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134
Scalespace Properties of the Multiscale Morphological DilationErosion
 IEEE TRANS. ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 1996
"... A multiscale morphological dilationerosion smoothing operation and its associated scalespace expansion for multidimensional signals are proposed. Properties of this smoothing operation are developed and, in particular a scalespace monotonic property for signal extrema is demonstrated. Scalespace ..."
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Cited by 64 (2 self)
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A multiscale morphological dilationerosion smoothing operation and its associated scalespace expansion for multidimensional signals are proposed. Properties of this smoothing operation are developed and, in particular a scalespace monotonic property for signal extrema is demonstrated. Scalespace fingerprints from this approach have advantages over Gaussian scalespace fingerprints in that they: are defined for negative values of the scale parameter; have
On scale selection for differential operators
 8TH SCIA
, 1993
"... Although traditional scalespace theory provides a wellfounded framework for dealing with image structures at different scales, it does not directly address the problem of how to select appropriate scales for further analysis. This paper introduces a new tool for dealing with this problem. A heur ..."
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Cited by 53 (11 self)
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Although traditional scalespace theory provides a wellfounded framework for dealing with image structures at different scales, it does not directly address the problem of how to select appropriate scales for further analysis. This paper introduces a new tool for dealing with this problem. A heuristic principle is proposed stating that local extrema over scales of different combinations of normalized scale invariant derivatives are likely candidates to correspond to interesting structures. Support is given by theoretical considerations and experiments on real and synthetic data. The resulting methodology lends itself naturally to twostage algorithms; feature detection at coarse scales followed by feature localization at ner scales. Experiments on blob detection, junction detection and edge detection demonstrate that the proposed method gives intuitively reasonable results.
Probabilistic multiscale image segmentation
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1997
"... Abstract—A method is presented to segment multidimensional images using a multiscale (hyperstack) approach with probabilistic linking. A hyperstack is a voxelbased multiscale data structure whose levels are constructed by convolving the original image with a Gaussian kernel of increasing width. Bet ..."
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Cited by 51 (3 self)
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Abstract—A method is presented to segment multidimensional images using a multiscale (hyperstack) approach with probabilistic linking. A hyperstack is a voxelbased multiscale data structure whose levels are constructed by convolving the original image with a Gaussian kernel of increasing width. Between voxels at adjacent scale levels, childparent linkages are established according to a modeldirected linkage scheme. In the resulting treelike data structure, roots are formed to indicate the most plausible locations in scale space where segments in the original image are represented by a single voxel. The final segmentation is obtained by tracing back the linkages for all roots. The present paper deals with probabilistic (or multiparent) linking, i.e., a setup in which a child voxel can be linked to more than one parent voxel. The multiparent linkage structure is translated into a list of probabilities that are indicative of which voxels are partial volume voxels and to which extent. Probability maps are generated to visualize the progress of weak linkages in scale space when going from fine to coarser scale. This is shown to be a valuable tool for the detection of voxels that are difficult to segment properly. The output of a probabilistic hyperstack can be directly related to the opacities used in volume renderers. Results are shown both for artificial and real world (medical) images. It is demonstrated that probabilistic linking gives a significantly improved segmentation as compared with conventional (singleparent) linking. The improvement is quantitatively supported by an objective evaluation method. Index Terms—Image segmentation, multiscale analysis, scale space, probability maps, partial volume artifact, object definition. 1
Sizebased Transfer Functions: A New Volume Exploration Technique
 IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS
, 2008
"... The visualization of complex 3D images remains a challenge, a fact that is magnified by the difficulty to classify or segment volume data. In this paper, we introduce sizebased transfer functions, which map the local scale of features to color and opacity. Features in a data set with similar or i ..."
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Cited by 50 (4 self)
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The visualization of complex 3D images remains a challenge, a fact that is magnified by the difficulty to classify or segment volume data. In this paper, we introduce sizebased transfer functions, which map the local scale of features to color and opacity. Features in a data set with similar or identical scalar values can be classified based on their relative size. We achieve this with the use of scale fields, which are 3D fields that represent the relative size of the local feature at each voxel. We present a mechanism for obtaining these scale fields at interactive rates, through a continuous scalespace analysis and a set of detection filters. Through a number of examples, we show that sizebased transfer functions can improve classification and enhance volume rendering techniques, such as maximum intensity projection. The ability to classify objects based on local size at interactive rates proves to be a powerful method for complex data exploration.
Geometric Heat Equation and Nonlinear Diffusion of Shapes and Images
 Computer Vision and Image Understanding
, 1993
"... We propose a geometric smoothing method based on local curvature in shapes and images which is governed by the geometric heat equation and is a special case of the reactiondiffusion framework proposed by [28]. For shapes, the approach is analogous to the classical heat equation smoothing, but with ..."
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Cited by 45 (5 self)
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We propose a geometric smoothing method based on local curvature in shapes and images which is governed by the geometric heat equation and is a special case of the reactiondiffusion framework proposed by [28]. For shapes, the approach is analogous to the classical heat equation smoothing, but with a renormalization by arclength at each infinitesimal step. For images, the smoothing is similar to anisotropic diffusion in that, since the component of diffusion in the direction of the brightness gradient is nil, edge location and sharpness are left intact. We present several properties of curvature deformation smoothing of shape: it preserves inclusion order, annihilates extrema and inflection points without creating new ones, decreases total curvature, satisfies the semigroup property allowing for local iterative computations, etc. Curvature deformation smoothing of an image is based on viewing it as a collection of isointensity level sets, each of which is smoothed by curvature and the...
Shape from texture from a multiscale perspective
 Fourth Int. Conf. Comp. Vision
, 1993
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BRIEF: Computing a local binary descriptor very fast
"... Binary descriptors are becoming increasingly popular as a means to compare feature points very fast and while requiring comparatively small amounts of memory. The typical approach to creating them is to first compute floatingpoint ones, using an algorithm such as SIFT, and then to binarize them. In ..."
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Cited by 39 (4 self)
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Binary descriptors are becoming increasingly popular as a means to compare feature points very fast and while requiring comparatively small amounts of memory. The typical approach to creating them is to first compute floatingpoint ones, using an algorithm such as SIFT, and then to binarize them. In this paper, we show that we can directly compute a binary descriptor we call BRIEF on the basis of simple intensity difference tests. As a result, BRIEF is very fast both to build and to match. We compare it against SURF and SIFT on standard benchmarks and show that it yields comparable recognition accuracy, while running in an almost vanishing fraction of the time required by either. Index Terms Image processing and computer vision, feature matching, augmented reality, realtime matching1
Discrete derivative approximations with scalespace properties: A basis for lowlevel feature extraction
 J. Math. Imaging Vision
, 1993
"... It is developed how discrete derivative approximations can be de ned so that scalespace properties hold exactly also in the discrete domain. Starting from a set of natural requirements on the rst processing stages of a visual system, the visual front end, an axiomatic derivation is given of how amu ..."
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Cited by 38 (15 self)
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It is developed how discrete derivative approximations can be de ned so that scalespace properties hold exactly also in the discrete domain. Starting from a set of natural requirements on the rst processing stages of a visual system, the visual front end, an axiomatic derivation is given of how amultiscale representation of derivative approximations can be constructed from a discrete signal, so that it possesses an algebraic structure similar to that possessed by the derivatives of the traditional scalespace representation in the continuous domain. A family of kernels is derived which constitute discrete analogues to the continuous Gaussian derivatives. The representation has theoretical advantages to other discretizations of the scalespace theory in the sense that operators which commute before discretization commute after discretization. Some computational implications of this are that derivativeapproximations can be computed directly from smoothed data, and that this will give exactly the same result as convolution with the corresponding derivative approximation kernel. Moreover, a number of normalization conditions are automatically satis ed. The proposed methodology leads to a conceptually very simple scheme of computations for multiscale lowlevel feature extraction, consisting of four basic steps � (i) large support convolution smoothing, (ii) small support di erence computations, (iii) point operations for computing di erential geometric entities, and (iv) nearest neighbour operations for feature detection. Applications are given demonstrating how the proposed scheme can be used for edge detection and junction detection based on derivatives up to order three.
Principles for automatic scale selection
 Handbook on Computer Vision and Applications
, 1999
"... 1Abstract: An inherent property of objects in the world is that they only exist as meaningful entities over certain ranges of scale. If one aims at describing the structure of unknown realworld signals, then a multiscale representation of data is of crucial importance. Whereas conventional scales ..."
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Cited by 36 (3 self)
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1Abstract: An inherent property of objects in the world is that they only exist as meaningful entities over certain ranges of scale. If one aims at describing the structure of unknown realworld signals, then a multiscale representation of data is of crucial importance. Whereas conventional scalespace theory provides a wellfounded framework for dealing with image structures at dierent scales, this theory does not directly address the problem of how to select appropriate scales for further analysis. This chapter outlines a systematic methodology of how mechanisms for automatic scale selection can be formulated in the problem domains of feature detection and image matching (
ow estimation), respectively. For feature detectors expressed in terms of Gaussian derivatives, hypotheses about interesting scale levels can be generated from scales at which normalized measures of feature strength assume local maxima with respect to scale. It is shown how the notion of normalized derivatives arises by necessity given the requirement that the scale selection mechanism should
General Intensity Transformations and Differential Invariants
, 1994
"... We consider the group of invertible image grayvalue transformations and propose a generating equation for a complete set of differential grayvalue invariants up to any order. Such invariants describe the image’s geometrical structure independent of how its grayvalues are mapped (contrast or brig ..."
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Cited by 35 (3 self)
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We consider the group of invertible image grayvalue transformations and propose a generating equation for a complete set of differential grayvalue invariants up to any order. Such invariants describe the image’s geometrical structure independent of how its grayvalues are mapped (contrast or brightness adjustments).