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226
The image foresting transform: Theory, algorithms, and applications
 IEEE TPAMI
, 2004
"... The image foresting transform (IFT) is a graphbased approach to the design of image processing operators based on connectivity. It naturally leads to correct and efficient implementations and to a better understanding of how different operators relate to each other. We give here a precise definiti ..."
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Cited by 95 (31 self)
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The image foresting transform (IFT) is a graphbased approach to the design of image processing operators based on connectivity. It naturally leads to correct and efficient implementations and to a better understanding of how different operators relate to each other. We give here a precise definition of the IFT, and a procedure to compute it—a generalization of Dijkstra’s algorithm—with a proof of correctness. We also discuss implementation issues and illustrate the use of the IFT in a few applications.
Improved watershed transform for medical image segmentation using prior information
 IEEE TMI
, 2004
"... Abstract—The watershed transform has interesting properties that make it useful for many different image segmentation applications: it is simple and intuitive, can be parallelized, and always produces a complete division of the image. However, when applied to medical image analysis, it has importan ..."
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Cited by 90 (3 self)
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Abstract—The watershed transform has interesting properties that make it useful for many different image segmentation applications: it is simple and intuitive, can be parallelized, and always produces a complete division of the image. However, when applied to medical image analysis, it has important drawbacks (oversegmentation, sensitivity to noise, poor detection of thin or low signal to noise ratio structures). We present an improvement to the watershed transform that enables the introduction of prior information in its calculation. We propose to introduce this information via the use of a previous probability calculation. Furthermore, we introduce a method to combine the watershed transform and atlas registration, through the use of markers. We have applied our new algorithm to two challenging applications: knee cartilage and gray matter/white matter segmentation in MR images. Numerical validation of the results is provided, demonstrating the strength of the algorithm for medical image segmentation. Index Terms—Biomedical imaging, image segmentation, morphological operations, tissue classification, watersheds.
Multilabel Random Walker Image Segmentation Using Prior Models
 In: IEEE Comp. Soc. Conf. Comp. Vision Pattern Recog
, 2005
"... The recently introduced random walker segmentation algorithm of [14] has been shown to have desirable theoretical properties and to perform well on a wide variety of images in practice. However, this algorithm requires userspecified labels and produces a segmentation where each segment is connected ..."
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Cited by 60 (4 self)
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The recently introduced random walker segmentation algorithm of [14] has been shown to have desirable theoretical properties and to perform well on a wide variety of images in practice. However, this algorithm requires userspecified labels and produces a segmentation where each segment is connected to a labeled pixel. We show that incorporation of a nonparametric probability density model allows for an extended random walkers algorithm that can locate disconnected objects and does not require userspecified labels. Finally, we show that this formulation leads to a deep connection with the popular graph cuts method of [8, 24]. 1
On topological watersheds
 JOURNAL OF MATHEMATICAL IMAGING AND VISION
, 2005
"... In this paper, we investigate topological watersheds [1]. One of our main results is a necessary and sufficient condition for a map G to be a watershed of a map F, this condition is based on a notion of extension. A consequence of the theorem is that there exists a (greedy) polynomial time algorit ..."
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Cited by 54 (12 self)
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In this paper, we investigate topological watersheds [1]. One of our main results is a necessary and sufficient condition for a map G to be a watershed of a map F, this condition is based on a notion of extension. A consequence of the theorem is that there exists a (greedy) polynomial time algorithm to decide whether a map G is a watershed of a map F or not. We introduce a notion of “separation between two points ” of an image which leads to a second necessary and sufficient condition. We also show that, given an arbitrary total order on the minima of a map, it is possible to define a notion of “degree of separation of a minimum ” relative to this order. This leads to a third necessary and sufficient condition for a map G to be a watershed of a map F. At last we derive, from our framework, a new definition for the dynamics of a minimum.
Quasilinear algorithms for the topological watershed
 JOURNAL OF MATHEMATICAL IMAGING AND VISION
, 2005
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Perceptionbased 3d triangle mesh segmentation using fast marching watersheds
 in Proceedings of the International Conference on Computer Vision and Pattern Recognition, II
, 2003
"... In this paper, we describe an algorithm called Fast Marching Watersheds that segments a triangle mesh into visual parts. This computer vision algorithm leverages a human vision theory known as the minima rule. Our implementation computes the principal curvatures and principal directions at each vert ..."
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Cited by 45 (3 self)
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In this paper, we describe an algorithm called Fast Marching Watersheds that segments a triangle mesh into visual parts. This computer vision algorithm leverages a human vision theory known as the minima rule. Our implementation computes the principal curvatures and principal directions at each vertex of a mesh, and then our hillclimbing watershed algorithm identifies regions bounded by contours of negative curvature minima. These regions fit the definition of visual parts according to the minima rule. We present evaluation analysis and experimental results for the proposed algorithm. 1.
Power Watershed: A Unifying GraphBased Optimization Framework
, 2011
"... In this work, we extend a common framework for graphbased image segmentation that includes the graph cuts, random walker, and shortest path optimization algorithms. Viewing an image as a weighted graph, these algorithms can be expressed by means of a common energy function with differing choices of ..."
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Cited by 40 (8 self)
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In this work, we extend a common framework for graphbased image segmentation that includes the graph cuts, random walker, and shortest path optimization algorithms. Viewing an image as a weighted graph, these algorithms can be expressed by means of a common energy function with differing choices of a parameter q acting as an exponent on the differences between neighboring nodes. Introducing a new parameter p that fixes a power for the edge weights allows us to also include the optimal spanning forest algorithm for watershed in this same framework. We then propose a new family of segmentation algorithms that fixes p to produce an optimal spanning forest but varies the power q beyond the usual watershed algorithm, which we term power watershed. In particular when q = 2, the power watershed leads to a multilabel, scale and contrast invariant, unique global optimum obtained in practice in quasilinear time. Placing the watershed algorithm in this energy minimization framework also opens new possibilities for using unary terms in traditional watershed segmentation and using watershed to optimize more general models of use in applications beyond image segmentation.
A Practical Approach to MorseSmale Complex Computation: Scalability and Generality
"... Abstract—The MorseSmale (MS) complex has proven to be a useful tool in extracting and visualizing features from scalarvalued data. However, efficient computation of the MS complex for large scale data remains a challenging problem. We describe a new algorithm and easily extensible framework for co ..."
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Cited by 36 (9 self)
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Abstract—The MorseSmale (MS) complex has proven to be a useful tool in extracting and visualizing features from scalarvalued data. However, efficient computation of the MS complex for large scale data remains a challenging problem. We describe a new algorithm and easily extensible framework for computing MS complexes for large scale data of any dimension where scalar values are given at the vertices of a closurefinite and weak topology (CW) complex, therefore enabling computation on a wide variety of meshes such as regular grids, simplicial meshes, and adaptive multiresolution (AMR) meshes. A new divideandconquer strategy allows for memoryefficient computation of the MS complex and simplification onthefly to control the size of the output. In addition to being able to handle various data formats, the framework supports implementationspecific optimizations, for example, for regular data. We present the complete characterization of critical point cancellations in all dimensions. This technique enables the topology based analysis of large data on offtheshelf computers. In particular we demonstrate the first full computation of the MS complex for a 1 billion/1024 3 node grid on a laptop computer with 2Gb memory. Index Terms—Topologybased analysis, MorseSmale complex, large scale data. 1