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Scalespace and edge detection using anisotropic diffusion
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1990
"... AbstractThe scalespace technique introduced by Witkin involves generating coarser resolution images by convolving the original image with a Gaussian kernel. This approach has a major drawback: it is difficult to obtain accurately the locations of the “semantically meaningful ” edges at coarse sca ..."
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Cited by 1267 (1 self)
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AbstractThe scalespace technique introduced by Witkin involves generating coarser resolution images by convolving the original image with a Gaussian kernel. This approach has a major drawback: it is difficult to obtain accurately the locations of the “semantically meaningful ” edges at coarse scales. In this paper we suggest a new definition of scalespace, and introduce a class of algorithms that realize it using a diffusion process. The diffusion coefficient is chosen to vary spatially in such a way as to encourage intraregion smoothing in preference to interregion smoothing. It is shown that the “no new maxima should be generated at coarse scales ” property of conventional scale space is preserved. As the region boundaries in our approach remain sharp, we obtain a high quality edge detector which successfully exploits global information. Experimental results are shown on a number of images. The algorithm involves elementary, local operations replicated over the image making parallel hardware implementations feasible. Index TermsAdaptive filtering, analog VLSI, edge detection, edge enhancement, nonlinear diffusion, nonlinear filtering, parallel algo
Efficient and Reliable Schemes for Nonlinear Diffusion Filtering
 IEEE Transactions on Image Processing
, 1998
"... Nonlinear diffusion filtering is usually performed with explicit schemes. They are only stable for very small time steps, which leads to poor efficiency and limits their practical use. Based on a recent discrete nonlinear diffusion scalespace framework we present semiimplicit schemes which are sta ..."
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Cited by 168 (18 self)
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Nonlinear diffusion filtering is usually performed with explicit schemes. They are only stable for very small time steps, which leads to poor efficiency and limits their practical use. Based on a recent discrete nonlinear diffusion scalespace framework we present semiimplicit schemes which are stable for all time steps. These novel schemes use an additive operator splitting (AOS) which guarantees equal treatment of all coordinate axes. They can be implemented easily in arbitrary dimensions, have good rotational invariance and reveal a computational complexity and memory requirement which is linear in the number of pixels. Examples demonstrate that, under typical accuracy requirements, AOS schemes are at least ten times more efficient than the widelyused explicit schemes.
A Review of Nonlinear Diffusion Filtering
, 1997
"... . This paper gives an overview of scalespace and image enhancement techniques which are based on parabolic partial differential equations in divergence form. In the nonlinear setting this filter class allows to integrate apriori knowledge into the evolution. We sketch basic ideas behind the differ ..."
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Cited by 79 (7 self)
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. This paper gives an overview of scalespace and image enhancement techniques which are based on parabolic partial differential equations in divergence form. In the nonlinear setting this filter class allows to integrate apriori knowledge into the evolution. We sketch basic ideas behind the different filter models, discuss their theoretical foundations and scalespace properties, discrete aspects, suitable algorithms, generalizations, and applications. 1 Introduction During the last decade nonlinear diffusion filters have become a powerful and wellfounded tool in multiscale image analysis. These models allow to include apriori knowledge into the scalespace evolution, and they lead to an image simplification which simultaneously preserves or even enhances semantically important information such as edges, lines, or flowlike structures. Many papers have appeared proposing different models, investigating their theoretical foundations, and describing interesting applications. For a n...
Fast Computation of a ContrastInvariant Image Representation
 IEEE Trans. on Image Proc
, 1998
"... This article sets out a new representation of an image which is contrast independent. The image is decomposed into a tree of "shapes" based on connected components of level sets, which provides a full and nonredundant representation of the image. A fast algorithm to compute the tree, the Fast Level ..."
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Cited by 62 (3 self)
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This article sets out a new representation of an image which is contrast independent. The image is decomposed into a tree of "shapes" based on connected components of level sets, which provides a full and nonredundant representation of the image. A fast algorithm to compute the tree, the Fast Level Lines Transform, is explained in details. Some simple and direct applications of this representation are shown. KeywordsImage representation, Image coding, Mathematical morphology, Contrast invariance. I. Introduction Image representations can be different depending on their purpose. For a deblurring, restoration, denoising purpose, the representations based on the Fourier transform are generally the best since they rely on the generation process of the image (Shannon theory), and/or on the frequency models of the degradation as for additive noise, or spurious convolution kernel. The wavelets theory, [1], [2], achieves a localization of the frequencies, and, due to the linear structur...
Multiresolution representations using the autocorrelation functions of compactly supported wavelets
 IEEE Trans. Signal Processing
, 1993
"... CT 06520 0 ..."
Image Segmentation and Analysis via Multiscale Gradient Watershed Hierarchies
, 1999
"... Multiscale image analysis has been used successfully in a number of applications to classify image features according to their relative scales. As a consequence, much has been learned about the scalespace behavior of intensity extrema, edges, intensity ridges, and greylevel blobs. In this paper, w ..."
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Cited by 45 (0 self)
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Multiscale image analysis has been used successfully in a number of applications to classify image features according to their relative scales. As a consequence, much has been learned about the scalespace behavior of intensity extrema, edges, intensity ridges, and greylevel blobs. In this paper, we investigate the multiscale behavior of gradient watershed regions. These regions are defined in terms of the gradient properties of the gradient magnitude of the original image. Boundaries of gradient watershed regions correspond to the edges of objects in an image. Multiscale analysis of intensity minima in the gradient magnitude image provides a mechanism for imposing a scalebased hierarchy on the watersheds associated with these minima. This hierarchy can be used to label watershed boundaries according to their scale. This provides valuable insight into the multiscale properties of edges in an image without following these curves through scalespace. In addition, the gradient watershed region hierarchy can be used for automatic or interactive image segmentation. By selecting subtrees of the region hierarchy, visually sensible objects in an image can be easily constructed.
The Monogenic ScaleSpace: A Unifying Approach to PhaseBased Image Processing in ScaleSpace
 Journal of Mathematical Imaging and Vision
, 2003
"... In this paper we address the topics of scalespace and phasebased image processing in a unifying framework. In contrast to the common opinion, the Gaussian kernel is not the unique choice for a linear scalespace. Instead, we chose the Poisson kernel since it is closely related to the monogenic ..."
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Cited by 32 (19 self)
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In this paper we address the topics of scalespace and phasebased image processing in a unifying framework. In contrast to the common opinion, the Gaussian kernel is not the unique choice for a linear scalespace. Instead, we chose the Poisson kernel since it is closely related to the monogenic signal, a 2D generalization of the analytic signal, where the Riesz transform replaces the Hilbert transform. The Riesz transform itself yields the flux of the Poisson scalespace and the combination of flux and scalespace, the monogenic scalespace, provides the local features attenuation and phasevector in scalespace. Under certain assumptions, the latter two again form a monogenic scalespace which gives deeper insight to lowlevel image processing. In particular, we discuss edge detection by a new approach to phase congruency and its relation to amplitude based methods, reconstruction from local amplitude and local phase, and the evaluation of the local frequency.
Linear ScaleSpace has First been Proposed in Japan
, 1999
"... Linear scalespace is considered to be a modern bottomup tool in computer vision. The American and European vision community, however, is unaware of the fact that it has already been axiomatically derived in 1959 in a Japanese paper by Taizo Iijima. This result formed the starting point of vast li ..."
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Cited by 26 (3 self)
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Linear scalespace is considered to be a modern bottomup tool in computer vision. The American and European vision community, however, is unaware of the fact that it has already been axiomatically derived in 1959 in a Japanese paper by Taizo Iijima. This result formed the starting point of vast linear scalespace research in Japan ranging from various axiomatic derivations over deep structure analysis to applications to optical character recognition. Since the outcomes of these activities are unknown to western scalespace researchers, we give an overview of the contribution to the development of linear scalespace theories and analyses. In particular, we review four Japanese axiomatic approaches that substantiate linear scalespace theories proposed between 1959 and 1981. By juxtaposing them to ten American or European axiomatics, we present an overview of the stateoftheart in Gaussian scalespace axiomatics. Furthermore, we show that many techniques for analysing linear scalespace have also been pioneered by Japanese researchers.
A semidiscrete nonlinear scalespace theory and its relation to the PeronaMalik paradox
 F. Solina (Ed.), Advances in computer vision
, 1997
"... We discuss a semidiscrete framework for nonlinear diffusion scalespaces, where the image is sampled on a finite grid and the scale parameter is continuous. This leads to a system of nonlinear ordinary differential equations. We investigate conditions under which one can guarantee wellposedness pro ..."
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Cited by 26 (3 self)
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We discuss a semidiscrete framework for nonlinear diffusion scalespaces, where the image is sampled on a finite grid and the scale parameter is continuous. This leads to a system of nonlinear ordinary differential equations. We investigate conditions under which one can guarantee wellposedness properties, an extremum principle, average grey level invariance, smoothing Lyapunov functionals, and convergence to a constant steadystate. These properties are in analogy to previously established results for the continuous setting. Interestingly, this semidiscrete framework helps to explain the socalled PeronaMalik paradox: The PeronaMalik equation is a forwardbackward diffusion equation which is widelyused in image processing since it combines intraregional smoothing with edge enhancement. Although its continuous formulation is regarded to be illposed, it turns out that a spatial discretization is sufficient to create a wellposed semidiscrete diffusion scalespace. We also pro...
Applications of Nonlinear Diffusion in Image Processing and Computer Vision
, 2001
"... Nonlinear diffusion processes can be found in many recent methods for image processing and computer vision. In this article, four applications are surveyed: nonlinear diffusion filtering, variational image regularization, optic flow estimation, and geodesic active contours. For each of these techniq ..."
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Cited by 24 (2 self)
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Nonlinear diffusion processes can be found in many recent methods for image processing and computer vision. In this article, four applications are surveyed: nonlinear diffusion filtering, variational image regularization, optic flow estimation, and geodesic active contours. For each of these techniques we explain the main ideas, discuss theoretical properties and present an appropriate numerical scheme. The numerical schemes are based on additive operator splittings (AOS). In contrast to