Least-squares-based fitting of paraboloids

Authors:
Min Dai;Timothy S. Newman;Chunguang Cao
Affiliations:
Department of Computer Science, University of Alabama in Huntsville, Huntsville, AL 35899, USA;Department of Computer Science, University of Alabama in Huntsville, Huntsville, AL 35899, USA;Department of Computer Science, University of Alabama in Huntsville, Huntsville, AL 35899, USA
Venue:
Pattern Recognition
Year:
2007

Citing 12
Cited 1

Segmentation and Classification of Range Images

IEEE Transactions on Pattern Analysis and Machine Intelligence
Recognition of 3-D objects in range images using a Butterfly multiprocessor

Pattern Recognition
Recognizing 3-D Objects Using Surface Descriptions

IEEE Transactions on Pattern Analysis and Machine Intelligence
Estimation of Planar Curves, Surfaces, and Nonplanar Space Curves Defined by Implicit Equations with Applications to Edge and Range Image Segmentation

IEEE Transactions on Pattern Analysis and Machine Intelligence
Model-based classification of quadric surfaces

CVGIP: Image Understanding
Approximate orthogonal distance regression method for fitting quadric surfaces to range data

Pattern Recognition Letters
Experiments in Curvature-Based Segmentation of Range Data

IEEE Transactions on Pattern Analysis and Machine Intelligence
A survey of automated visual inspection

Computer Vision and Image Understanding
Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography

Communications of the ACM
A survey of methods for recovering quadrics in triangle meshes

ACM Computing Surveys (CSUR)
Curvature-Augmented Tensor Voting for Shape Inference from Noisy 3D Data

IEEE Transactions on Pattern Analysis and Machine Intelligence
Measuring Curved Surfaces for Robot Vision

Computer

A simple least squares method for fitting of ellipses and circles depends on border points of a two-tone image and their 3-D extensions

Pattern Recognition Letters

Quantified Score

Hi-index	0.01

Visualization

Abstract

A technique for reconstructing a class of quadric surfaces from 3D data is presented. The technique is driven by a linear least-squares-based fitting mechanism. Previously, such fitting was restricted to recovery of central quadrics; here, extension of that basic mechanism to allow recovery of one commonly-occurring class of non-central quadric, the elliptic paraboloids, is described. The extension uses an indirect solution approach that involves introducing a variable to the basic mechanism that is a function of a quadric surface invariant. Results from fitting real and synthetic data are also exhibited.