3DPO: A three-dimensional part orientation system
International Journal of Robotics Research
IEEE Transactions on Pattern Analysis and Machine Intelligence
Direct least-squares fitting of algebraic surfaces
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Bayesian Clustering for Unsupervised Estimation of Surface and Texture Models
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
Invariant Descriptors for 3D Object Recognition and Pose
IEEE Transactions on Pattern Analysis and Machine Intelligence - Special issue on interpretation of 3-D scenes—part I
From Uncertainty to Visual Exploration
IEEE Transactions on Pattern Analysis and Machine Intelligence - Special issue on interpretation of 3-D scenes—part I
Object recognition based on moment (or algebraic) invariants
Geometric invariance in computer vision
Describing Complicated Objects by Implicit Polynomials
IEEE Transactions on Pattern Analysis and Machine Intelligence
Parts of Visual Form: Computational Aspects
IEEE Transactions on Pattern Analysis and Machine Intelligence
Parameterized Families of Polynomials for Bounded Algebraic Curve and Surface Fitting
IEEE Transactions on Pattern Analysis and Machine Intelligence
COSMOS-A Representation Scheme for 3D Free-Form Objects
IEEE Transactions on Pattern Analysis and Machine Intelligence
Linear Programming Fitting of Implicit Polynomials
IEEE Transactions on Pattern Analysis and Machine Intelligence
Recognition Using Region Correspondences
International Journal of Computer Vision
Fitting Curves and Surfaces With Constrained Implicit Polynomials
IEEE Transactions on Pattern Analysis and Machine Intelligence
On Interactive Object Shape Modeling Using Algebraic Curves
Journal of VLSI Signal Processing Systems - special issue on multimedia signal processing
The 3L Algorithm for Fitting Implicit Polynomial Curves and Surfaces to Data
IEEE Transactions on Pattern Analysis and Machine Intelligence
Recognizing 3D Objects Using Tactile Sensing and Curve Invariants
Journal of Mathematical Imaging and Vision
Reconstruction of Three-Dimensional Objects through Matching of Their Parts
IEEE Transactions on Pattern Analysis and Machine Intelligence
Implicitization of Parametric Curves by Matrix Annihilation
International Journal of Computer Vision - Special Issue on Computational Vision at Brown University
The Classical Theory of Invariants and Object Recognition Using Algebraic Curve and Surfaces
Journal of Mathematical Imaging and Vision
Covariant-Conics Decomposition of Quartics for 2D Shape Recognition and Alignment
Journal of Mathematical Imaging and Vision
Topologically Faithful Fitting of Simple Closed Curves
IEEE Transactions on Pattern Analysis and Machine Intelligence
Stable Fitting of 2D Curves and 3D Surfaces by Implicit Polynomials
IEEE Transactions on Pattern Analysis and Machine Intelligence
Curves vs. skeletons in object recognition
Signal Processing - Special section on content-based image and video retrieval
Kernel PCA for similarity invariant shape recognition
Neurocomputing
Multilevel algebraic invariants extraction by incremental fitting scheme
ACCV'09 Proceedings of the 9th Asian conference on Computer Vision - Volume Part I
A representation of time series based on implicit polynomial curve
Pattern Recognition Letters
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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 2, 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: 1) the problem of recognizing these polynomials by comparing them in terms of their coefficients, which are global descriptors, or in terms of algebraic invariants, i.e., functions of the polynomial coefficients that are independent of translations, rotations, and general linear transformation of the data; and 2) the problem of where to collect data so as to improve the parameter estimates as quickly as possible. We solve these problems by formulating them within a probabilistic framework. We use an asymptotic Bayesian approximation which results in computationally attractive solutions to the two problems. Among the key ideas discussed in this paper are the intrinsic dimensionality of polynomials and the use of the Mahalanobis distance as an effective tool for comparing polynomials in terms of their coefficients or algebraic invariants.