METHOD FOR CHARACTERISING THE ANISOTROPY OF THE TEXTURE OF A DIGITAL IMAGE

• US 20190325591A1
• Filed: 11/23/2017
• Published: 10/24/2019
• Est. Priority Date: 11/24/2016
• Status: Active Grant

• Current Assignee: Aix-Marseille University, Centre National De La Recherche Scientifique
• Original Assignee: Aix-Marseille University, Centre National De La Recherche Scientifique
• Inventors: RICHARD, Frederic
• Granted Patent: US 10,872,429 B2
• Time in Patent Office: Days
• CPC Class Codes: G06T 2207/20056 Discrete and fast Fourier transform, [DFT, FFT]
• CPC Class Codes: G06T 2207/30068 Mammography; Breast
• CPC Class Codes: G06T 7/0012 Biomedical image inspection
• CPC Class Codes: G06T 7/42 using transform domain methods
• CPC Class Codes: G06T 7/44 using image operators, e.g. filters, edge density metrics or local histograms
• CPC Class Codes: G06T 7/45 using co-occurrence matrix computation
• CPC Class Codes: G06T 7/46 using random fields
• CPC Class Codes: G06T 7/90 Determination of colour characteristics

Abstract

This characterizing method comprises:

• • estimating (28) the scalar coefficients τ_m of an even function τ(θ) defined in [0; 2π] that minimizes the following criterion C:

$C=\sum _{j=1}^{n_i}{\left({\beta }_j-\tau *\Gamma \left({\alpha }_j\right)\right)}^2$

where:

• • β_j are terms estimated from an acquired digital image,
  • τ(θ) is a π-periodic function defined in the interval [0; 2π],
  • Γ(θ) is the function defined by the following relationship:

$\Gamma \left(\theta \right)={\int }_{ℝ+}{\hat{v}\left(\rho \theta \right)}^2{\rho }^{-2H-1}d\rho$

• • • where:
      • {circumflex over (V)} is the discrete Fourier transform of a convolution kernel v,
      • H is an estimated Hurst exponent of the acquired image,
        f) then, calculating (30), depending on the estimate of the scalar coefficients τ_m, an anisotropy index that characterizes the anisotropy of the image, this index varying monotonically as a function of the statistical dispersion of the values of the function τ(θ) for θ varying between 0 and π.

Claims

1. A method comprising characterizing the anisotropy of the texture of a digital image, wherein characterizing comprises:

a) acquiring a digital image formed from pixels, each pixel being associated with a light intensity and with a position in space ^d, where d is a natural integer higher than or equal to two;

b) automatically converting) the acquired image in order to obtain a converted image I_j,k, the conversion comprising applying a modification T_j,k of the image that makes each pixel of the acquired image rotate from one position to the next by an angle α

_j about a point or an axis and that enlarges or shrinks the image by a factor γ

_k, where α

_j=arg(u_jk) and γ

_k=|u_jk|², u_jk being a vector that completely characterizes the modification T_j,k, the indices j and k uniquely identifying the angle α

_j and the factor γ

_k, respectively,

then, for each converted image, calculating a K-increment V_j,k[m] for each pixel of position m of the converted image, this K-increment being calculated by applying a convolution kernel v by means of the following formula;

2. The method as claimed in claim 1, wherein the kernel v used in step b) is equal to the convolution of any convolution kernel and the kernel defined in the following way:

3. The method as claimed in claim 2, wherein:

the functions f_m are functions of the Fourier basis and the function τ

(θ

) is defined by the following relationship;

4. The method as claimed in claim 3, wherein the method comprises:

calculating a value λ

* defined by the following relationship;

5. The method as claimed in claim 1, wherein the anisotropy index is calculated from the sum of the following deviations:

6. The method as claimed in claim 5, wherein the anisotropy index A is calculated using the following relationship:

7. The method as claimed in claim 1, wherein:

the vector u_jk is a vector of ²\{(0,0)}, the modification T_j,k has;

for d=2, the following matrix form;

8. The method as claimed in claim 7, wherein the p-variations calculated in step c) are quadratic variations calculated using the following formula:

9. A method for automatically classifying digital images depending on the anisotropy of their texture, this method comprising acquiring a plurality of images each formed from a plurality of pixels;

wherein the method further comprises automatically calculating, for each of the acquired images, a respective anisotropy index by means of a method as claimed in claim 1, and classifying the acquired digital images using an automatic classifier, depending on the anisotropy index calculated for each of said images.

10. A non-transitory computer-readable data storage medium having encoded thereon instructions for performing a method as claimed in claim 1, when these instructions are executed by a computer.

11. A computer for implementing claim 1, said computer being programmed to execute the following steps:

a) acquiring a digital image formed from pixels, each pixel being associated with a light intensity and with a position in space ^d, where d is a natural integer higher than or equal to two;

b) automatically converting) the acquired image in order to obtain a converted image I_j,k, the conversion comprising applying a modification T_j,k of the image that makes each pixel of the acquired image rotate from one position to the next by an angle α

_j about a point or an axis and that enlarges or shrinks the image by a factor γ

_k, where α

_j=arg(u_jk) and γ

_k=|u_jk|², u_jk being a vector that completely characterizes the modification T_j,k, the indices j and k uniquely identifying the angle α

_j and the factor γ

_k, respectively,

then, for each converted image, calculating a K-increment V_j,k[m] for each pixel of position m of the converted image, this K-increment being calculated by applying a convolution kernel v by means of the following formula;