Measuring the Coverage of Interest Point Detectors

Repeatability is widely used as an indicator of the performance of an image feature detector but, although useful, it does not convey all the information that is required to describe performance. This paper explores the spatial distribution of interest points as an alternative indicator of performance, presenting a metric that is shown to concur with visual assessments. This metric is then extended to provide a measure of complementarity for pairs of detectors. Several state-of-the-art detectors are assessed, both individually and in combination. It is found that Scale Invariant Feature Operator (SFOP) is dominant, both when used alone and in combination with other detectors

Stellar Kinematics of the Andromeda II Dwarf Spheroidal Galaxy

We present kinematical profiles and metallicity for the M31 dwarf spheroidal (dSph) satellite galaxy Andromeda II (And II) based on Keck DEIMOS spectroscopy of 531 red giant branch stars. Our kinematical sample is among the largest for any M31 satellite and extends out to two effective radii (r_eff = 5.3' = 1.1 kpc). We find a mean systemic velocity of -192.4+-0.5 km/s and an average velocity dispersion of sigma_v = 7.8+-1.1 km/s. While the rotation velocity along the major axis of And II is nearly zero (<1 km/s), the rotation along the minor axis is significant with a maximum rotational velocity of v_max=8.6+-1.8 km/s. We find a kinematical major axis, with a maximum rotational velocity of v_max=10.9+-2.4 km/s, misaligned by 67 degrees to the isophotal major axis. And II is thus the first dwarf galaxy with evidence for nearly prolate rotation with a v_max/sigma_v = 1.1, although given its ellipticity of epsilon = 0.10, this object may be triaxial. We measured metallicities for a subsample of our data, finding a mean metallicity of [Fe/H] = -1.39+- 0.03 dex and an internal metallicity dispersion of 0.72+-0.03 dex. We find a radial metallicity gradient with metal-rich stars more centrally concentrated, but do not observe a significant difference in the dynamics of two metallicity populations. And II is the only known dwarf galaxy to show minor axis rotation making it a unique system whose existence offers important clues on the processes responsible for the formation of dSphs.Comment: 14 pages, 10 figures, 4 tables, accepted for publication in Ap

Rapid Online Analysis of Local Feature Detectors and Their Complementarity

A vision system that can assess its own performance and take appropriate actions online to maximize its effectiveness would be a step towards achieving the long-cherished goal of imitating humans. This paper proposes a method for performing an online performance analysis of local feature detectors, the primary stage of many practical vision systems. It advocates the spatial distribution of local image features as a good performance indicator and presents a metric that can be calculated rapidly, concurs with human visual assessments and is complementary to existing offline measures such as repeatability. The metric is shown to provide a measure of complementarity for combinations of detectors, correctly reflecting the underlying principles of individual detectors. Qualitative results on well-established datasets for several state-of-the-art detectors are presented based on the proposed measure. Using a hypothesis testing approach and a newly-acquired, larger image database, statistically-significant performance differences are identified. Different detector pairs and triplets are examined quantitatively and the results provide a useful guideline for combining detectors in applications that require a reasonable spatial distribution of image features. A principled framework for combining feature detectors in these applications is also presented. Timing results reveal the potential of the metric for online applications. © 2013 by the authors; licensee MDPI, Basel, Switzerland

On the Analysis and Decomposition of Intrinsically One-Dimensional Signals and their Superpositions

Computer and machine vision tasks can roughly be divided into a hierarchy of processing steps applied to input signals captured by a measuring device. In the case of image signals, the first stage in this hierarchy is also referred to as low-level vision or low-level image processing. The field of low-level image processing includes the mathematical description of signals in terms of certain local signal models. The choice of the signal model is often task dependent. A common task is the extraction of features from the signal. Since signals are subject to transformations, for example camera movements in the case of image signals, the features are supposed to fulfill the properties of invariance or equivariance with respect to these transformations. The chosen signal model should reflect these properties in terms of its parameters. This thesis contributes to the field of low-level vision. Local signal structures are represented by (sinusoidal) intrinsically one-dimensional signals and their superpositions. Each intrinsically one-dimensional signal consists of certain parameters such as orientation, amplitude, frequency and phase. If the affine group acts on these signals, the transformations induce a corresponding action in the parameter space of the signal model. Hence, it is reasonable, to estimate the model parameters in order to describe the invariant and equivariant features. The first and main contribution studies superpositions of intrinsically one-dimensional signals in the plane. The parameters of the signal are supposed to be extracted from the responses of linear shift invariant operators: the generalized Hilbert transform (Riesz transform) and its higher-order versions and the partial derivative operators. While well known signal representations, such as the monogenic signal, allow to obtain the local features amplitude, phase and orientation for a single intrinsically one-dimensional signal, there exists no general method to decompose superpositions of such signals into their corresponding features. A novel method for the decomposition of an arbitrary number of sinusoidal intrinsically one-dimensional signals in the plane is proposed. The responses of the higher-order generalized Hilbert transforms in the plane are interpreted as symmetric tensors, which allow to restate the decomposition problem as a symmetric tensor decomposition. Algorithms, examples and applications for the novel decomposition are provided. The second contribution studies curved intrinsically one-dimensional signals in the plane. This signal model introduces a new parameter, the curvature, and allows the representation of curved signal structures. Using the inverse stereographic projection to the sphere, these curved signals are locally identified with intrinsically one-dimensional signals in the three-dimensional Euclidean space and analyzed in terms of the generalized Hilbert transform and partial derivatives therein. The third contribution studies the generalized Hilbert transform in a non-Euclidean space, the two-sphere. The mathematical framework of Clifford analysis proposes a further generalization of the generalized Hilbert transform to the two-sphere in terms of the corresponding Cauchy kernel. Nonetheless, this transform lacks an intuitive interpretation in the frequency domain. A decomposition of the Cauchy kernel in terms of its spherical harmonics is provided. Its coefficients not only provide insights to the generalized Hilbert transform on the sphere, but also allow for fast implementations in terms of analogues of the convolution theorem on the sphere

Appearance Preserving Rendering of Out-of-Core Polygon and NURBS Models

In Computer Aided Design (CAD) trimmed NURBS surfaces are widely used due to their flexibility. For rendering and simulation however, piecewise linear representations of these objects are required. A relatively new field in CAD is the analysis of long-term strain tests. After such a test the object is scanned with a 3d laser scanner for further processing on a PC. In all these areas of CAD the number of primitives as well as their complexity has grown constantly in the recent years. This growth is exceeding the increase of processor speed and memory size by far and posing the need for fast out-of-core algorithms. This thesis describes a processing pipeline from the input data in the form of triangular or trimmed NURBS models until the interactive rendering of these models at high visual quality. After discussing the motivation for this work and introducing basic concepts on complex polygon and NURBS models, the second part of this thesis starts with a review of existing simplification and tessellation algorithms. Additionally, an improved stitching algorithm to generate a consistent model after tessellation of a trimmed NURBS model is presented. Since surfaces need to be modified interactively during the design phase, a novel trimmed NURBS rendering algorithm is presented. This algorithm removes the bottleneck of generating and transmitting a new tessellation to the graphics card after each modification of a surface by evaluating and trimming the surface on the GPU. To achieve high visual quality, the appearance of a surface can be preserved using texture mapping. Therefore, a texture mapping algorithm for trimmed NURBS surfaces is presented. To reduce the memory requirements for the textures, the algorithm is modified to generate compressed normal maps to preserve the shading of the original surface. Since texturing is only possible, when a parametric mapping of the surface - requiring additional memory - is available, a new simplification and tessellation error measure is introduced that preserves the appearance of the original surface by controlling the deviation of normal vectors. The preservation of normals and possibly other surface attributes allows interactive visualization for quality control applications (e.g. isophotes and reflection lines). In the last part out-of-core techniques for processing and rendering of gigabyte-sized polygonal and trimmed NURBS models are presented. Then the modifications necessary to support streaming of simplified geometry from a central server are discussed and finally and LOD selection algorithm to support interactive rendering of hard and soft shadows is described

Matching using local invariant

This paper presents an alternative to standard matching methods . Its main novel feature is to rely on greylevel invariants that ar e computed locally. This allows matching even in presence of large image change in rotation or scaling . These invariants are the se t of differential invariants in rotation with an additional multiscale approach for taking into account scale changes . Such invariants were also expanded towards illumination changes allowing therefore large illumination variations . The overall method is quite easy to be understood and implemented and provides surprisingly good results .Le but de cet article est de proposer une alternative aux méthodes de mise en correspondance. Cette dernière repose sur le calcul d'invariants de la fonction de luminosité. Ceci permet d'effectuer une mise en correspondance dans le cas d'une transformation importante entre deux images. Pour ce faire, nous utilisons des mesures différentielles invariantes en rotation et une approche multi-échelle. Pour autoriser la mise en correspondance entre des images éclairées de façon différente, les invariants utilisés sont également robustes à de tel changement. Une mise en oeuvre simple de la méthode fournit des résultats de bonne qualité autorisant des applications variées

Sur la Restauration et l'Edition de Vidéo : Détection de Rayures et Inpainting de Scènes Complexes

The inevitable degradation of visual content such as images and films leads to the goal ofimage and video restoration. In this thesis, we look at two specific restoration problems : the detection ofline scratches in old films and the automatic completion of videos, or video inpainting as it is also known.Line scratches are caused when the film physically rubs against a mechanical part. This origin resultsin the specific characteristics of the defect, such as verticality and temporal persistence. We propose adetection algorithm based on the statistical approach known as a contrario methods. We also proposea temporal filtering step to remove false alarms present in the first detection step. Comparisons withprevious work show improved recall and precision, and robustness with respect to the presence of noiseand clutter in the film.The second part of the thesis concerns video inpainting. We propose an algorithm based on theminimisation of a patch-based functional of the video content. In this framework, we address the followingproblems : extremely high execution times, the correct handling of textures in the video and inpaintingwith moving cameras. We also address some convergence issues in a very simplified inpainting context.La degradation inévitable des contenus visuels (images, films) conduit nécessairementà la tâche de la restauration des images et des vidéos. Dans cetre thèse, nous nous intéresserons àdeux sous-problèmes de restauration : la détection des rayures dans les vieux films, et le remplissageautomatique des vidéos (“inpainting vidéo en anglais).En général, les rayures sont dues aux frottements de la pellicule du film avec un objet lors de laprojection du film. Les origines physiques de ce défaut lui donnent des caractéristiques très particuliers.Les rayures sont des lignes plus ou moins verticales qui peuvent être blanches ou noires (ou parfois encouleur) et qui sont temporellement persistantes, c’est-à-dire qu’elles ont une position qui est continuedans le temps. Afin de détecter ces défauts, nous proposons d’abord un algorithme de détection basésur un ensemble d’approches statistiques appelées les méthodes a contrario. Cet algorithme fournitune détection précise et robuste aux bruits et aux textures présentes dans l’image. Nous proposonségalement une étape de filtrage temporel afin d’écarter les fausses alarmes de la première étape dedétection. Celle-ci améliore la précision de l’algorithme en analysant le mouvement des détections spatiales.L’ensemble de l’algorithme (détection spatiale et filtrage temporel) est comparé à des approchesde la littérature et montre un rappel et une précision grandement améliorés.La deuxième partie de cette thèse est consacrée à l’inpainting vidéo. Le but ici est de remplirune région d’une vidéo avec un contenu qui semble visuellement cohérent et convaincant. Il existeune pléthore de méthodes qui traite ce problème dans le cas des images. La littérature dans le casdes vidéos est plus restreinte, notamment car le temps d’exécution représente un véritable obstacle.Nous proposons un algorithme d’inpainting vidéo qui vise l’optimisation d’une fonctionnelle d’énergiequi intègre la notion de patchs, c’est-à-dire des petits cubes de contenu vidéo. Nous traitons d’abord leprobl’‘eme du temps d’exécution avant d’attaquer celui de l’inpainting satisfaisant des textures dans lesvidéos. Nous traitons également le cas des vidéos dont le fond est en mouvement ou qui ont été prisesavec des caméras en mouvement. Enfin, nous nous intéressons à certaines questions de convergencede l’algorithme dans des cas très simplifiés

Contributions to the Completeness and Complementarity of Local Image Features

Tese de doutoramento em Engenharia Informática apresentada à Faculdade de Ciências e Tecnologia da Universidade de CoimbraLocal image feature detection (or extraction, if we want to use a more semantically correct term) is a central and extremely active research topic in the field of computer vision. Reliable solutions to prominent problems such as matching, content-based image retrieval, object (class) recognition, and symmetry detection, often make use of local image features. It is widely accepted that a good local feature detector is the one that efficiently retrieves distinctive, accurate, and repeatable features in the presence of a wide variety of photometric and geometric transformations. However, these requirements are not always the most important. In fact, not all the applications require the same properties from a local feature detector. We can distinguish three broad categories of applications according to the required properties. The first category includes applications in which the semantic meaning of a particular type of features is exploited. For instance, edge or even ridge detection can be used to identify blood vessels in medical images or watercourses in aerial images. Another example in this category is the use of blob extraction to identify blob-like organisms in microscopic images. A second category includes tasks such as matching, tracking, and registration, which mainly require distinctive, repeatable, and accurate features. Finally, a third category comprises applications such as object (class) recognition, image retrieval, scene classification, and image compression. For this category, it is crucial that features preserve the most informative image content (robust image representation), while requirements such as repeatability and accuracy are of less importance. Our research work is mainly focused on the problem of providing a robust image representation through the use of local features. The limited number of types of features that a local feature extractor responds to might be insufficient to provide the so-called robust image representation. It is fundamental to analyze the completeness of local features, i.e., the amount of image information preserved by local features, as well as the often neglected complementarity between sets of features. The major contributions of this work come in the form of two substantially different local feature detectors aimed at providing considerably robust image representations. The first algorithm is an information theoretic-based keypoint extraction that responds to complementary local structures that are salient (highly informative) within the image context. This method represents a new paradigm in local feature extraction, as it introduces context-awareness principles. The second algorithm extracts Stable Salient Shapes, a novel type of regions, which are obtained through a feature-driven detection of Maximally Stable Extremal Regions (MSER). This method provides compact and robust image representations and overcomes some of the major shortcomings of MSER detection. We empirically validate the methods by investigating the repeatability, accuracy, completeness, and complementarity of the proposed features on standard benchmarks. Under these results, we discuss the applicability of both methods