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45
On Photometric Issues in 3D Visual Recognition From A Single 2D Image
 International Journal of Computer Vision
, 1997
"... . We describe the problem of recognition under changing illumination conditions and changing viewing positions from a computational and human vision perspective. On the computational side we focus on the mathematical problems of creating an equivalence class for images of the same 3D object undergo ..."
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Cited by 109 (6 self)
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. We describe the problem of recognition under changing illumination conditions and changing viewing positions from a computational and human vision perspective. On the computational side we focus on the mathematical problems of creating an equivalence class for images of the same 3D object undergoing certain groups of transformations  mostly those due to changing illumination, and briefly discuss those due to changing viewing positions. The computational treatment culminates in proposing a simple scheme for recognizing, via alignment, an image of a familiar object taken from a novel viewing position and a novel illumination condition. On the human vision aspect, the paper is motivated by empirical evidence inspired by Mooney images of faces that suggest a relatively high level of visual processing is involved in compensating for photometric sources of variability, and furthermore, that certain limitations on the admissible representations of image information may exist. The psycho...
Recognition and Structure from one 2D Model View: Observations on Prototypes, Object Classes and Symmetries
 Laboratory, Massachusetts Institute of Technology
, 1992
"... According to the 1.5 views theorem (Poggio, 1990; Ullman and Basri, 1991) recog nition of a specific 3D object (defined in terms of pointwise features) from a novel 2D view can be achieved from at least two 2D model views (in the data basis, for each object, for orthographic projection). In this ..."
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Cited by 86 (29 self)
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According to the 1.5 views theorem (Poggio, 1990; Ullman and Basri, 1991) recog nition of a specific 3D object (defined in terms of pointwise features) from a novel 2D view can be achieved from at least two 2D model views (in the data basis, for each object, for orthographic projection). In this note we discuss how recognition can be achieved from a single 2D model view. The basic idea is to exploit transformations that are specific for the object class corresponding to the object  and that may be known a priori or may be learned from views of other "prototypical" objects of the same class  to generate new model views from the only one available. The paper is organized in two distinct parts. In the first part, we discuss how to exploit prior knowledge of an object's symmetry. We prove that for any bilaterally symmetric 3D object one nonaccidental 2D model view is sufficient for recognition. We also prove that for bilaterally symmetric objects the correspondence of four points between two views determines the correspondence of all other points. Symmetries of higher order allow the recovery of structure from one 2D view. In the second part of the paper, we study a very simple type of object classes that we call linear object classes. Linear transformations can be learned exactly from a small set of examples in the case of linear object classes and used to produce new views of an object from a single view. We also provide natural examples of linear object classes induced by symmetry properties of the objects.
Projective Structure from Uncalibrated Images: Structure from Motion and Recognition
, 1994
"... We address the problem of reconstructing 3D space in a projective framework from two or more views, and the problem of artificially generating novel views of the scene from two given views (reprojection). We describe an invariance relation which provides a new description of structure, we call proj ..."
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Cited by 62 (14 self)
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We address the problem of reconstructing 3D space in a projective framework from two or more views, and the problem of artificially generating novel views of the scene from two given views (reprojection). We describe an invariance relation which provides a new description of structure, we call projective depth, which is captured by a single equation relating image point correspondences across two or more views and the homographies of two arbitrary virtual planes. The framework is based on knowledge of correspondence of features across views, is linear, extremely simple, and the computations of structure readily extends to overdetermination using multiple views. Experimental results demonstrate a high degree of accuracy in both tasks  reconstruction and reprojection. KeywordsVisual Recognition, 3D Reconstruction from 2D Views, Projective Geometry, Algebraic and Geometric Invariants. I. Introduction The geometric relation between objects (or scenes) in the world and their imag...
Synthesis of Novel Views From a Single Face Image
, 1996
"... Images formed by a human face change with viewpoint. A new technique is described for synthesizing images of faces from new viewpoints, when only a single 2D image is available. A novel 2D image of a face can be computed without knowledge about the 3D structure of the head. The technique draws on a ..."
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Cited by 52 (5 self)
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Images formed by a human face change with viewpoint. A new technique is described for synthesizing images of faces from new viewpoints, when only a single 2D image is available. A novel 2D image of a face can be computed without knowledge about the 3D structure of the head. The technique draws on a single generic 3D model of a human head and on prior knowledge of faces based on example images of other faces seen in different poses. The example images are used to "learn" a poseinvariant shape and texture description of a new face. The 3D model is used to solve the correspondence problem between images showing faces in different poses. Examples of synthetic "rotations" over 24 ffi based on a training set of 100 faces are shown. This document is available as /pub/mpimemos/TR026.ps.Z via anonymous ftp from ftp.mpiktueb.mpg.de or from the World Wide Web, http://www.mpiktueb.mpg.de/projects/TechReport/list.html. 1 Introduction Given only a driver's license photograph of a person's ...
ModelBased Invariants for 3D Vision
 International Journal of Computer Vision
, 1993
"... Invariance under a group of 3D transformations seems a desirable component of an efficient 3D shape representation. We propose representations which are invariant under weak perspective to either rigid or affine 3D transformations, and we show how they can be computed efficiently from a sequence of ..."
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Cited by 35 (8 self)
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Invariance under a group of 3D transformations seems a desirable component of an efficient 3D shape representation. We propose representations which are invariant under weak perspective to either rigid or affine 3D transformations, and we show how they can be computed efficiently from a sequence of images with a linear and incremental algorithm. We show simulated results with perspective projection and noise, and the results of model acquisition from a real sequence of images. The use of linear computation, together with the integration through time of invariant representations, offers improved robustness and stability. Using these invariant representations, we derive modelbased projective invariant functions of general 3D objects. We discuss the use of the modelbased invariants with existing recognition strategies: alignment without transformation, and constant time indexing from 2D images of general 3D objects.
Projective Structure from two Uncalibrated Images: Structure from Motion and Recognition
 A.I. MEMO
, 1992
"... This paper addresses the problem of recovering relative structure, in the form of an invariant, from two views of a 3D scene. The invariant structure is computed without any prior knowledge of camera geometry, or internal calibration, and with the property that perspective and orthographic project ..."
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Cited by 32 (3 self)
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This paper addresses the problem of recovering relative structure, in the form of an invariant, from two views of a 3D scene. The invariant structure is computed without any prior knowledge of camera geometry, or internal calibration, and with the property that perspective and orthographic projections are treated alike, namely, the system makes no assumption regarding the existence of perspective distortions in the input images. We show that
Rigidity Checking of 3D Point Correspondences Under Perspective Projection
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1996
"... An algorithm is described which rapidly verifies the potential rigidity of three dimensional point correspondences from a pair of two dimensional views under perspective projection. The output of the algorithm is a simple yes or no answer to the question "Could these corresponding points from two vi ..."
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Cited by 29 (3 self)
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An algorithm is described which rapidly verifies the potential rigidity of three dimensional point correspondences from a pair of two dimensional views under perspective projection. The output of the algorithm is a simple yes or no answer to the question "Could these corresponding points from two views be the projection of a rigid configuration?" Potential applications include 3D object recognition from a single previous view and correspondence matching for stereo or motion over widely separated views. Our analysis begins with the observation that it is often the case that two views cannot provide an accurate structurefrommotion estimate because of ambiguity and illconditioning. However, it is argued that an accurate yes/no answer to the rigidity question is possible and experimental results support this assertion with as few as six pairs of corresponding points over a wide range of scene structures and viewing geometries. Rigidity checking verifies point correspondences by using 3D ...
Rigid Body Segmentation and Shape Description from Dense Optical Flow under Weak Perspective
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1997
"... We present an algorithm for identifying and tracking independently moving rigid objects from optical flow. Some previous attempts at segmentation via optical flow have focused on finding discontinuities in the flow field. While discontinuities do indicate a change in scene depth, they do not in gene ..."
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Cited by 25 (0 self)
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We present an algorithm for identifying and tracking independently moving rigid objects from optical flow. Some previous attempts at segmentation via optical flow have focused on finding discontinuities in the flow field. While discontinuities do indicate a change in scene depth, they do not in general signal a boundary between two separate objects. The proposed method uses the fact that each distinct object has a unique epipolar constraint associated with its motion. Thus motion discontinuities based on selfocclusion are distinguished from those due to separate objects. The use of epipolar geometry allows for the determination of individual motion parameters for each object as well as the recovery of relative depth for each point on the object. The segmentation problem is formulated as a scene partitioning problem and a statisticbased algorithm which uses only nearest neighbor interactions and a finite number of iterations is developed. After the initial segmentation, each rigid obj...
On Geometric and Algebraic Aspects of 3D Affine and Projective Structures from Perspective 2D Views
 In Proceedings of the 2nd European Workshop on Invariants, Ponta Delagada, Azores
, 1993
"... Part I of this paper investigates 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 ..."
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Cited by 23 (8 self)
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Part I of this paper investigates 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. The projective extension is then derived, showing that it is necessary only for tasks for which a reference view is not available  such as happens when updating scene structure from a moving stereo rig. The geometric difference between the two proposed invariants are that the affine invariant measures the relative deviation from a single reference plane, whereas the projective invariant measures the relative deviation from two reference planes. The affine invariant can be computed from three correspondin...