Images as Embedded Maps and Minimal Surfaces: Movies, Color, Texture, and Volumetric Medical Images

By Ron Kimmel, R. Malladi, Nir A. Sochen. International Journal of Computer Vision, 2000

319 citations recorded by the source corpus.

Subfields: Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/96d9b1af1ec59e6ddf5727c77ace0911fe3e0c71

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In Computer Vision and Pattern Recognition

Citations in the corpus

Computing geodesics and minimal surfaces via graph cuts (2003, background): “Further generalizations of geodesic active contours and some anisotropic metrics are discussed in [17].”
Recent Developments in Total Variation Image Restoration (2004, background): “(cid:82) Moreover, it is shown in [9] that the equality constraint Ω ( u − f ) 2 d x = σ 2 in the non-convex ROF model (1) is equivalent to the convex inequality constraint (cid:82) Ω ( u − f ) 2 d x ≤ σ 2 .”
Image enhancement and denoising by complex diffusion processes (2004, background): “features in low-level vision (e.g., Whitaker and Gerig [35], Barbaresco [4], Kimmel et al. [ 19 ]).”
Affine Invariant Flows in the Beltrami Framework (2004, background): “Let us briefly review the Beltrami framework for nonlinear diffusion in computer vision [10, 20, 21].”
Forward-and-backward diffusion processes for adaptive image enhancement and denoising (2002, methodology): “Indeed, the original and modified schemes of [ 14 ] enhanced the 8 8 block boundaries whereas our scheme smoothed them out.”
Fast Anisotropic Smoothing of Multi-Valued Images using Curvature-Preserving PDE's (2006, background): “Choosing different smoothing functions f−, f and diffusion PDE’s detailed below leads to the unification o f m st unconstrained image regularization methods proposed in th e literature [1, 4, 7, 8, 13, 15, 16, 23, 28, 30, 33, 36, 37, 38].”
Vector-valued image regularization with PDEs: a common framework for different applications (2005, unknown): “This particularly includes the works done in [10], [20], [22], [33], [37], [39], [42], [48], [51] among others.”
Fundamental relationship between bilateral filtering, adaptive smoothing, and the nonlinear diffusion equation (2002, background): “The general hybrid spatial-color formulation [ 4 ], [8] provide a geometric interpretation with which the bilateral convolution kernel can be viewed as an approximation to the geometric arclength in the 5D hybrid spatial-color space.”
A Theoretical Framework for Convex Regularizers in PDE-Based Computation of Image Motion (2001, background): “In the nonlinear anisotropic case, Weickert (1994, 1999) and Kimmel et al. (2000) proposed to filter a multichannel image by using a joint diffusion tensor that depends on the gradients of all image channels.”
Nonlocal Operators with Applications to Image Processing (2008, methodology): “A related framework in the context of PDE’s is the Beltrami ﬂow on Riemannian manifolds [51, 31] where the metric is image-driven and textures can be handled [48].”