Gradient flows and geometric active contour models

By Satyanad Kichenassamy, Arun Kumar, Peter J. Olver, Allen R. Tannenbaum, Anthony J. Yezzi Jr.. 1995

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Citations in the corpus

Deep Level Sets: Implicit Surface Representations for 3D Shape Inference (2019, methodology): “The level set method introduced in [8, 26], and successfully applied in segmentation and medical image analysis [18, 32], is a mathematically elegant way of implicitly representing shape of an object and its boundary evolution in time, which can be represented as a zero level set of an embedding fun”
Natural Image Statistics for Natural Image Segmentation (2003, unknown): “In this sense, our work is similar to Paragios and Deriche [18] who successfully enhance the geodesic active contour model [3, 12] with a Gaussian mixt ure model of filter response statistics for supervised texture segmentation.”
A Review of Statistical Approaches to Level Set Segmentation: Integrating Color, Texture, Motion and Shape (2007, background): “See Caselles et al. (1995) and Kichenassamy et al. (1995) for details.”
Distance Regularized Level Set Evolution and Its Application to Image Segmentation (2010, background): “These desirable features, among others, have greatly promoted further development of level set methods and their applications in image segmentation [10]–[12], [7], [13]–[16], tracking [14],”
CURVES: Curve evolution for vessel segmentation (2001, methodology): “Curve evolution schemes for segmentation, implemented with level set methods, have become an important approach in computer vision (Caselleset al. 1997; Kichenassamy et al. 1995; Malladi et al. 1994; Sethian 1996).”
Reconciling distance functions and level sets (2000, methodology): “These evolutions were reformulated by Caselles, Kimmel and Sapiro [7] and by Kichenassamy et al. [ 16 ] in the context of PDE-driven curves and surfaces.”
Active Contours without Edges for Vector-Valued Images (2000, unknown): “For another related approach, see also [9].”
TouchCut: Fast image and video segmentation using single-touch interaction (2014, background): “Further, in some use cases (e.g. deployment in high throughput, or multi-tasking situations such as driving) the high cognitive load required to trace outlines or regions may also be undesirable.”
Motion Competition: A Variational Approach to Piecewise Parametric Motion Segmentation (2005, background): “Level set based contour representations have become a popular framework in image segmentation (cf. Caselles et al. 1995; Kichenassamy et al., 1995; Chan and Vese, 2001), because they do not depend on a particular choice of parameterization, and because they do not restrict the topology of the evolvi”
Shape Priors for Level Set Representations (2002, unknown): “In the absence of regional information, we can consider the geodesic active contour model [3,9] that only makes use of boundary information.”
State of the art survey on MRI brain tumor segmentation. (2013, unknown): “[98] and Yezzi et al.”
Continuous Global Optimization in Multiview 3D Reconstruction (2007, background): “the snakes and the geodesic active contours (Caselles et al. 1995; Kichenassamy et al. 1995) can then be expressed by means of a weighted total variation (TV) norm (Rudin et al.”
Implicit Surface Representations As Layers in Neural Networks (2019, methodology): “The level set method introduced in [8, 27], and successfully applied in segmentation and medical image analysis [18, 33], is a mathematically elegant way of implicitly representing shape of an object and its boundary evolution in time, which can be represented as a zero level set of an embedding fun”
Images as Embedded Maps and Minimal Surfaces: Movies, Color, Texture, and Volumetric Medical Images (2000, background): “, 1994; El-Fallah and Ford, 1998; Yanowitz and Bruckstein, 1989; Malladi and Sethian, 1996), some even used the image information to build a Riemannian metric for segmentation (Caselles et al., 1995; Kichenassamy et al., 1995; Shah, 1996a).”
MRI Segmentation of the Human Brain: Challenges, Methods, and Applications (2015, background): “Intraditional deformable models, image forces come primarily from the local edge-based information (e.g., based on the gradients of sharp image intensities) [95–97].”
A general framework for low level vision (1998, background): “If we further specify , where is the original image, we arrive at div which is the core (up to the normalization factor) of what is known in the literature as the geodesic active contours [4]–[6], [21], [40].”
A quasi-dense approach to surface reconstruction from uncalibrated images (2005, methodology): “…properties have been established, the weighted minimal surface formulation was introduced by Caselles and Kimmel [5] and Kichenassamy et al. [23] for 3D segmentation from 3D images, i.e., the 3D surfaces they seek are those minimizing the functional R R wds using the weight w ¼ g ðr I Þ…”