Affine Matching with Bounded Sensor Error: A Study of Geometric Hashing and Alignment

Affine transformations are often used in recognition systems, to approximate the effects of perspective projection. The underlying mathematics is for exact feature data, with no positional uncertainty. In practice, heuristics are added to handle uncertainty. We provide a precise analysis of affine point matching, obtaining an expression for the range of affine-invariant values consistent with bounded uncertainty. This analysis reveals that the range of affine-invariant values depends on the actual $x$-$y$-positions of the features, i.e. with uncertainty, affine representations are not invariant with respect to the Cartesian coordinate system. We analyze the effect of this on geometric hashing and alignment recognition methods.

Geometric and Algebraic Aspects of 3D Affine and Projective Structures from Perspective 2D Views

We investigate the differences --- conceptually and algorithmically --- between affine and projective frameworks for the tasks of visual recognition and reconstruction from perspective views. It is shown that an affine invariant exists between any view and a fixed view chosen as a reference view. This implies that for tasks for which a reference view can be chosen, such as in alignment schemes for visual recognition, projective invariants are not really necessary. We then use the affine invariant to derive new algebraic connections between perspective views. It is shown that three perspective views of an object are connected by certain algebraic functions of image coordinates alone (no structure or camera geometry needs to be involved).

Relative Affine Structure: Canonical Model for 3D from 2D Geometry and Applications

We propose an affine framework for perspective views, captured by a single extremely simple equation based on a viewer-centered invariant we call "relative affine structure". Via a number of corollaries of our main results we show that our framework unifies previous work --- including Euclidean, projective and affine --- in a natural and simple way, and introduces new, extremely simple, algorithms for the tasks of reconstruction from multiple views, recognition by alignment, and certain image coding applications.

Object Recognition By Alignment Using Invariant Projections of Planar Surfaces

In order to recognize an object in an image, we must determine the best transformation from object model to the image. In this paper, we show that for features from coplanar surfaces which undergo linear transformations in space, there exist projections invariant to the surface motions up to rotations in the image field. To use this property, we propose a new alignment approach to object recognition based on centroid alignment of corresponding feature groups. This method uses only a single pair of 2D model and data. Experimental results show the robustness of the proposed method against perturbations of feature positions.

Pose-Invariant Face Recognition Using Real and Virtual Views

The problem of automatic face recognition is to visually identify a person in an input image. This task is performed by matching the input face against the faces of known people in a database of faces. Most existing work in face recognition has limited the scope of the problem, however, by dealing primarily with frontal views, neutral expressions, and fixed lighting conditions. To help generalize existing face recognition systems, we look at the problem of recognizing faces under a range of viewpoints. In particular, we consider two cases of this problem: (i) many example views are available of each person, and (ii) only one view is available per person, perhaps a driver's license or passport photograph. Ideally, we would like to address these two cases using a simple view-based approach, where a person is represented in the database by using a number of views on the viewing sphere. While the view-based approach is consistent with case (i), for case (ii) we need to augment the single real view of each person with synthetic views from other viewpoints, views we call 'virtual views'. Virtual views are generated using prior knowledge of face rotation, knowledge that is 'learned' from images of prototype faces. This prior knowledge is used to effectively rotate in depth the single real view available of each person. In this thesis, I present the view-based face recognizer, techniques for synthesizing virtual views, and experimental results using real and virtual views in the recognizer.

Rotation Invariant Real-time Face Detection and Recognition System

In this report, a face recognition system that is capable of detecting and recognizing frontal and rotated faces was developed. Two face recognition methods focusing on the aspect of pose invariance are presented and evaluated - the whole face approach and the component-based approach. The main challenge of this project is to develop a system that is able to identify faces under different viewing angles in realtime. The development of such a system will enhance the capability and robustness of current face recognition technology. The whole-face approach recognizes faces by classifying a single feature vector consisting of the gray values of the whole face image. The component-based approach first locates the facial components and extracts them. These components are normalized and combined into a single feature vector for classification. The Support Vector Machine (SVM) is used as the classifier for both approaches. Extensive tests with respect to the robustness against pose changes are performed on a database that includes faces rotated up to about 40 degrees in depth. The component-based approach clearly outperforms the whole-face approach on all tests. Although this approach isproven to be more reliable, it is still too slow for real-time applications. That is the reason why a real-time face recognition system using the whole-face approach is implemented to recognize people in color video sequences.

A Detailed Look at Scale and Translation Invariance in a Hierarchical Neural Model of Visual Object Recognition

The HMAX model has recently been proposed by Riesenhuber & Poggio as a hierarchical model of position- and size-invariant object recognition in visual cortex. It has also turned out to model successfully a number of other properties of the ventral visual stream (the visual pathway thought to be crucial for object recognition in cortex), and particularly of (view-tuned) neurons in macaque inferotemporal cortex, the brain area at the top of the ventral stream. The original modeling study only used ``paperclip'' stimuli, as in the corresponding physiology experiment, and did not explore systematically how model units' invariance properties depended on model parameters. In this study, we aimed at a deeper understanding of the inner workings of HMAX and its performance for various parameter settings and ``natural'' stimulus classes. We examined HMAX responses for different stimulus sizes and positions systematically and found a dependence of model units' responses on stimulus position for which a quantitative description is offered. Interestingly, we find that scale invariance properties of hierarchical neural models are not independent of stimulus class, as opposed to translation invariance, even though both are affine transformations within the image plane.

Rotation Invariant Object Recognition from One Training Example

Local descriptors are increasingly used for the task of object recognition because of their perceived robustness with respect to occlusions and to global geometrical deformations. Such a descriptor--based on a set of oriented Gaussian derivative filters-- is used in our recognition system. We report here an evaluation of several techniques for orientation estimation to achieve rotation invariance of the descriptor. We also describe feature selection based on a single training image. Virtual images are generated by rotating and rescaling the image and robust features are selected. The results confirm robust performance in cluttered scenes, in the presence of partial occlusions, and when the object is embedded in different backgrounds.

Matching Interest Points Using Projective Invariant Concentric Circles

We present a new method to perform reliable matching between different images. This method exploits a projective invariant property between concentric circles and the corresponding projected ellipses to find complete region correspondences centered on interest points. The method matches interest points allowing for a full perspective transformation and exploiting all the available luminance information in the regions. Experiments have been conducted on many different data sets to compare our approach to SIFT local descriptors. The results show the new method offers increased robustness to partial visibility, object rotation in depth, and viewpoint angle change.

An Efficient Correspondence Based Algorithm for 2D and 3D Model Based Recognition

A polynomial time algorithm (pruned correspondence search, PCS) with good average case performance for solving a wide class of geometric maximal matching problems, including the problem of recognizing 3D objects from a single 2D image, is presented. Efficient verification algorithms, based on a linear representation of location constraints, are given for the case of affine transformations among vector spaces and for the case of rigid 2D and 3D transformations with scale. Some preliminary experiments suggest that PCS is a practical algorithm. Its similarity to existing correspondence based algorithms means that a number of existing techniques for speedup can be incorporated into PCS to improve its performance.

Green Theorems and Qualitative Properties of the Optical Flow

How can one compute qualitative properties of the optical flow, such as expansion or rotation, in a way which is robust and invariant to the position of the focus of expansion or the center of rotation? We suggest a particularly simple algorithm, well-suited to VLSI implementations, that exploits well-known relations between the integral and differential properties of vector fields and their linear behaviour near singularities.

Limitations of Non Model-Based Recognition Schemes

Different approaches to visual object recognition can be divided into two general classes: model-based vs. non model-based schemes. In this paper we establish some limitation on the class of non model-based recognition schemes. We show that every function that is invariant to viewing position of all objects is the trivial (constant) function. It follows that every consistent recognition scheme for recognizing all 3-D objects must in general be model based. The result is extended to recognition schemes that are imperfect (allowed to make mistakes) or restricted to certain classes of objects.

On The Uniqueness of Correspondence Under Orthographic and Perspective Projections

The task of shape recovery from a motion sequence requires the establishment of correspondence between image points. The two processes, the matching process and the shape recovery one, are traditionally viewed as independent. Yet, information obtained during the process of shape recovery can be used to guide the matching process. This paper discusses the mutual relationship between the two processes. The paper is divided into two parts. In the first part we review the constraints imposed on the correspondence by rigid transformations and extend them to objects that undergo general affine (non rigid) transformation (including stretch and shear), as well as to rigid objects with smooth surfaces. In all these cases corresponding points lie along epipolar lines, and these lines can be recovered from a small set of corresponding points. In the second part of the paper we discuss the potential use of epipolar lines in the matching process. We present an algorithm that recovers the correspondence from three contour images. The algorithm was implemented and used to construct object models for recognition. In addition we discuss how epipolar lines can be used to solve the aperture problem.

Distance Metric Between 3D Models and 3D Images for Recognition and Classification

Similarity measurements between 3D objects and 2D images are useful for the tasks of object recognition and classification. We distinguish between two types of similarity metrics: metrics computed in image-space (image metrics) and metrics computed in transformation-space (transformation metrics). Existing methods typically use image and the nearest view of the object. Example for such a measure is the Euclidean distance between feature points in the image and corresponding points in the nearest view. (Computing this measure is equivalent to solving the exterior orientation calibration problem.) In this paper we introduce a different type of metrics: transformation metrics. These metrics penalize for the deformatoins applied to the object to produce the observed image. We present a transformation metric that optimally penalizes for "affine deformations" under weak-perspective. A closed-form solution, together with the nearest view according to this metric, are derived. The metric is shown to be equivalent to the Euclidean image metric, in the sense that they bound each other from both above and below. For Euclidean image metric we offier a sub-optimal closed-form solution and an iterative scheme to compute the exact solution.

Viewer-Centered Object Recognition in Monkeys

How does the brain recognize three-dimensional objects? We trained monkeys to recognize computer rendered objects presented from an arbitrarily chosen training view, and subsequently tested their ability to generalize recognition for other views. Our results provide additional evidence in favor of with a recognition model that accomplishes view-invariant performance by storing a limited number of object views or templates together with the capacity to interpolate between the templates (Poggio and Edelman, 1990).