Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Image selective smoothing and edge detection by nonlinear diffusion. II
SIAM Journal on Numerical Analysis
Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
Image processing: flows under min/max curvature and mean curvature
Graphical Models and Image Processing
International Journal of Computer Vision
International Journal of Computer Vision
Images as Embedded Maps and Minimal Surfaces: Movies, Color, Texture, and Volumetric Medical Images
International Journal of Computer Vision - Special issue on computer vision research at the Technion
Geometry-Driven Diffusion in Computer Vision
Geometry-Driven Diffusion in Computer Vision
Subjective Surfaces: A Geometric Model for Boundary Completion
International Journal of Computer Vision
Multidimensional Transfer Functions for Interactive Volume Rendering
IEEE Transactions on Visualization and Computer Graphics
Fast Difference Schemes for Edge Enhancing Beltrami Flow
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part I
From High Energy Physics to Low Level Vision
SCALE-SPACE '97 Proceedings of the First International Conference on Scale-Space Theory in Computer Vision
A Real-Time Algorithm for Medical Shape Recovery
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
A general framework for low level vision
IEEE Transactions on Image Processing
Modified curvature motion for image smoothing and enhancement
IEEE Transactions on Image Processing
Efficient and reliable schemes for nonlinear diffusion filtering
IEEE Transactions on Image Processing
Fast, robust total variation-based reconstruction of noisy, blurred images
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
ISCIS'06 Proceedings of the 21st international conference on Computer and Information Sciences
Image denoising using the lyapunov equation from non-uniform samples
ICIAR'06 Proceedings of the Third international conference on Image Analysis and Recognition - Volume Part I
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In many instances, numerical integration of space-scale PDEs is the most time consuming operation of image processing. This is because the scale step is limited by conditional stability of explicit schemes. In this work, we introduce the unconditionally stable semi-implicit linearized difference scheme that is fashioned after additive operator split (AOS) [1], [2] for Beltrami and the subjective surface computation. The Beltrami flow [3], [4], [5] is one of the most effective denoising algorithms in image processing. For gray-level images, we show that the flow equation can be arranged in an advection-diffusion form, revealing the edge-enhancing properties of this flow. This also suggests the application of AOS method for faster convergence. The subjective surface [6] deals with constructing a perceptually meaningful interpretation from partial image data by mimicking the human visual system. However, initialization of the surface is critical for the final result and its main drawbacks are very slow convergence and the huge number of iterations required. In this paper, we first show that the governing equation for the subjective surface flow can be rearranged in an AOS implementation, providing a near real-time solution to the shape completion problem in 2D and 3D. Then, we devise a new initialization paradigm where we first "condition驴 the viewpoint surface using the Fast-Marching algorithm. We compare the original method with our new algorithm on several examples of real 3D medical images, thus revealing the improvement achieved.