A general framework for low level vision

By Nir A. Sochen, Ron Kimmel, R. Malladi. 1998

Subfields: Computer Vision and Pattern Recognition

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Citations in the corpus

Geometric Deep Learning on Graphs and Manifolds Using Mixture Model CNNs (2016, methodology): “35], suggesting the use of non-shift-invariant image ﬁltering preserving the edge structures. This work was the precursor of a whole new class of PDE-based methods for image processing. Sochen et al. [50] brought geometric models into image processing, considering images as manifolds and employing t”
Shape recovery algorithms using level sets in 2-D/3-D medical imagery: a state-of-the-art review (2002, methodology): “... et al. [22]‐[24]); 8) object tracking/image sequence analysis in images: (see the recent work by Mansouri et al. [25]‐[27], Paragios et al. [28], [29] and Kornprobst et al. [30]); 9) stereo vision: (see the recent work by Faugeras and his coworkers at INRIA [31]); 10) shape from shading: (see Ki”
Sparse Shape Representation using the Laplace-Beltrami Eigenfunctions and Its Application to Modeling Subcortical Structures (2012, background): “Many previous surface data smoothing approaches have used heat diffusion type of smoothing to reduce surface noise [3, 7, 18, 20, 27, 31, 32].”
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].”
Partial Similarity of Objects, or How to Compare a Centaur to a Horse (2009, background): “For example, Sochen et al. (1998) suggested that images can be considered as Riemannian manifolds embedded into R 3 (in case of grayscale images) or R 5 (in case of color images), with the metric structure induced by the embedding.”
Graph spectral image smoothing using the heat kernel (2008, background): “A gray-scale image I can be regarded as a two-dimensional manifold M embedded in R3 [17], i.”
Forward-and-backward diffusion processes for adaptive image enhancement and denoising (2002, methodology): “[27] unifies several approaches by means of the Beltrami framework, and offers new definitions and solutions for various image processing tasks.”
An Efficient TVL1 Algorithm for Deblurring Multichannel Images Corrupted by Impulsive Noise (2009, background): “Another approach of coupling channels in regularization is the Beltrami flow proposed in [45], where a multichannel image is treated as a surface in higher dimensional space and then the area of the surface was minimized.”
A Fast Approximation of the Bilateral Filter Using a Signal Processing Approach (2006, background): “Sochen et al. (1998) describe the geometric framework that handles images as manifolds in the S × R space.”
Nonlocal Linear Image Regularization and Supervised Segmentation (2007, background): “This study relates to many image processing disciplines and mathematical methods, some of which are not necessarily related to PDE’s: spectral graph theory [20, 42], segmentation by seeded region growing [1, 65], graph-based segmentation [52, 48, 60], the Beltrami flow on Riemannian manifolds [34, 5”
Regularizing Flows for Constrained Matrix-Valued Images (2004, unknown): “Along the same line of ideas, we can mention the Polyakov action functional and the Beltrami framework proposed in [23, 34].”
Images as Embedded Maps and Minimal Surfaces: Movies, Color, Texture, and Volumetric Medical Images (2000, methodology): “In Sochen et al. (1998) and Kimmel et al. (1997), methods for constraining the evolution and the construction of convergent schemes based on the knowledge of the noise variance, were reported.”