scholarly journals Stochastic analysis of image acquisition, interpolation and scale-space smoothing

1999 ◽  
Vol 31 (4) ◽  
pp. 855-894 ◽  
Author(s):  
Kalle Åström ◽  
Anders Heyden
Keyword(s):  
Stochastic Analysis ◽  
Traditional Approach ◽  
Image Acquisition ◽  
Scale Space ◽  
Image Features ◽  
Space Theory ◽  
Random Errors ◽  
Feature Detectors ◽  
Stochastic Properties ◽  
Discrete Scale

In the high-level operations of computer vision it is taken for granted that image features have been reliably detected. This paper addresses the problem of feature extraction by scale-space methods. There has been a strong development in scale-space theory and its applications to low-level vision in the last couple of years. Scale-space theory for continuous signals is on a firm theoretical basis. However, discrete scale-space theory is known to be quite tricky, particularly for low levels of scale-space smoothing. The paper is based on two key ideas: to investigate the stochastic properties of scale-space representations and to investigate the interplay between discrete and continuous images. These investigations are then used to predict the stochastic properties of sub-pixel feature detectors.The modeling of image acquisition, image interpolation and scale-space smoothing is discussed, with particular emphasis on the influence of random errors and the interplay between the discrete and continuous representations. In doing so, new results are given on the stochastic properties of discrete and continuous random fields. A new discrete scale-space theory is also developed. In practice this approach differs little from the traditional approach at coarser scales, but the new formulation is better suited for the stochastic analysis of sub-pixel feature detectors.The interpolated images can then be analysed independently of the position and spacing of the underlying discretisation grid. This leads to simpler analysis of sub-pixel feature detectors. The analysis is illustrated for edge detection and correlation. The stochastic model is validated both by simulations and by the analysis of real images.

scholarly journals Stochastic analysis of image acquisition, interpolation and scale-space smoothing

1999 ◽  
Vol 31 (04) ◽  
pp. 855-894 ◽  
Author(s):  
Kalle Åström ◽  
Anders Heyden
Keyword(s):  
Stochastic Analysis ◽  
Traditional Approach ◽  
Image Acquisition ◽  
Scale Space ◽  
Image Features ◽  
Space Theory ◽  
Random Errors ◽  
Feature Detectors ◽  
Stochastic Properties ◽  
Discrete Scale

In the high-level operations of computer vision it is taken for granted that image features have been reliably detected. This paper addresses the problem of feature extraction by scale-space methods. There has been a strong development in scale-space theory and its applications to low-level vision in the last couple of years. Scale-space theory for continuous signals is on a firm theoretical basis. However, discrete scale-space theory is known to be quite tricky, particularly for low levels of scale-space smoothing. The paper is based on two key ideas: to investigate the stochastic properties of scale-space representations and to investigate the interplay between discrete and continuous images. These investigations are then used to predict the stochastic properties of sub-pixel feature detectors. The modeling of image acquisition, image interpolation and scale-space smoothing is discussed, with particular emphasis on the influence of random errors and the interplay between the discrete and continuous representations. In doing so, new results are given on the stochastic properties of discrete and continuous random fields. A new discrete scale-space theory is also developed. In practice this approach differs little from the traditional approach at coarser scales, but the new formulation is better suited for the stochastic analysis of sub-pixel feature detectors. The interpolated images can then be analysed independently of the position and spacing of the underlying discretisation grid. This leads to simpler analysis of sub-pixel feature detectors. The analysis is illustrated for edge detection and correlation. The stochastic model is validated both by simulations and by the analysis of real images.

scholarly journals Bayesian modeling and significant features exploration in wavelet power spectra

2007 ◽  
Vol 14 (1) ◽  
pp. 79-88 ◽  
Author(s):  
D. V. Divine ◽  
F. Godtliebsen
Keyword(s):  
Data Analysis ◽  
Traditional Approach ◽  
Statistical Significance ◽  
Power Spectra ◽  
Simulated Data ◽  
Scale Space ◽  
Independent Random Variables ◽  
Discrete Wavelet ◽  
Wavelet Coefficients ◽  
Testing Procedures

Abstract. This study proposes and justifies a Bayesian approach to modeling wavelet coefficients and finding statistically significant features in wavelet power spectra. The approach utilizes ideas elaborated in scale-space smoothing methods and wavelet data analysis. We treat each scale of the discrete wavelet decomposition as a sequence of independent random variables and then apply Bayes' rule for constructing the posterior distribution of the smoothed wavelet coefficients. Samples drawn from the posterior are subsequently used for finding the estimate of the true wavelet spectrum at each scale. The method offers two different significance testing procedures for wavelet spectra. A traditional approach assesses the statistical significance against a red noise background. The second procedure tests for homoscedasticity of the wavelet power assessing whether the spectrum derivative significantly differs from zero at each particular point of the spectrum. Case studies with simulated data and climatic time-series prove the method to be a potentially useful tool in data analysis.

Explaining feature detection Mechanisms: A Survey

2021 ◽  
pp. 51-64
Author(s):  
Ahmed A. Elngar ◽  
◽  
◽  
◽  
◽  
...  
Keyword(s):  
Feature Detection ◽  
Feature Matching ◽  
Image Features ◽  
Mathematical Concepts ◽  
Detection Algorithms ◽  
Feature Detectors ◽  
Essential Components ◽  
Basic Notation ◽  
Computer Vision Applications ◽  
Detection Mechanisms

Feature detection, description and matching are essential components of various computer vision applications; thus, they have received a considerable attention in the last decades. Several feature detectors and descriptors have been proposed in the literature with a variety of definitions for what kind of points in an image is potentially interesting (i.e., a distinctive attribute). This chapter introduces basic notation and mathematical concepts for detecting and describing image features. Then, it discusses properties of perfect features and gives an overview of various existing detection and description methods. Furthermore, it explains some approaches to feature matching. Finally, the chapter discusses the most used techniques for performance evaluation of detection algorithms.

Image features using scale-space FAST corner detector and SURF descriptor

2014 ◽  
Vol 29 (4) ◽  
pp. 598-604
Author(s):  
王飞宇 WANG Fei-yu ◽  
邸男 DI Nan ◽  
贾平 JIA Ping
Keyword(s):  
Scale Space ◽  
Image Features
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