Direct least-squares fitting of algebraic surfaces
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
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Heteroscedastic Regression in Computer Vision: Problems with Bilinear Constraint
International Journal of Computer Vision - Special issue on a special section on visual surveillance
Computational Line Geometry
Shape segmentation using local slippage analysis
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Further Improving Geometric Fitting
3DIM '05 Proceedings of the Fifth International Conference on 3-D Digital Imaging and Modeling
3D Shape Recognition and Reconstruction Based on Line Element Geometry
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision - Volume 2
On the Convergence of Fitting Algorithms in Computer Vision
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Computer-Aided Design
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Kinematic surfaces form a general class of surfaces, including surfaces of revolution, helices, spirals, and more. Standard methods for fitting such surfaces are either specialized to a small subset of these surface types (either focusing exclusively on cylinders or exclusively on surfaces of revolution) or otherwise are basis-dependent (leading to scale-dependent results). Previous work has suggested re-scaling data to a fixed size bounding box to avoid the basis-dependence issues. We show that this method fails on some simple, common cases such as a box or a cone with small noise. We propose instead adapting a well-studied approximate maximum-likelihood method to the kinematic surface fitting problem, which solves the basis-dependence issue. Because this technique is not designed for a specific type of kinematic surface, it also opens the door to the possibility of new variants of kinematic surfaces, such as affinely-scaled surfaces of revolution.