Regularization of inverse visual problems involving discontinuities
IEEE Transactions on Pattern Analysis and Machine Intelligence
The Computation of Visible-Surface Representations
IEEE Transactions on Pattern Analysis and Machine Intelligence
Singular value decompositions of complex symmetric matrices
Journal of Computational and Applied Mathematics
ACM Transactions on Graphics (TOG)
Reconstruction of a color image from nonuniformly distributed sparse and noisy data
CVGIP: Graphical Models and Image Processing
IEEE Computer Graphics and Applications - Special issue on computer-aided geometric design
Stable Numerical Algorithms for Equilibrium Systems
SIAM Journal on Matrix Analysis and Applications
Matrix computations (3rd ed.)
Large steps in cloth simulation
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Non-distorted texture mapping for sheared triangulated meshes
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
Numerical Recipes in C++: the art of scientific computing
Numerical Recipes in C++: the art of scientific computing
Computing Symmetric Rank-Revealing Decompositions via Triangular Factorization
SIAM Journal on Matrix Analysis and Applications
A Note on the LDLT Decomposition of Matrices from Saddle-Point Problems
SIAM Journal on Matrix Analysis and Applications
Image Warping with Scattered Data Interpolation
IEEE Computer Graphics and Applications
Efficient and Stable Numerical Algorithms on Equilibrium Equations for Geometric Modeling
GMP '04 Proceedings of the Geometric Modeling and Processing 2004
Image Processing, Analysis, and Machine Vision
Image Processing, Analysis, and Machine Vision
Repoussé: automatic inflation of 2D artwork
SBM'08 Proceedings of the Fifth Eurographics conference on Sketch-Based Interfaces and Modeling
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In this paper, we present a feature-based free-form shape modelling technique based on solving a fundamental problem of reconstructing the depth information from 2D sketch planes. First, to mathematically define the problem with the human perception, the proposed technique (1) formulates the 2D shaded regions on sketches by a hybrid thin plate surface model that can exhibit controlled continuity over the recovered 3D surface and (2) formulates the 1D salient open free-form curves and salient corners as linear sketch constraints. The 3D free-form shape from sketch planes is then achieved by solving a linearly constrained quadratic optimization problem which unifies both 2D region-based and 1D contour-based shape information over 2D sketches. Secondly, to solve the formulated optimization problem with an interactive-rate performance, a fast and stable numerical engine is proposed with a rigorous proof that for our specially formulated problem, system decomposition with reduced computational cost is always possible. Stability, accuracy and efficiency are studied in depth for the proposed numerical engine. Finally a prototype system utilizing the proposed technique is presented with two applications that demonstrate the usefulness and effectiveness of the proposed technique.