Optimal ℒ/sub 1/ approximation of the Gaussian kernel with application to scale-space construction

1995 ◽  
Vol 17 (10) ◽  
pp. 1015-1019 ◽  
Author(s):  
Xiaoping Li ◽  
Tongwen Chen
Keyword(s):  
Scale Space ◽  
Gaussian Kernel ◽  
Space Construction

scholarly journals Image segmentation through the scale-space random walker

2021 ◽  
Author(s):  
Richard Rzeszutek
Keyword(s):  
Random Walks ◽  
Graphics Processing Unit ◽  
Scale Space ◽  
Gaussian Kernel ◽  
Processing Unit ◽  
Random Walker ◽  
User Input ◽  
Segmentation Boundary ◽  
Vector Matrix ◽  
Graphics Processing

This thesis proposes an extension to the Random Walks assisted segmentation algorithm that allows it to operate on a scale-space. Scale-space is a multi-resolution signal analysis method that retains all of the structures in an image through progressive blurring with a Gaussian kernel. The input of the algorithm is setup so that Random Walks will operate on the scale-space, rather than the image itself. The result is that the finer scales retain the detail in the image and the coarser scales filter out the noise. This augmented algorithm is referred to as "Scale-Space Random Walks" (SSRW) and it is shown in both artifical and natural images to be superior to Random Walks when an image has been corrupted by noise. It is also shown that SSRW can impove the segmentation when texture, such as the artifical edges created by JPEG compression, has made the segmentation boundary less accurate. This thesis also presents a practical application of the SSRW in an assisted rotoscoping tool. The tool is implemented as a plugin for a popular commerical compositing application that leverages the power of a Graphics Processing Unit (GPU) to improve the algorithm's performance so that it is near-realtime. Issues such as memory handling, user input and performing vector-matrix algebra are addressed.

Uniqueness of the Gaussian Kernel for Scale-Space Filtering

1986 ◽  
Vol PAMI-8 (1) ◽  
pp. 26-33 ◽  
Author(s):  
Jean Babaud ◽  
Andrew P. Witkin ◽  
Michel Baudin ◽  
Richard O. Duda
Keyword(s):  
Scale Space ◽  
Gaussian Kernel

scholarly journals Image segmentation through the scale-space random walker

2021 ◽  
Author(s):  
Richard Rzeszutek
Keyword(s):  
Random Walks ◽  
Graphics Processing Unit ◽  
Scale Space ◽  
Gaussian Kernel ◽  
Processing Unit ◽  
Random Walker ◽  
User Input ◽  
Segmentation Boundary ◽  
Vector Matrix ◽  
Graphics Processing

This thesis proposes an extension to the Random Walks assisted segmentation algorithm that allows it to operate on a scale-space. Scale-space is a multi-resolution signal analysis method that retains all of the structures in an image through progressive blurring with a Gaussian kernel. The input of the algorithm is setup so that Random Walks will operate on the scale-space, rather than the image itself. The result is that the finer scales retain the detail in the image and the coarser scales filter out the noise. This augmented algorithm is referred to as "Scale-Space Random Walks" (SSRW) and it is shown in both artifical and natural images to be superior to Random Walks when an image has been corrupted by noise. It is also shown that SSRW can impove the segmentation when texture, such as the artifical edges created by JPEG compression, has made the segmentation boundary less accurate. This thesis also presents a practical application of the SSRW in an assisted rotoscoping tool. The tool is implemented as a plugin for a popular commerical compositing application that leverages the power of a Graphics Processing Unit (GPU) to improve the algorithm's performance so that it is near-realtime. Issues such as memory handling, user input and performing vector-matrix algebra are addressed.

scholarly journals A Novel Method for Generating Scale Space Kernels Based on Wavelet Theory

2008 ◽  
Vol 15 (2) ◽  
pp. 121-138
Author(s):  
Dionísio Doering ◽  
Adalberto Schuck Junior
Keyword(s):  
Scale Space ◽  
Gaussian Kernel ◽  
Edge Detector ◽  
Wavelet Theory ◽  
One Dimensional ◽  
Poisson Function ◽  
Canny Edge ◽  
Novel Method ◽  
Fundamental Equations ◽  
The Relationship

The linear scale-space kernel is a Gaussian or Poisson function. These functions were chosen based on several axioms. This representation creates a good base for visualization when there is no information (in advanced) about which scales are more important. These kernels have some deficiencies, as an example, its support region goes from minus to plus infinite. In order to solve these issues several others scale-space kernels have been proposed. In this paper we present a novel method to create scale-space kernels from one-dimensional wavelet functions. In order to do so, we show the scale-space and wavelet fundamental equations and then the relationship between them. We also describe three different methods to generate two-dimensional functions from one-dimensional functions. Then we show results got from scale-space blob detector using the original and two new scale-space bases (Haar and Bi-ortogonal 4.4), and a comparison between the edges detected using the Gaussian kernel and Haar kernel for a noisy image. Finally we show a comparison between the scale space Haar edge detector and the Canny edge detector for an image with one known square in it, for that case we show the Mean Square Error (MSE) of the edges detected with both algorithms.

Quantification of Capillary Density and Inter-Capillary Distance in Nailfold Capillary Images Using Scale Space Capillary Detection and Ordinate Clust

2017 ◽  
Vol 6 (1) ◽  
pp. 32-49
Author(s):  
K. V. Suma ◽  
Bheemsain Rao
Keyword(s):  
Clustering Algorithm ◽  
Visual Analysis ◽  
Capillary Density ◽  
Scale Space ◽  
Automated System ◽  
Computer Assisted ◽  
Space Construction ◽  
Sensitivity Specificity ◽  
Very High

The visual analysis of Nailfold Capillary images manually requires trained medical staff and also, the intra-observer variations can be very high. A computer assisted capillary analysis reduces this burden to a great extent. The authors propose an automated system using advanced techniques such as Scale Space construction using Anisotropic Diffusion and Ordinate clustering algorithm. The classification of capillaries is evaluated on the basis of Sensitivity, Specificity and Classification Accuracy. The effectiveness of anisotrpic filtering and Ordinate clustering in eliminating erroneous detection is demonstrated. The capillary density and inter-capillary distance are important capillary parameters which can contribute to the diagnosis of different diseases.

Helicopter main reduction planetary gear fault diagnosis method based on SVDD

2020 ◽  
Vol 64 (1-4) ◽  
pp. 137-145
Author(s):  
Yubin Xia ◽  
Dakai Liang ◽  
Guo Zheng ◽  
Jingling Wang ◽  
Jie Zeng
Keyword(s):  
Fault Diagnosis ◽  
Planetary Gear ◽  
Gaussian Kernel ◽  
Support Vector ◽  
Support Vector Data Description ◽  
Vector Data ◽  
Energy Characteristics ◽  
Gear Fault ◽  
Channel Information ◽  
Diagnosis Method

Aiming at the irregularity of the fault characteristics of the helicopter main reducer planetary gear, a fault diagnosis method based on support vector data description (SVDD) is proposed. The working condition of the helicopter is complex and changeable, and the fault characteristics of the planetary gear also show irregularity with the change of working conditions. It is impossible to diagnose the fault by the regularity of a single fault feature; so a method of SVDD based on Gaussian kernel function is used. By connecting the energy characteristics and fault characteristics of the helicopter main reducer running state signal and performing vector quantization, the planetary gear of the helicopter main reducer is characterized, and simultaneously couple the multi-channel information, which can accurately characterize the operational state of the planetary gear’s state.

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