There have been various developments in shape analysis in the last decade. We describe here some relationships of shape analysis with directional statistics. For shape, rotations are to be integrated out or to be optimized over whilst they are the basis for directional statistics. However, various concepts are connected. In particular, certain distributions of directional statistics have emerged in shape analysis, such a distribution is Complex Bingham Distribution. This paper first gives some background to shape analysis and then it goes on to directional distributions and their applications to shape analysis. Note that the idea of using tangent space for analysis is common to both manifold as well. 1 Introduction Consider shapes of configurations of points in Euclidean space. There are various contexts in which k labelled points (or "landmarks") x 1 ; :::; x k in IR m are given and interest is in the shape of (x 1 ; :::; x k ). Example 1 The microscopic fossil Globorotalia truncat...

. Many object classes, including human faces, can be modeled as a set of characteristic parts arranged in a variable spatial configuration. We introduce a simplified model of a deformable object class and derive the optimal detector for this model. However, the optimal detector is not realizable except under special circumstances (independent part positions). A cousin of the optimal detector is developed which uses "soft" part detectors with a probabilistic description of the spatial arrangement of the parts. Spatial arrangements are modeled probabilistically using shape statistics to achieve invariance to translation, rotation, and scaling. Improved recognition performance over methods based on "hard" part detectors is demonstrated for the problem of face detection in cluttered scenes. 1 Introduction Visual recognition of objects (chairs, sneakers, faces, cups, cars) is one of the most challenging problems in computer vision and artificial intelligence. Historically, there has been a...

An algorithm for locating quasi-frontal views of human faces in cluttered scenes is presented. The algorithm works by coupling a set of local feature detectors with a statistical model of the mutual distances between facial features; it is invariant with respect to translation, rotation (in the plane), and scale and can handle partial occlusions of the face. On a challenging database with complicated and varied backgrounds, the algorithm achieved a correct localization rate of 95% in images where the face appeared quasi-frontally. 1 Introduction The problem of face recognition has received considerable attention from the computer vision community, and a number of techniques have been proposed in the literature [3, 11, 12, 13, 14, 16, 17, 19]. However, in most of these studies the face was in a benign environment from which it could easily be extracted, or it was assumed to have been pre-segmented. For any of these recognition algorithms to work in a general setting, we need a system...

We present a new framework for recognizing planar object classes, which is based on local feature detectors and a probabilistic model of the spatial arrangement of the features. The allowed object deformations are represented through shape statistics, which are learned from examples. Instances of an object in an image are detected by finding the appropriate features in the correct spatial configuration. The algorithm is robust with respect to partial occlusion, detector false alarms, and missed features. A 94% success rate was achieved for the problem of locating quasi-frontal views of faces in cluttered scenes. 1 Introduction Many early pattern recognition algorithms were based on template matching [13], which is optimal for detecting a known signal in white noise. However, since the underlying assumption that "the signal is known exactly" rarely holds true, considerable effort has been devoted to extending this method to handle variability in the target signal. For example, approach...

In this paper, a face localization system is proposed in which local detectors are coupled with a statistical model of the spatial arrangement of facial features to yield robust performance. The outputs from the local detectors are treated as candidate locations and constellations are formed from these. The effects of translation, rotation, and scale are eliminated by mapping to a set of shape variables. The constellations are then ranked according to the likelihood that the shape variables correspond to a face versus an alternative model. Incomplete constellations, which occur when some of the true features are missed, are handled in a principled way. 1 Introduction The problem of face recognition has received considerable attention in the literature [11, 24, 21, 4, 19, 17, 22, 10]; however, in most of these studies, the faces were either embedded in a benign background or were assumed to have been pre-segmented. For any of these recognition algorithms to work in realworld applicati...

Under a weak perspective camera model, the image plane coordinates in different views of a planar object are related by an affine transformation. Because of this property, researchers have attempted to use affine invariants for recognition. However, there are two problems with this approach: (1) objects or object classes with inherent variability cannot be adequately treated using invariants; and (2) in practice the calculated affine invariants can be quite sensitive to errors in the image plane measurements. In this paper we use probability distributions to address both of these difficulties. Under the assumption that the feature positions of a planar object can be modeled using a jointly Gaussian density, we have derived the joint density over the corresponding set of affine coordinates. Even when the assumptions of a planar object and a weak perspective camera model do not strictly hold, the results are useful because deviations from the ideal can be treated as deformability in the ...

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The paper reviews various topics in shape analysis. In particular, matching configurations using regression is emphasized. Connections with general shape spaces and shape distances are discussed. Kendall's shape space and the affine shape space are considered in particular detail. Matching two configurations and the extension to generalized matching are illustrated with applications in electrophoresis and biology. Shape distributions are briefly discussed and inference in tangent spaces is considered. Finally, some robustness and smoothing issues are highlighted. 1 Introduction The geometrical description of an object can be decomposed into registration and shape information. For example, an object's location, rotation and size could be the registration information and the geometrical information that remains is the object's shape. An object's shape is invariant under registration transformations and two objects have the same shape if they can be registered to match exactly. Depending...

Different instances of a handwritten word consist of the same basic features (humps, cusps, crossings, etc.) arranged in a deformable spatial pattern. Thus, keywords in cursive text can be detected by looking for the appropriate features in the "correct" spatial configuration. A keyword can be modeled hierarchically as a set of word fragments, each of which consists of lowerlevel features. To allow flexibility, the spatial configuration of keypoints within a fragment is modeled using a Dryden-Mardia (DM) probability density over the shape of the configuration. In a writer-dependent test on a transcription of the Declaration of Independence (¸1300 words, ¸7500 characters), the method detected all eleven instances of the keyword "government " with only four false positives. 1 Introduction Handwriting offers a more natural human-computer interface than the traditional keyboard. A keyboard is frustrating for children and other novice users who possess limited typing skills. Even advance...

Object recognition is both about recognizing specific objects, e.g., "That is my dog Spot." and about recognizing classes of objects, e.g., "That is a dog." Our focus is on the latter problem, even though we do not offer a precise definition for what constitutes a class. In some cases, for example with human faces, the objects in a class are visually similar and form a visual object class. In other cases, say chairs, objects in the class may not look at all alike---the only similarities are in function. Recognition of functional object classes requires higher-level cognitive reasoning, we restrict here our attention to visual object classes. The main difficulty in object recognition is the problem of invariance. The pixel representation provided by the camera is dependent upon the lighting conditions, object pose, camera position, etc. Further, there is inherent variability between different instances from the same object class. Our approach to this problem is to model an object class ...