Spin Glass Models of Markov Random Fields

This paper presents a novel algorithm for robust object recognition. We propose to model the visual appearance of objects via probability density functions. The algorithm consists of a fully connected Markov random field with energy function derived from results of statistical physics of spin glasses. Markov random fields and spin glass energy functions are combined together via nonlinear kernel functions; we call the model Spin Glass\--Markov Random Field. Full connectivity enables to take into account the global appearance of the object, and its specific local characteristics at the same time, resulting in robustness to noise, occlusions and cluttered background. We show with theoretical analysis and experiments that this new model is competitive with state-of-the-art algorithms

Object recognition and retrieval by context dependent similarity kernels

International audienceThe success of kernel methods including support vector machines (SVMs) strongly depends on the design of appropriate kernels. While initially kernels were designed in order to handle fixed-length data, their extension to unordered, variable-length data became more than necessary for real pattern recognition problems such as object recognition and bioinformatics. We focus in this paper on object recognition using a new type of kernel referred to as "context-dependent". Objects, seen as constellations of local features (interest points, regions, etc.), are matched by minimizing an energy function mixing (1) a fidelity term which measures the quality of feature matching, (2) a neighborhood criteria which captures the object geometry and (3) a regularization term. We will show that the fixed-point of this energy is a "context-dependent" kernel ("CDK") which also satisfies the Mercer condition. Experiments conducted on object recognition show that when plugging our kernel in SVMs, we clearly outperform SVMs with "context-free" kernels

Verfahren zur Analyse von Ähnlichkeit im Ortsbereich

The increasing use of high-resolution image sensors in both stationary and mobile applications require improved image recognition algorithms. The Hausdorff distance is a measure of the likeness of two sets of points, and can be used to determine the resemblance of two sets of image points. However, is not widely used. Therefore, this dissertation deals with a method of using the Hausdorff distance to determine the resemblance of image regions. We introduce a suitable model to describe linear deviations. We show how to compensate for these linear deviations and use a probability distribution for their classification. We give bounds for the non-linear deviations and minimize noise. Our starting point is the mathematical description of the mentioned criterion for deviation. We calculate deviation of pairs of image points and encode it in a three-dimensional vector field. This vector field also contains the directions in which differences are decreasing. Using this information we obtain a probability density function which gives a measure of similarity. We interpret transformation of distances as a stochastic vector process. This opens up new directions for compensating for geometric displacements of image regions. We then use our deviation model in a control loop to minimize linear deformations. Our filter proves robust with respect to Gaussian noise. We show equivalence of the metrics $d_2$ and $d_1$ for Gaussian noise. This is the main prerequisite for hardwired speed improvements, and we use it in the design of a distance processor. With the help of our distance processor we show that our control loop is stable. When using the directional information in the distance vector field we observe an increase of the correlation of image regions in question. A correction transformation greatly reduces sensitivity to noise of the Hausdorff distance. Our resource-friendly VHDL design allows the real-time calculation of distance vector fields with current FPGAs. The stability of our control loop improves when we include neighboring regions to evaluate the likeness of image regions. This is particularly true when comparing faces.Aus der zunehmenden Nutzung von hochauflösenden Bildsensoren in stationären sowie mobilen Anwendungsbereichen erwachsen neue Anforderungen an die Algorithmen der Bilderkennnung. Eines der ursprünglichsten Kriterien zur Beurteilung der Ähnlichkeit von Bildpunkten als Mengen findet aber nur wenig Beachtung, die Hausdorff-Distanz. Daher behandelt die vorliegende Arbeit ein Verfahren zum Einsatz dieses Abstandsmaßes. Die Darlegungen umfassen die Einführung eines geeigneten Modells zur Beschreibung von linearen Abweichungen, deren Kompensation und Beurteilung anhand zugehöriger Wahrscheinlichkeitsverteilungen. Ausgangspunkt dieser Arbeit sind die mathematische Beschreibung des genannten Kriteriums und die Berechnung einer Abweichungsinformation, die als dreidimensionales Distanzvektorfeld auch die Richtung zur Verringerung der Unterschiede enthält. Sie bilden die Grundlage für die Darstellungsformen der Häufigkeitsverteilungen und Wahrscheinlichkeitsdichten, anhand derer die Entscheidungen in Bezug auf Ähnlichkeit gefällt werden. Die Interpretation der Distanztransformation als vektorieller Zufallsprozeß eröffnet völlig neue Möglichkeiten zur Kompensation von geometrischem Versatz der Bildinhalte. Unter Nutzung des eingeführten Abweichungsmodells erfolgt die Anwendung einer Regelschleife zur Minimierung der linearen Deformation. Gleichzeit erweist sich das Filtersystem als unempfindlich gegenüber normalverteilten Störsignalen. Die Zulässigkeit einer gewissen Gleichberechtigung der Metriken $d_2$ und $d_1$ für normalverteiles Rauschen wird gezeigt. Daraus ergibt sich die wesentliche Voraussetzung für den Einsatz von schaltungstechnischen Beschleunigungsmaßnahmen, die im Entwurf eines Distanzprozessors münden. Mit der Unterstützung des Distanzprozessors gelingt der Nachweis der Stabilität der Regelschleife. Gleichzeitig ist eine Erhöhung des Korrelationsfaktors der betrachteten Bildausschnitte unter Nutzung der Richtungsinformation des Distanzvektorfeldes zu beobachten. Die Einbeziehung der Nachbarschaftsregionen in die Beurteilung der Ähnlichkeit zur Korrektur von Verformungen erzielt besonders beim Vergleich von Gesichtern hervorragende Ergebnisse in Bezug auf Stabilität der Regelschleife und Erhöhung der Aussagekraft der Häufigkeitsverteilungen

Hausdorff Kernel for 3D Object Acquisition and Detection

Learning one class at a time can be seen as an effective solution to classification problems in which only the positive examples are easily identifiable. A kernel method to accomplish this goal consists of a representation stage - which computes the smallest sphere in feature space enclosing the positive examples - and a classification stage - which uses the obtained sphere as a decision surface to determine the positivity of new examples. In this paper we describe a kernel well suited to represent, identify, and recognize 3D objects from unconstrained images. The kernel we introduce, based on Hausdorff distance, is tailored to deal with grey-level image matching. The effectiveness of the proposed method is demonstrated on several data sets of faces and objects of artistic relevance, like statues