Free-form deformation of solid geometric models
SIGGRAPH '86 Proceedings of the 13th annual conference on Computer graphics and interactive techniques
Direct manipulation of free-form deformations
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Image metamorphosis using snakes and free-form deformations
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Feature-based volume metamorphosis
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Three-dimensional distance field metamorphosis
ACM Transactions on Graphics (TOG)
Graphical Models and Image Processing
Digital Image Warping
Image Metamorphosis with Scattered Feature Constraints
IEEE Transactions on Visualization and Computer Graphics
Rendering with Parallel Stripes
IEEE Computer Graphics and Applications
A Constrained Non-rigid Registration Algorithm for Use in Prostate Image-Guided Radiotherapy
MICCAI '08 Proceedings of the 11th international conference on Medical Image Computing and Computer-Assisted Intervention - Part I
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Uniform cubic B-spline functions have been used for mapping functions in various areas such as image warping and morphing, 3D deformation, and volume morphing. The injectivity (one-to-one property) of a mapping function is important to obtain good results in these areas. This paper considers the local injectivity conditions of 2D and 3D uniform cubic B-spline functions. We propose a geometric interpretation of the local injectivity of a uniform cubic B-spline function, with which 2D and 3D cases can be handled in a similar way. Based on the geometric interpretation, we present sufficient conditions for the local injectivity that are represented in terms of control point displacements. These sufficient conditions are simple and easy to check and will be useful to guarantee the injectivity of mapping functions in application areas.