Image analysis – Image enhancement or restoration – Image filter
Patent
1996-03-18
1998-10-13
Boudreau, Leo
Image analysis
Image enhancement or restoration
Image filter
382168, 382210, 382255, 382264, 382275, 382278, 382279, G06K 900, G06K 976, G06K 940, G06K 964
Patent
active
058224661
DESCRIPTION:
BRIEF SUMMARY
BACKGROUND OF THE INVENTION
1. Field of the Invention
The invention relates to a method and a means of spatial filtering, enabling structures in n-dimensional spaces to be identified, even when these structures are buried in noise.
2. Description of the Related Art
For this purpose it is known to make use of the so-called "maximum entropy" and "maximum-likelihood" techniques of locally searching for density fluctuations. These known techniques, however, necessitate assumptions or advance information to be able to identify the structures concerned. Further drawbacks of these known methods are that an extension to more than two dimensions requires highly complicated computations, that non-uniform measurement parameters and many different correlations defeat processing and that the sensitivity in the case of irregular patterns having strongly uncorrelated noise is low.
Furthermore, from the publication by H. Atmanspacher et al. in PHYSICAL REVIEW A (GENERAL PHYSICS), Vol. 40, No. 7, October 1989, USA, pages 3954-3963; ATMANSPACHER H. ET AL. "Determination of F (alpha) for a Limited Random Point Set (Galaxy Distribution)" a technique is known with which by determining the f(.alpha.) spectrum in a mainly uncorrelated point set any correlated subsets existing may be identifed. A further technique is known from the publication by H. Ebeling et al. in PHYSICAL REVIEW E (STATISTICAL PHYSICS, PLASMAS, FLUIDS AND RELATED INTERDISCIPLINARY TOPICS), Vol. 47, No. 1 January 1993, USA, pages 704-710; EBELING H. & WIEDENMANN G "Detecting Structure in Two Dimensions Combining Voronoi Tessellation and Percolation". In this technique the raw data point field is split up into individual cells (Voronoi Tesselation) and the distribution of the cells compared to those anticipated in a statistical Poisson distribution.
SUMMARY OF THE INVENTION
The present invention is thus based with reference to this prior art on the object of defining a method and a means with which n-dimensional structures buried in noise are detectable relatively simply.
This object is achieved by the invention as characterized in the claims and as discussed in more detail in the following.
In accordance with a first aspect of the invention a method of spatial filtering a distribution of points, representing a structure buried in noise, each point of which is defined by n coordinate values of an n-dimensional space, is characterized by the following steps: number (N) of the points in an area around the point concerned as a function of a dimension (d) of area, (a) of a simple power function determined in step a) in a certain range of the dimension (d), point distribution of a type equivalent to the point distribution to be filtered are determined, distribution to be filtered and the scaling coefficients of the stochastic point distribution is determined, difference and which represent the structure substantially free of noise, are represented in at least a two-dimensional space.
In accordance with a second aspect of the invention a method of spatial filtering a distribution of points, representing a structure buried in noise, each point of which is defined by n coordinate values of an n-dimensional space, is characterized by the following steps: the number (N) of the points in an area around the point concerned as a function of a dimension (d) of the area, (a) of a simple power function determined in step a) in a certain range of the dimension (d), point distribution of a type equivalent to the point distribution to be filtered are determined, distribution to be filtered stochastic point distribution is assigned a cumulative number (P(<a)) equal to the number of scaling coefficients of the distribution concerned which are greater than or equal to the corresponding scaling coefficients, divided by the total number of the measured scaling coefficients of the distribution concerned, the cumulative numbers of the stochastic distribution determined in this step being scaled such that they agree by their highest numerical values with the highest numerical valu
REFERENCES:
Determination of f (x) for a limited random point set, Physical Review A, l. 40, No. 7, Oct. 1, 1989.
Chaos and Fractal Algorithms Applied to Signal Processing and Analysis, Simulation, vol. 60 No. 4, Apr. 1993.
Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Physical Review E, APS-AIP, vol. 47 3rd series Jan.-Jun. 1993.
Morfill Gregor Eugen
Scheingraber Herbert
Wiedenmann Gerda
Boudreau Leo
Mariam Daniel G.
Max-Planck-Gesselschaft zur Forderburg der Wissenschaften e. V
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