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Practical Reliable Bayesian Recognition of 2D and 3D Objects Using Implicit Polynomials and Algebraic Invariants
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1996
"... Patches of quadric curves and surfaces such as spheres, planes and cylinders have found widespread use in modeling and recognition of objects of interest in computer vision. In this paper, we treat use of more complex higher degree polynomial curves and surfaces of degree higher than two, which have ..."
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Cited by 47 (11 self)
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Patches of quadric curves and surfaces such as spheres, planes and cylinders have found widespread use in modeling and recognition of objects of interest in computer vision. In this paper, we treat use of more complex higher degree polynomial curves and surfaces of degree higher than two, which have many desirable properties for object recognition and position estimation, and attack the instability problem arising in their use with partial and noisy data. The scenario discussed in this paper is one where we have a set of objects that are modeled as implicit polynomial functions, or a set of representations of classes of objects with each object in a class modeled as an implicit polynomial function, stored in the database. Then, given partial data from one of the objects, we want to recognize the object (or the object class) or collect more data in order to get better parameter estimates for more reliable recognition. Two problems arising in this scenario are discussed in this paper : (...
Robust Segmentation of Primitives from Range Data in the Presence of Geometric Degeneracy
 IEEE TRANS. PATTERN ANAL. MACH. INTELL
, 2001
"... This paper presents methods for the leastsquares fitting of spheres, cylinders, cones, and tori to 3D point data, and their application within a segmentation framework. Leastsquares fitting of surfaces other than planes, even of simple geometric type, has been rarely studied. Our main application ..."
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Cited by 40 (0 self)
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This paper presents methods for the leastsquares fitting of spheres, cylinders, cones, and tori to 3D point data, and their application within a segmentation framework. Leastsquares fitting of surfaces other than planes, even of simple geometric type, has been rarely studied. Our main application areas of this research are reverse engineering of solid models from depthmaps and automated 3D inspection where reliable extraction of these surfaces is essential. Our fitting method has the particular advantage of being robust in the presence of geometric degeneracy, i.e., as the principal curvatures of the surfaces being fitted decrease (or become more equal), the results returned naturally become closer and closer to those surfaces of simpler type, i.e., planes, cylinders, cones, or spheres, which best describe the data. Many other methods diverge because, in such cases, various parameters or their combination become infinite.
Faithful LeastSquares Fitting of Spheres, Cylinders, Cones and Tori for Reliable Segmentation
 PROC. 5TH EUROPEAN CONF. COMPUTER VISION
, 1998
"... This paper addresses a problem arising in the reverse engineering of solid models from depthmaps. We wish to identify and fit surfaces of known type wherever these are a good fit. This paper presents a set of methods for the leastsquares fitting of spheres, cylinders, cones and tori to threed ..."
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Cited by 37 (7 self)
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This paper addresses a problem arising in the reverse engineering of solid models from depthmaps. We wish to identify and fit surfaces of known type wherever these are a good fit. This paper presents a set of methods for the leastsquares fitting of spheres, cylinders, cones and tori to threedimensional point data. Leastsquares fitting of surfaces other planes, even of simple geometric type, has been little studied. Our method
Stochastic Plans for Robotic Manipulation
, 1990
"... Geometric uncertainty is unavoidable when programming robots for physical applications. We propose a stochastic framework for manipulation planning where plans are ranked on the basis of expected cost. That is, we express the desirability of states and actions with a cost function and describe uncer ..."
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Cited by 35 (7 self)
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Geometric uncertainty is unavoidable when programming robots for physical applications. We propose a stochastic framework for manipulation planning where plans are ranked on the basis of expected cost. That is, we express the desirability of states and actions with a cost function and describe uncertainty with probability distributions. We illustrate the approach with a new design for a programmable parts feeder, a mechanism that orients twodimensional parts using a sequence of openloop mechanical motions. We present a planning algorithm that accepts an nsided polygonal part as input and, in time O(n²), generates a stochastically optimal plan for orienting the part.
Locally Bayesian Learning with Applications to Retrospective Revaluation and Highlighting
 Psychological Review
, 2006
"... A scheme is described for locally Bayesian parameter updating in models structured as successions of component functions. The essential idea is to backpropagate the target data to interior modules, such that an interior component’s target is the input to the next component that maximizes the probab ..."
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Cited by 26 (7 self)
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A scheme is described for locally Bayesian parameter updating in models structured as successions of component functions. The essential idea is to backpropagate the target data to interior modules, such that an interior component’s target is the input to the next component that maximizes the probability of the next component’s target. Each layer then does locally Bayesian learning. The approach assumes online trialbytrial learning. The resulting parameter updating is not globally Bayesian but can better capture human behavior. The approach is implemented for an associative learning model that first maps inputs to attentionally filtered inputs and then maps attentionally filtered inputs to outputs. The Bayesian updating allows the associative model to exhibit retrospective revaluation effects such as backward blocking and unovershadowing, which have been challenging for associative learning models. The backpropagation of target values to attention allows the model to show trialorder effects, including highlighting and differences in magnitude of forward and backward blocking, which have been challenging for Bayesian learning models.
A Bayesian Segmentation Methodology for Parametric Image Models
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1993
"... Regionbased image segmentation methods require some criterion for determining when to merge regions. This paper presents a novel approach by introducing a Bayesian probability of homogeneity in a general statistical context. Our approach does not require parameter estimation, and is therefore pa ..."
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Cited by 22 (4 self)
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Regionbased image segmentation methods require some criterion for determining when to merge regions. This paper presents a novel approach by introducing a Bayesian probability of homogeneity in a general statistical context. Our approach does not require parameter estimation, and is therefore particularly beneficial for cases in which estimationbased methods are most prone to error: when little information is contained in some of the regions and, therefore, parameter estimates are unreliable. We apply this formulation to three distinct parametric model families that have been used in past segmentation schemes: implicit polynomial surfaces, parametric polynomial surfaces, and Gaussian Markov random fields. We present results on a variety of real range and intensity images. 1 Introduction The problem of image segmentation, partitioning an image into a set of homogeneous regions, is a fundamental problem in computer vision. Approaches to the segmentation problem can be grouped...
Representing Partial and Uncertain Sensorial Information Using the Theory of Symmetries
 IEEE International Conference on Robotics and Automation
, 1992
"... In this paper, we propose a general model for representing sensorial information and its uncertainty, the Symmetries and Perturbation model (SPmodel). In it, the intrinsic partiality of geometric information is represented in terms of the symmetries of the involved geometric elements. Location uncer ..."
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Cited by 18 (7 self)
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In this paper, we propose a general model for representing sensorial information and its uncertainty, the Symmetries and Perturbation model (SPmodel). In it, the intrinsic partiality of geometric information is represented in terms of the symmetries of the involved geometric elements. Location uncertainty due to sensor imprecision is represented by means of a local perturbation, expressed in a reference frame attached to the geometric element, with an associated probabilistic model. Using the SPmodel, we develop a method for integrating geometric information that allows to estimate the location of a feature or an object from a set of partial and uncertain observations. The integration mechanism is based on extended Kalman filter theory. 1
Object Reconstruction By Incorporating Geometric Constraints in Reverse Engineering
 ComputerAided Design
, 1999
"... This paper deals with the constrained reconstruction of 3D geometric models of objects from range data. It describes a new technique of global shape improvement based upon feature positions and geometric constraints. It suggests a general incremental framework whereby constraints can be added and in ..."
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Cited by 15 (3 self)
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This paper deals with the constrained reconstruction of 3D geometric models of objects from range data. It describes a new technique of global shape improvement based upon feature positions and geometric constraints. It suggests a general incremental framework whereby constraints can be added and integrated in the model reconstruction process, resulting in an optimal tradeoff between minimization of the shape fitting error and the constraint tolerances. After defining sets of constraints for planar and special case quadric surface classes based on feature coincidence, position and shape, the paper shows through application on synthetic model that our scheme is well behaved. The approach is then validated through experiments on different real parts. This work is the first to give such a large framework for the integration of geometric relationships in object modelling. The technique is expected to have a great impact in reverse engineering applications and manufactured object modelling where the majority of parts are designed with intended feature relationships. Keywords Reverse engineering, Geometric constraints, constrained shape reconstruction, shape optimization. 2
Toward a ModelBased Bayesian Theory for Estimating and Recognizing Parameterized 3D Objects Using Two or More Images Taken from Different Positions
 IEEE Trans. on PAMI
, 1989
"... AbstractA new approach is introduced to estimating object surfaces in threedimensional space from two or more images. A surface of interest here is modeled as a 3D function known up to the values of a few parameters. Although the approach will work with any parameterization, we model objects as p ..."
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Cited by 15 (4 self)
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AbstractA new approach is introduced to estimating object surfaces in threedimensional space from two or more images. A surface of interest here is modeled as a 3D function known up to the values of a few parameters. Although the approach will work with any parameterization, we model objects as patches of spheres, cylinders, planes, and general quadricsprimitive objects. Primitive surface estimation is treated as the general problem of maximum likelihood parameter estimation of the a priori unknown primitive surface parameters based on two or more functionally related data sets. In our case, these data sets constitute two or more images taken by cameras at different locations and orientations. A simple geometric explanation is given for the estimation algorithm. Although various techniques can be used to implement this nonlinear estimation, we discuss the use of gradient descent. Experiments are run and discussed. Our approach includes the commonly used stereo approaches as special cases. The Cramer
Probabilistic Identity Characterization for Face Recognition
"... We present a general framework for characterizing the object identity in a single image or a group of images with each image containing a transformed version of the object, with applications to face recognition. In terms of the transformation, the group is made of either many still images or frames ..."
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Cited by 13 (4 self)
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We present a general framework for characterizing the object identity in a single image or a group of images with each image containing a transformed version of the object, with applications to face recognition. In terms of the transformation, the group is made of either many still images or frames of a video sequence. The object identity is either discrete or continuousvalued. This probabilistic framework integrates all the evidence of the set and handles the localization problem, illumination and pose variations through subspace identity encoding. Issues and challenges arising in this framework are addressed and efficient computational schemes are presented. Good face recognition results using the PIE database are reported.