IEEE Transactions on Pattern Analysis and Machine Intelligence
Scaling Theorems for Zero Crossings
IEEE Transactions on Pattern Analysis and Machine Intelligence
On the classification of views of piecewise smooth objects
Image and Vision Computing - Special issue: papers from the second Alvey Vision Conference
Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Artificial Intelligence
Solid shape
Computing exact aspect graphs of curved objects: solid of revolution
International Journal of Computer Vision
Visibility, occlusion, and the aspect graph
International Journal of Computer Vision
A new curve tracing algorithm and some applications
Curves and surfaces
Efficiently Computing and Representing Aspect Graphs of Polyhedral Objects
IEEE Transactions on Pattern Analysis and Machine Intelligence
Global bifurcation sets and stable projections of nonsingular algebraic surfaces
International Journal of Computer Vision
Computing exact aspect graphs of curved objects: algebraic surfaces
International Journal of Computer Vision
International Journal of Computer Vision
Parabolic curves of evolving surfaces
International Journal of Computer Vision
Ridges, crests and sub-parabolic lines of evolving surfaces
International Journal of Computer Vision
Finite-Resolution Aspect Graphs of Polyhedral Objects
IEEE Transactions on Pattern Analysis and Machine Intelligence
On computing aspect graphs of smooth shapes from volumetric data
Computer Vision and Image Understanding
Generic Sign Systems in Medical Imaging
IEEE Computer Graphics and Applications
IEEE Transactions on Pattern Analysis and Machine Intelligence
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As a surface undergoes a one-parameter family of deformations, its shape and its appearance change smoothly except at certain critical parameter values where abrupt structural changes occur. This paper considers the case of surfaces defined as the zero set of smooth density functions undergoing a Gaussian diffusion process and addresses the problem of computing the critical parameter values corresponding to structural changes in the parabolic curves of a surface and in its aspect graph. An algorithm based on homotopy continuation and curve tracing is proposed in the case of polynomial density functions, whose zero set is an algebraic surface. It has been implemented and examples are presented.