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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 53 (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
Gradient Watersheds in Morphological ScaleSpace
 IEEE Transactions on Image Processing
, 1996
"... this paper. ..."
On Dimensionality in Multiscale Morphological ScaleSpace with Elliptic Poweroid Structuring Functions
, 1995
"... "Dimensionality" has recently been shown to be an important property in image measurement and image processing operators. It is often thought that morphological operations on an image with "volumic" (nonflat) structuring elements lead to the breakdown of dimensionality. After a brief review of a ne ..."
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Cited by 6 (2 self)
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"Dimensionality" has recently been shown to be an important property in image measurement and image processing operators. It is often thought that morphological operations on an image with "volumic" (nonflat) structuring elements lead to the breakdown of dimensionality. After a brief review of a new morphological scalespace, we show here that any dimensional functional of the scalespace image is also a dimensional functional of the underlying image if multiscale structuring functions from the "elliptic poweroid" family, which are in general volumic, are used to construct the scalespace. Further, from a large class of structuring functions, the elliptic poweroids are the only functions that preserve dimensionality.
Morphological Multiscale Gradient Watershed Image Analysis
, 1995
"... We introduce a scalespace causality theorem for regions of a image defined by watersheds of a gradient function modified to retain only the local minima or maxima of its parent function. We then illustrate an application of the new theorem to the scale dependent extraction of texture elements from ..."
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Cited by 4 (1 self)
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We introduce a scalespace causality theorem for regions of a image defined by watersheds of a gradient function modified to retain only the local minima or maxima of its parent function. We then illustrate an application of the new theorem to the scale dependent extraction of texture elements from the nucleii of cervical cells. 1. Background As background, in the next two subsections we introduce morphological scalespace, and the watershed transform, then in section 2 we outline the new theory of the morphological multiscale gradient watershed which is the central topic of this paper. Finally we demonstrate a potential application to the scale dependent extraction of texture features from the nucleii of cervical cells. 1..1 Morphological ScaleSpace The scalespace concept was introduced to image analysis by Witkin [1]. Scalespace theory provides a way to associate signal descriptions through multiple scales, this approach emphasises the relationship between signal descriptions ...
Families of Generalised Morphological Scale Spaces
"... Abstract. Morphological and linear scale spaces are wellestablished instruments in image analysis. They display interesting analogies which make a deeper insight into their mutual relation desirable. A contribution to the understanding of this relation is presented here. We embed morphological dila ..."
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Cited by 3 (0 self)
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Abstract. Morphological and linear scale spaces are wellestablished instruments in image analysis. They display interesting analogies which make a deeper insight into their mutual relation desirable. A contribution to the understanding of this relation is presented here. We embed morphological dilation and erosion scale spaces with paraboloid structure functions into families of scale spaces which are found to include linear Gaussian scale space as limit cases. The scalespace families are obtained by deforming the algebraic operations underlying the morphological scale spaces within a family of algebraic operations related to l p norms and generalised means. Alternatively, the deformation of the morphological scale spaces can be described in terms of greyscale isomorphisms. We discuss aspects of the newly constructed scale space families such as continuity, invariance, and separability, and the limiting procedure leading to linear scale space. This limiting procedure requires a suitable renormalisation of the scaling parameter. In this sense, our approach turns out to be complementary to that proposed by L. Florack et al. in 1999 which comprises a continuous deformation of linear scale space including morphological scale spaces as limit cases provided an appropriate renormalisation.
Morphological ScaleSpace Fingerprints And Their Use In Object Recognition In Range Images
, 1994
"... In this paper we review the theory of multiscale dilation erosion scalespace and the process of feature extraction via morphological scalespace fingerprints. We then discuss the reduced form of the fingerprints and state the scalespace causality theorem. These fingerprints are then applied to th ..."
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Cited by 2 (2 self)
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In this paper we review the theory of multiscale dilation erosion scalespace and the process of feature extraction via morphological scalespace fingerprints. We then discuss the reduced form of the fingerprints and state the scalespace causality theorem. These fingerprints are then applied to the efficient recognition of multiple objects from range data. The proposed recognition system is invariant to translation, rotation, scale, and partial occlusion. We demonstrate results for the recognition of human faces in a scene, and the recognition of mountain features in a digital elevation map. 1. THEORY 1.1. Gaussian ScaleSpace Scalespace filtering has previously been introduced by Witkin [1]. In this technique the signal f(x;y) : R 2 ! R is expanded into its "scalespace image" F (x; y; oe) : R 2 \Theta R + ! R by convolution with a scaledependent Laplacianof Gaussian kernel, F (x; y; oe) = (f r 2 G oe )(x; y) (1) = ZZ f(x \Gamma s; y \Gamma t)r 2 G oe (s; t) dsdt o...
Classification In ScaleSpace: Applications To Texture Analysis
, 1995
"... this paper we propose a technique for classifying images by modeling features extracted at different scales. Specifically, we use texture measures derived from Pap Smear cell nuclei images using a Grey Level Cooccurrence Matrix (GLCM). For a texture feature extracted from the GLCM at a number of di ..."
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Cited by 2 (2 self)
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this paper we propose a technique for classifying images by modeling features extracted at different scales. Specifically, we use texture measures derived from Pap Smear cell nuclei images using a Grey Level Cooccurrence Matrix (GLCM). For a texture feature extracted from the GLCM at a number of distances we hypothesise that by modeling the feature as a continuous function of scale we can obtain information as to the shape of this function and hence improve its discriminatory power. This hypothesis is compared to the traditional method of selecting a given number of the best single distance measures. It is found, on the limited data set available, that the classification accuracy can be improved by modeling the texture features in this way.
Segmentation in morphological scalespace
 in ISMM'94: Mathematical Morphology and its Applications to Image Processing  Poster Contributions
, 1994
"... and their applications. SMC is sponsored by the Netherlands Organization for Scientific Research (NWO). CWI is a member of ..."
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Cited by 1 (0 self)
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and their applications. SMC is sponsored by the Netherlands Organization for Scientific Research (NWO). CWI is a member of
Scale Space Properties Of The Multiscale Morphological ClosingOpening Filter
 IEEE Trans. PAJffl
, 1992
"... "Scalespace" is an important recent concept used in image and signal processing and pattern recognition. Traditional scalespace is generated by a linear Gaussian smoothing operation. We present here a nonlinear type of smoother corresponding to the multiscale opening and closing operations of math ..."
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Cited by 1 (0 self)
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"Scalespace" is an important recent concept used in image and signal processing and pattern recognition. Traditional scalespace is generated by a linear Gaussian smoothing operation. We present here a nonlinear type of smoother corresponding to the multiscale opening and closing operations of mathematical morphology which also generates a "scalespace." We show that a parabolic structuring element possesses desirable properties and we demonstrate the necessary monotonic scalespace property for this structuring element. Introduction The multiscale filtering of signals and images is an important recent concept in image analysis and vision, especially following Witkin's elegant concept of scalespace filtering [1] which provides a means (via a continuous scale parameter) to relate signal features at one scale to those at another. The signal features chosen are usually zerocrossings of the secondderivative (1D signals) or in images, zerocrossings of the Laplacian [2]. It is importa...