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Zoominvariant vision of figural shape: The mathematics of cores
 Computer Vision and Image Understanding
"... Believing that figural zoom invariance and the crossfigural boundary linking implied by medial loci are important aspects of object shape, we present the mathematics of and algorithms for the extraction of medial loci directly from image intensities. The medial loci called cores are defined as gene ..."
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Cited by 52 (19 self)
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Believing that figural zoom invariance and the crossfigural boundary linking implied by medial loci are important aspects of object shape, we present the mathematics of and algorithms for the extraction of medial loci directly from image intensities. The medial loci called cores are defined as generalized maxima in scale space of a form of medial information that is invariant to translation, rotation, and in particular, zoom. These loci are very insensitive to image disturbances, in strong contrast to previously available medial loci, as demonstrated in a companion paper. Corerelated geometric properties and image object representations are laid out which, together with the aforementioned insensitivities, allow the core to be used effectively for a variety of image analysis objectives. 2
Multiscale Medial Loci and Their Properties
 INTERNATIONAL JOURNAL OF COMPUTER VISION
, 2003
"... Blum's medial axes have great strengths, in principle, in intuitively describing object shape in terms of a quasihierarchy of figures. But it is well known that, derived from a boundary, they are damagingly sensitive to detail in that boundary. The development of notions of spatial scale has led to ..."
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Cited by 37 (9 self)
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Blum's medial axes have great strengths, in principle, in intuitively describing object shape in terms of a quasihierarchy of figures. But it is well known that, derived from a boundary, they are damagingly sensitive to detail in that boundary. The development of notions of spatial scale has led to some definitions of multiscale medial axes different from the Blum medial axis that considerably overcame the weakness. Three major multiscale medial axes have been proposed: iteratively pruned trees of Voronoi edges (Ogniewicz, 1993; Szekely, 1996; Naf, 1996), shock loci of reactiondiffusion equations (Kimia et al., 1995; Siddiqi and Kimia, 1996), and height ridges of medialness (cores) (Fritsch et al., 1994; Morse et al., 1993; Pizer et al., 1998). These are different from the Blum medial axis, and each has different mathematical properties of generic branching and ending properties, singular transitions, and geometry of implied boundary, and they have different strengths and weaknesses for computing object descriptions from images or from object boundaries. These mathematical properties and computational abilities are laid out and compared and contrasted in this paper.
Retinal Vessel Centerline Extraction Using Multiscale Matched Filters, Confidence and Edge Measures
 IEEE TMI
, 2006
"... Motivated by the goals of improving detection of lowcontrast and narrow vessels and eliminating false detections at nonvascular structures, a new technique is presented for extracting vessels in retinal images. The core of the technique is a new likelihood ratio test that combines matchedfilter re ..."
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Cited by 18 (0 self)
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Motivated by the goals of improving detection of lowcontrast and narrow vessels and eliminating false detections at nonvascular structures, a new technique is presented for extracting vessels in retinal images. The core of the technique is a new likelihood ratio test that combines matchedfilter responses, confidence measures and vessel boundary measures. Matched filter responses are derived in scalespace to extract vessels of widely varying widths. A vessel confidence measure is defined as a projection of a vector formed from a normalized pixel neighborhood onto a normalized ideal vessel profile. Vessel boundary measures and associated confidences are computed at potential vessel boundaries. Combined, these responses form a 6dimensional measurement vector at each pixel. A training technique is used to develop a mapping of this vector to a likelihood ratio that measures the "vesselness" at each pixel. Results comparing this vesselness measure to matched filters alone and to measures based on the Hessian of intensities show substantial improvements both qualitatively and quantitatively. The Hessian can be used in place of the matched filter to obtain similar but lesssubstantial improvements or to steer the matched filter by preselecting kernel orientations. Finally, the new vesselness likelihood ratio is embedded into a vessel tracing framework, resulting in an e#cient and e#ective vessel centerline extraction algorithm.
MultiScale Gradient Magnitude Watershed Segmentation
 In ICIAP’97  9th International Conference on Image Analysis and Processing
, 1997
"... . A partitioning of an nD image is defined as the watersheds of some locally computable inhomogeneity measure. Dependent on the scale of the inhomogeneity measure a coarse or fine partitioning is defined. By analysis of the structural changes (catastrophes) in the measure introduced when scale is in ..."
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Cited by 11 (1 self)
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. A partitioning of an nD image is defined as the watersheds of some locally computable inhomogeneity measure. Dependent on the scale of the inhomogeneity measure a coarse or fine partitioning is defined. By analysis of the structural changes (catastrophes) in the measure introduced when scale is increased, an multiscale linking of segments can be defined. This paper describes the multiscale linking based on recent results of the deep structure of the squared gradient field[1]. An interactive semiautomatic segmentation tool is described and results on synthetic and real 3D medical images are presented. 1 Introduction The goal of an image segmentation is a description of the shape of some image structure of predefined semantics. However, addressing the shape of an object is not simple since the shape is not intrinsically defined[2]; shape is defined through an interpretation of measurements. This introduces the measurements apparatus and its intrinsic resolution as an important part...
Generic Events for the Gradient Squared with Application to MultiScale Segmentation
 In ScaleSpace Theory in Computer Vision, Proc. 1st International Conference
, 1997
"... . In the Gaussian scalespace formalism, image features are often defined as loci of differential invariants. A typical behavior of these is topological stability in open intervals of the scale axis. However, it is generic that the feature topology changes at specific scales in socalled catastrophe ..."
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Cited by 6 (2 self)
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. In the Gaussian scalespace formalism, image features are often defined as loci of differential invariants. A typical behavior of these is topological stability in open intervals of the scale axis. However, it is generic that the feature topology changes at specific scales in socalled catastrophe events. In this paper, we show that the generic Gaussian scalespace catastrophe events for the gradient magnitude squared, L i L i , are the fold catastrophe and the cusp catastrophe. These results are applied to a scalespace formulation of segmentation with catchment basins/watersheds. The common problem of oversegmentation when segmenting with catchment basins of the gradient magnitude is solved by the multiscale formulation. The necessary linking of segments across scale is based naturally on the catastrophe analysis for L i L i . Verified segmentation results on 3D medical images are presented. 1 Introduction The very introduction of the scalespace formalism [18, 7] emphasised the...
www.elsevier.com/locate/media Pulmonary fissure segmentation on CT
, 2006
"... A pulmonary fissure is a boundary between the lobes in the lungs. Its segmentation is of clinical interest as it facilitates the assessment of lung disease on a lobar level. This paper describes a new approach for segmenting the major fissures in both lungs on thinsection computed tomography (CT). ..."
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A pulmonary fissure is a boundary between the lobes in the lungs. Its segmentation is of clinical interest as it facilitates the assessment of lung disease on a lobar level. This paper describes a new approach for segmenting the major fissures in both lungs on thinsection computed tomography (CT). An image transformation called ‘‘ridge map’ ’ is proposed for enhancing the appearance of fissures on CT. A curvegrowing process, modeled by a Bayesian network, is described that is influenced by both the features of the ridge map and prior knowledge of the shape of the fissure. The process is implemented in an adaptive regularization framework that balances these influences and reflects the causal dependencies in the Bayesian network using an entropy measure. The method effectively alleviates the problem of inappropriate weights of regularization terms, an effect that can occur with static regularization methods. The method was applied to segment and visualize the lobes of the lungs on chest CT of 10 patients with pulmonary nodules. Only 78 out of 3286 left or right lung regions with fissures (2.4%) required manual correction. The average distance between the automatically segmented and the manually delineated ‘‘ground–truth’ ’ fissures was 1.01 mm, which was similar to the average distance of 1.03 mm between two sets of manually segmented fissures. The method has a lineartime worstcase complexity and segments the upper lung from the lower lung on a standard computer in less than 5 min.
Kluwer Academic Publishers 2D & 3D FIGURAL MODELS OF ANATOMIC OBJECTS FROM MEDICAL IMAGES
"... www.cs.unc.edu/Research/Image Abstract. Figural object models represent object shape in terms of a hierarchy of simple shapes, protrusions, and indentations that we call "figures". Each figure has an unbranching, coarsely sampled net of medial primitives which carr>.: width information. The figural ..."
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www.cs.unc.edu/Research/Image Abstract. Figural object models represent object shape in terms of a hierarchy of simple shapes, protrusions, and indentations that we call "figures". Each figure has an unbranching, coarsely sampled net of medial primitives which carr>.: width information. The figural hierarchy and its medial primitives thus define the boundary with atolerance proportional to the corresponding medial widths, and associate with eacl ~ boundary location a normal vector representing the figural boundary at a scale proportional to the medial width. Such a model is efficiently and effectively deformable to match image information according to, and producing, probabilistic measures of object shape and measures of image match. This paper specifies the makeup of figural object models and describes methods for building models of anatomic objects. 1. Figural Models YVe have developed a shapebased segmentation, registration, rendering, and shapeanalysis technique that performs unusually effectively, as tested in a number of medical image analysis applications in 2D and 3D. The method is based on a figural model of shape, which we believe has merit for a variety of purposes of image analysis,
COMPUTER GRAPHICS forum Extraction of Dominant Extremal Structures in Volumetric Data using Separatrix Persistence
"... Extremal lines and surfaces are features of a 3D scalar field where the scalar function becomes minimal or maximal with respect to a local neighborhood. These features are important in many applications, e.g., computer tomography, fluid dynamics, cell biology. We present a novel topological method t ..."
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Extremal lines and surfaces are features of a 3D scalar field where the scalar function becomes minimal or maximal with respect to a local neighborhood. These features are important in many applications, e.g., computer tomography, fluid dynamics, cell biology. We present a novel topological method to extract these features using discrete Morse theory. In particular, we extend the notion of Separatrix Persistence from 2D to 3D, which gives us a robust estimation of the feature strength for extremal lines and surfaces. Not only does it allow us to determine the most important (parts of) extremal lines and surfaces, it also serves as a robust filtering measure of noiseinduced structures. Our purely combinatorial method does not require derivatives or any other numerical computations.
for those with access. Multiscale Medial Loci and Their Properties
"... Blum's medial axes have great strengths, in principle, in intuitively describing object shape in terms of a quasihierarchy of figures. But it is well known that, derived from a boundary, they are damagingly sensitive to detail in that boundary. The development of notions of spatial scale has led to ..."
Abstract
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Blum's medial axes have great strengths, in principle, in intuitively describing object shape in terms of a quasihierarchy of figures. But it is well known that, derived from a boundary, they are damagingly sensitive to detail in that boundary. The development of notions of spatial scale has led to some definitions of multiscale medial axes different from the Blum medial axis that considerably overcame the weakness. Three major multiscale medial axes have been proposed: iteratively pruned trees of Voronoi edges [Ogniewicz 1993, Székely 1996, Näf 1996], shock loci of reactiondiffusion equations [Kimia et al. 1995, Siddiqi & Kimia 1996], and height ridges of medialness (cores) [Fritsch et al. 1994, Morse et al. 1993, Pizer et al. 1998]. These are different from the Blum medial axis, and each has different mathematical properties of generic branching and ending properties, singular transitions, and geometry of implied boundary, and they have different strengths and weaknesses for computing object descriptions from images or from object boundaries. These mathematical properties and computational abilities are laid out and compared and contrasted in this paper. 1.