dissertation demonstrates the use of optimization and calculus of variation in imaging science and other different disciplines.Study 1 focuses on coherent diffractive imaging (CDI) or phase retrieval, a non-linear inverse problem that aims to recover 2D image from it Fourier transforms in modulus taking into account that extra information provided by oversampling as a second constraint. To solve this two-constraint minimization, we proceed from Hamilton-Jacobi partial differential equation (HJ-PDE) and its Hopf-Lax formula. Introducing generalized Bregman distance to the HJ-PDE and applying Legendre transform, we derive our generalized proximal smoothing (GPS) algorithm under the form of primal-dual hybrid gradient (PDHG). While the reflection operator, known as extrapolating momentum, helps overcome local minima, the smoothing by the generalized Bregman distance is adjusted to improve convergence and consistency of phase retrieval.Study 2 focuses on electron tomography, 3D image reconstruction from a set of 2D projections obtained from a transmission electron microscope (TEM) or X-ray microscope. Notice that current tomography algorithms limit to a single tilt axis and fail to work with fully or partially missing data. In the light of calculus of variations and Fourier slice theorem (FST), we develop a highly accurate tomography iterative algorithm that can provide higher resolution imaging and work with missing data as well as has capability to perform multiple-tilt-axis tomography. The algorithm is further developed to work with non-isolated objects and partially-blocked projections which have become more popular in experiment. The success of real space iterative reconstruction engine (RESIRE) opens a new era to the study of tomography in material science and magnetic structures (vector Tomography).Study 3 and 4 are applications of our algorithms to machine learning. Study 3 develops a backward Euler method in a stochastic manner to solve K-mean clustering, a well-known non-convex optimization problem. The algorithm has been shown to improve minimums and consistency, providing a new powerful tool to the class of classification techniques. Study 4 is a direct application of GPS to deep learning gradient descent algorithms. Linearizing the Hopf-Lax formula derived in GPS, we derive our method Laplacian smoothing gradient descent (LSGD), simply known as gradient smoothing. Our experiment shows that LSGD has the ability to search for better and flatter minimums, reduce variation, and obtain higher accuracy and consistency

Analysis of Polarimetric Synthetic Aperture Radar and Passive Visible Light Polarimetric Imaging Data Fusion for Remote Sensing Applications

The recent launch of spaceborne (TerraSAR-X, RADARSAT-2, ALOS-PALSAR, RISAT) and airborne (SIRC, AIRSAR, UAVSAR, PISAR) polarimetric radar sensors, with capability of imaging through day and night in almost all weather conditions, has made polarimetric synthetic aperture radar (PolSAR) image interpretation and analysis an active area of research. PolSAR image classification is sensitive to object orientation and scattering properties. In recent years, significant work has been done in many areas including agriculture, forestry, oceanography, geology, terrain analysis. Visible light passive polarimetric imaging has also emerged as a powerful tool in remote sensing for enhanced information extraction. The intensity image provides information on materials in the scene while polarization measurements capture surface features, roughness, and shading, often uncorrelated with the intensity image. Advantages of visible light polarimetric imaging include high dynamic range of polarimetric signatures and being comparatively straightforward to build and calibrate. This research is about characterization and analysis of the basic scattering mechanisms for information fusion between PolSAR and passive visible light polarimetric imaging. Relationships between these two modes of imaging are established using laboratory measurements and image simulations using the Digital Image and Remote Sensing Image Generation (DIRSIG) tool. A novel low cost laboratory based S-band (2.4GHz) PolSAR instrument is developed that is capable of capturing 4 channel fully polarimetric SAR image data. Simple radar targets are formed and system calibration is performed in terms of radar cross-section. Experimental measurements are done using combination of the PolSAR instrument with visible light polarimetric imager for scenes capturing basic scattering mechanisms for phenomenology studies. The three major scattering mechanisms studied in this research include single, double and multiple bounce. Single bounce occurs from flat surfaces like lakes, rivers, bare soil, and oceans. Double bounce can be observed from two adjacent surfaces where one horizontal flat surface is near a vertical surface such as buildings and other vertical structures. Randomly oriented scatters in homogeneous media produce a multiple bounce scattering effect which occurs in forest canopies and vegetated areas. Relationships between Pauli color components from PolSAR and Degree of Linear Polarization (DOLP) from passive visible light polarimetric imaging are established using real measurements. Results show higher values of the red channel in Pauli color image (|HH-VV|) correspond to high DOLP from double bounce effect. A novel information fusion technique is applied to combine information from the two modes. In this research, it is demonstrated that the Degree of Linear Polarization (DOLP) from passive visible light polarimetric imaging can be used for separation of the classes in terms of scattering mechanisms from the PolSAR data. The separation of these three classes in terms of the scattering mechanisms has its application in the area of land cover classification and anomaly detection. The fusion of information from these particular two modes of imaging, i.e. PolSAR and passive visible light polarimetric imaging, is a largely unexplored area in remote sensing and the main challenge in this research is to identify areas and scenarios where information fusion between the two modes is advantageous for separation of the classes in terms of scattering mechanisms relative to separation achieved with only PolSAR