Robust estimation of adaptive tensors of curvature by tensor voting

• Published in: IEEE transactions on pattern analysis and machine intelligence Vol. 27; no. 3; pp. 434 - 449
• Main Authors: TONG, Wai-Shun, TANG, Chi-Keung
• Format: Journal Article
• Language: English
• Published: Los Alamitos, CA IEEE 01.03.2005; IEEE Computer Society; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Applied sciences; Artificial Intelligence; Clouds; Computer errors; Computer science; control theory; systems; Computer vision; Curvature; curvature tensor; Error correction; Errors; Exact sciences and technology; Feedback; Image Enhancement - methods; Image Interpretation, Computer-Assisted - methods; Index Terms- Curvature; Information Storage and Retrieval - methods; Mathematical analysis; Misalignment; Noise; Noise robustness; Numerical Analysis, Computer-Assisted; Pattern Recognition, Automated - methods; Pattern recognition. Digital image processing. Computational geometry; Quantization; Reproducibility of Results; Scattering; Sensitivity and Specificity; Studies; Subtraction Technique; Surface fitting; Tensile stress; tensor voting; Tensors; Voting; Curvature tensor; Computer vision; tensor voting; Robust estimation; Curvature
• ISSN: 0162-8828; 1939-3539
• DOI: 10.1109/TPAMI.2005.62

Although curvature estimation from a given mesh or regularly sampled point set is a well-studied problem, it is still challenging when the input consists of a cloud of unstructured points corrupted by misalignment error and outlier noise. Such input is ubiquitous in computer vision. In this paper, we propose a three-pass tensor voting algorithm to robustly estimate curvature tensors, from which accurate principal curvatures and directions can be calculated. Our quantitative estimation is an improvement over the previous two-pass algorithm, where only qualitative curvature estimation (sign of Gaussian curvature) is performed. To overcome misalignment errors, our improved method automatically corrects input point locations at subvoxel precision, which also rejects outliers that are uncorrectable. To adapt to different scales locally, we define the RadiusHit of a curvature tensor to quantify estimation accuracy and applicability. Our curvature estimation algorithm has been proven with detailed quantitative experiments, performing better in a variety of standard error metrics (percentage error in curvature magnitudes, absolute angle difference in curvature direction) in the presence of a large amount of misalignment noise.