Grayscale morphology

Sternberg, S.

doi:10.1016/0734-189x(86)90004-6

Cited by 650 publications

(191 citation statements)

References 3 publications

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“…The blending function C j (x) must be continuous through at least its second derivative, in order for the nonlinearly smoothed signalf(x, a j ) to have continuous first and second derivatives. Rearranging the factors in equation (1) and denoting the first and second derivatives of C j (x) by C (1) j (x) and C (2) j (x), respectively, one obtains the following expressions for the first and second derivatives of the nonlinearly smoothed signalf(x, a j ):…”

Section: B Defining the Blending Functionsmentioning

confidence: 99%

“…Linear smoothing was performed at four scales using uniform cubic B-spline basis functions with scale parameters a 1 = 1, a 2 = 2, a 3 = 4, and a 4 = 8. Nonlinear smoothing was performed at the scales a 2 , a 3 , and a 4 , using equation (1). Results at the scale a 4 are shown in Figure 3(a).…”

Section: A Simulated 1-d Edgementioning

confidence: 99%

“…Rather than irreversibly altering the image data prior to 1 This work was supported by US Department of Health and Human Services grant P01-HL25840, by US Department of Energy contract DE-AC03-76SF00098, and by the University of California MICRO program. This work was developed in part using the resources at the US Department of Energy National Energy Research Scientific Computing (NERSC) Center.…”

Section: Introductionmentioning

confidence: 99%

“…The goal of the nonlinear smoothing is to improve the accuracy of the segmentation by preserving changes in image intensity at the boundaries of structures of interest, while smoothing random variations due to noise in the interiors of the structures. Methods include median filtering and morphology operations such as gray scale erosion and dilation [1], as well as spatially varying smoothing driven by local contrast measures [2,3]. By comparison, linear smoothing via spatially invariant convolution uniformly blurs structure boundaries, as well as noise.…”

Section: Introductionmentioning

confidence: 99%

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Computationally efficient nonlinear edge preserving smoothing of n-D medical images via scale-space fingerprint analysis

Reutter

Algazi²,

Huesman³

2000 IEEE Nuclear Science Symposium. Conference Record (Cat. No.00CH37149)

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Nonlinear edge preserving smoothing often is performed prior to medical image segmentation. The goal of the nonlinear smoothing is to improve the accuracy of the segmentation by preserving changes in image intensity at the boundaries of structures of interest, while smoothing random variations due to noise in the interiors of the structures. Methods include median filtering and morphology operations such as gray scale erosion and dilation, as well as spatially varying smoothing driven by local contrast measures.Rather than irreversibly altering the image data prior to segmentation, the approach described here has the potential to unify nonlinear edge preserving smoothing with segmentation based on differential edge detection at multiple scales. The analysis of n-D image data is decomposed into independent 1-D problems that can be solved quickly. Smoothing in various directions along 1-D profiles through the n-D data is driven by a measure of local structure separation, rather than by a local contrast measure. Isolated edges are preserved independent of their contrast, given an adequate contrast to noise ratio.

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Section: B Defining the Blending Functionsmentioning

confidence: 99%

Section: A Simulated 1-d Edgementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Computationally efficient nonlinear edge preserving smoothing of n-D medical images via scale-space fingerprint analysis

Reutter

Algazi²,

Huesman³

2000 IEEE Nuclear Science Symposium. Conference Record (Cat. No.00CH37149)

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“…It considers images as sets which permits geometry-oriented transformations of the images. For the multiscale image decomposition we have used basic morphological operators dilation (D) and erosion (E), [14,15]:…”

Section: Proposed Morphological Multi-scale Metricmentioning

confidence: 99%

Multi–Scale Synthesized View Assessment Based on Morphological Pyramids

Sandic-Stankovic¹,

Kukolj

Callet

2016

Journal of Electrical Engineering

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The Depth-Image-Based-Rendering (DIBR) algorithms used for 3D video applications introduce geometric distortions affecting the edge coherency in the synthesized images. In order to better deal with specific geometric distortions in the DIBR synthesized images, we propose full-reference metric based on multi-scale pyramid decompositions using morphological filters. The non-linear morphological filters used in multi-scale image decompositions maintain important geometric information such as edges across different resolution levels. We show that PSNR has particularly good agreement with human judgment when it is calculated between detailed images at higher scales of morphological pyramids. Consequently, we propose reduced morphological pyramid peak signal-to-noise ratio metric (MP-PSNR), taking into account only mean squared errors between pyramids' images at higher scales. Proposed computationally efficient metric achieves significantly higher correlation with human judgment compared to the state-of-the-art image quality assessment metrics and compared to the tested metric dedicated to synthesis-related artifacts.

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On a generalization of Blaschke's Rolling Theorem and the smoothing of surfaces

Walther

1999

Math. Meth. Appl. Sci.

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Grayscale morphology

Cited by 650 publications

References 3 publications

Computationally efficient nonlinear edge preserving smoothing of n-D medical images via scale-space fingerprint analysis

Computationally efficient nonlinear edge preserving smoothing of n-D medical images via scale-space fingerprint analysis

Multi–Scale Synthesized View Assessment Based on Morphological Pyramids

On a generalization of Blaschke's Rolling Theorem and the smoothing of surfaces

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