WO2013078451A1 - Procédé permettant de déterminer un spectre local au niveau d'un pixel au moyen d'une transformée s invariante en rotation (rist) - Google Patents

Procédé permettant de déterminer un spectre local au niveau d'un pixel au moyen d'une transformée s invariante en rotation (rist) Download PDF

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Publication number
WO2013078451A1
WO2013078451A1 PCT/US2012/066450 US2012066450W WO2013078451A1 WO 2013078451 A1 WO2013078451 A1 WO 2013078451A1 US 2012066450 W US2012066450 W US 2012066450W WO 2013078451 A1 WO2013078451 A1 WO 2013078451A1
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determining
values
pixel
roi
matrix
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PCT/US2012/066450
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English (en)
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Chun Hing Cheng
Joseph Ross Mitchell
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Mayo Foundation For Medical Education And Research
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Priority to US14/360,294 priority Critical patent/US20150193671A1/en
Publication of WO2013078451A1 publication Critical patent/WO2013078451A1/fr
Priority to US15/276,667 priority patent/US9818187B2/en

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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T7/00—Image analysis
    • G06T7/40—Analysis of texture
    • G06T7/41—Analysis of texture based on statistical description of texture
    • G06T7/42—Analysis of texture based on statistical description of texture using transform domain methods
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06V—IMAGE OR VIDEO RECOGNITION OR UNDERSTANDING
    • G06V10/00—Arrangements for image or video recognition or understanding
    • G06V10/40—Extraction of image or video features
    • G06V10/42—Global feature extraction by analysis of the whole pattern, e.g. using frequency domain transformations or autocorrelation
    • G06V10/431—Frequency domain transformation; Autocorrelation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
    • G06T2207/10—Image acquisition modality
    • G06T2207/10072—Tomographic images
    • G06T2207/10088—Magnetic resonance imaging [MRI]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
    • G06T2207/20—Special algorithmic details
    • G06T2207/20048—Transform domain processing
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
    • G06T2207/30—Subject of image; Context of image processing
    • G06T2207/30004—Biomedical image processing
    • G06T2207/30016—Brain

Definitions

  • Continuous S-transform (ST) ca n be regarded as a hybrid of Gabor and continuous wavelet transforms, providing a "time frequency representation" (TFR) of a signal by localizing with a Gaussian window that depends on the frequency.
  • TFR time frequency representation
  • ID ST discrete 1- dimensional form
  • 2D ST discrete 2-dimensional form
  • SFR space frequency representation
  • Fast Time Frequency Transform tools have been developed, such as a FTFT-1D and FTFT-2D (Fast Time Frequency Transform), that generate discrete ID ST values and 2D ST magnitudes fast and accurately.
  • the FTFT-2D can produce local ST magnitudes at each pixel in a medical image, as well as ST statistics over a region of interest (ROI) in the image.
  • ROI region of interest
  • the discretization of 2D ST renderings are not rotationally invariant.
  • rotational invariance of an SFR it is meant that when the image is rotated by any angle, the radial component of the SFR is unchanged. This is desirable as the pathology inferred from this radial component should not be affected when the patient is positioned at a different orientation on the imaging couch.
  • a method of determining rotational invariant local spectrum at a pixel in an image processing device may include receiving an input image; receiving an input coordinate of the pixel; and determining the values of a rotational invariant form of two- dimensional S-Transform (RIST) at the input coordinate.
  • RIST two- dimensional S-Transform
  • the method further includes determining the S- Transform (ST) magnitudes (Al) using positive discretization at the input coordinate of the pixel; flipping the input image along x direction; determining the ST magnitudes (A2) using positive discretization at the coordinate of the corresponding pixel in the flipped image; and determining the average of the above two sets Al and A2 of magnitudes.
  • ST S- Transform
  • the RIST algorithm may be implemented using a modified form of a FTFT-2D method.
  • the method may be implemented by a computing device executing the method as computer-executable instructions read from a tangible computer-readable medium.
  • Figures 1A-1C show the magnitudes of the ST values for a real chirp signal and the values found by a "positive discretization” and a "symmetric discretization” definition;
  • Figure 2A illustrates a 256 x 256 MRI image of a diseased brain with a white cross at pixel P(174, 176);
  • Figure 2B illustrates the 256 x 256 MRI image of the diseased brain of Figure 2A rotated by about -42°, with a white cross at pixel P'(134, 68);
  • Figures 2C and 2D illustrate ST magnitudes at P and P' obtained by positive discretization, with x and y frequency indices on the axes;
  • Figures 2E and 2F illustrate radial components at P and P', with a radius on horizontal axis and radial ST magnitude on vertical axis;
  • Figure 2G illustrates radial components at P and P' put together for comparison
  • Figures 2H and 2L illustrate the same features a Figures 2C-2G, however using symmetric discretization
  • Figure 3A illustrates 256 x 256 MRI image I with a white cross at pixel P(174,
  • Figure 3B illustrates the image of Figure 3A flipped with a white cross at corresponding (81, 176);
  • Figure 4A illustrates a 256 x 256 MRI image of a diseased brain, with a white cross at pixel P(174, 176);
  • Figure 4B illustrates a 256 x 256 MRI image of the diseased brain rotated by about -42° with a white cross at pixel P'(134, 68);
  • Figures 4C and 4D illustrate RIST magnitudes at P and P', with x and y frequency indices on the axes;
  • Figures 4E and 4F illustrate radial components at P and P', with a radius on a horizontal axis and radial ST magnitude on vertical axis;
  • Figure 4G illustrates radial components at P and P' put together for comparison
  • Figures 4H-4L illustrates the same images as Figures 4C-4G, but using a FTFT- 2D modified for RIST.
  • Figure 5A illustrates a 256 x 256 MRI image of a uniform line pattern with sinusoidal intensities inclined at 45° with a white cross at any point P;
  • Figure 5B illustrates a 256 x 256 MRI image of the uniform line pattern with same separation inclined at 22.5° with a white cross at any point P';
  • Figures 5C and 5D illustrates RIST magnitudes of the two patterns, with x and y frequency indices on the axes;
  • Figures 5E and 5F illustrates radial components of the two patterns, with a radius on a horizontal axis and radial ST magnitude on vertical axis; [0030] Figure 5G illustrates radial components of the two patterns put together for comparison;
  • Figure 6A illustrates 256 x 256 MRI image of a diseased brain with a white cross at pixel P(174, 176);
  • Figure 6B illustrates a 256 x 256 MRI image of the diseased brain rotated by about -42° with a white cross at pixel P'(134, 68);
  • Figures 6C and 6D illustrate ST magnitudes at P and P' obtained by RIST* with x and y frequency indices on the axes;
  • Figures 6E and 6F illustrate radial components at P and P' from RIST* with a radius on a horizontal axis and radial ST magnitude on vertical axis. ;
  • Figures 7A-7D illustrate screenshots of a FTFT-RIST tool for an artificial image of concentric circles. It is rotated by four angles such that a specific pixel (shown as a cross) makes angles 15, 61, 127 and 143 degrees with the x-axis; and
  • FIG. 8 is a block diagram of an example computing device.
  • the present disclosure describes a variant of a 2D S-transform (ST), called a "Rotationally Invariant S-Transform” (RIST), that is substantially rotationally invariant.
  • ST 2D S-transform
  • RIST Rotationally Invariant S-Transform
  • the formula of RIST provides a magnitude (modulus) of the complex number, but not the phases.
  • RIST may be used for square images; as such because most medical images are square or can be made so by cropping and padding the image, RIST has applicability to such images.
  • the RIST values obtained by the original formulae are inherently not smooth.
  • a FTFT-2D may be used to generate RIST magnitudes for pixels and RIST statistics for regions of interest quickly and accurately.
  • the FTFT-2D algorithm and tools are disclosed in U.S. Provisional Patent Application No. 61/562,486, filed on November 22, 2011, entitled “FTFT-2D Patent Detailed Description," and U.S. Provisional Patent Application No. 61/562,498, filed on November 22, 2011, entitled “FTFT-2D Patent Detailed Description,” the disclosures of which are expressly incorporated herein by reference in their entireties.
  • RIST magnitudes produced by the FTFT-2D tool may be used for SRF in many medical applications, such as virtual biopsy. Also described herein is another rotationally invariant ST, called RIST*. RIST* may be used in both SFT visualization and spectral analysis.
  • a FTFT-RIST tool displays the values and graphs of RIST* for each pixel or a region of interest (ROI). It also outputs a vector of texture and spectral features based on RIST*.
  • the 1-dimensional Continuous ST of a complex function of time h(t) is a joint complex function of time t and fre uency/:
  • the discrete ST for a signal or time series can be found using the frequency domain, derived by the Convolution Theorem. There are two ways to perform the above, which differ in the summation endpoints.
  • a first is as follows:
  • a second is as follows:
  • the values n and k are the time and frequency indices respectively.
  • the value k is equal to /V/where / is the frequency.
  • the usage of " [ ]” is for discrete functions of integers, while “( )” is for continuous functions of rea l or complex numbers. In practice, by Nyquist Theorem, the present disclosure seeks to find the ST for/from
  • Symmetric discretization provides better results than positive discretization, as such estimates of symmetric-discretization ST values are used.
  • n x , k x , n y , k y are the time and frequency indices respectively in each H ⁇ k k 1
  • x ' y is the 2-dimensional Fourier Transform.
  • Figure 2A illustrates a 256 x 256 MRI image of a diseased brain with a white cross at pixel P(174, 176).
  • Figure 2B illustrates the 256 x 256 MRI image of the diseased brain of Figure 2A rotated by about -42°, with a white cross at pixel P'(134, 68).
  • Figures 2C and 2D illustrate ST magnitudes at P and P' obtained by positive discretization, with x and y frequency indices on the axes.
  • Figures 2E and 2F illustrate radial components at P and P', with a radius on horizontal axis and radial ST magnitude on vertical axis.
  • Figure 2G illustrates radial components at P and P' put together for comparison.
  • Figures 2H and 2L illustrate the same features a Figures 2C-2G, however using symmetric discretization.
  • Figures 2C and 2H show the 2D ST magnitudes of a pixel in a 256 x 256 MRI of Figure 2A found using relationship (4) and relationship (5) respectively.
  • r is the radius in the k-space.
  • round() means the nearest integer of a real number.
  • the ST magnitudes for those points in the k-space whose magnitudes do not exceed N/2 are considered.
  • Figures 2A-2L and all other figures only a circular sector is displayed. The points outside the sector do not contribute to the texture curve.
  • An SFR possesses a "translational invariance" property if the following is true: For any image I and its translation ⁇ by any vector (u, v), and for any pixel P(n x , n y ) on I and the corresponding pixel P'(n x + u, n y + v) on ⁇ , the SFR magnitude at every (k x , k y ) in the k-space for P on I is equal to the SFR magnitude at (k x , k y ) for P' on .
  • Tra nslational invariance is well satisfied by most SFR. It is easy to show that ST magnitude is translationally invariant (except for the edge effects), and so for RIST, which is formed in terms of ST.
  • An SFR possesses "rotational invariance" property if the following is true: For any image / and its rotation /' by any angle ⁇ about any point (a, b), and for any pixel P on I and the corresponding pixel P' on , the radial component of SFR magnitudes at any radius r in the k-space for P on I is identical to that for P' on . Thus, given translational invariance, an SFR that is rotationally invariant about a point (a, b) is also rotationally invariant about any other point ( ⁇ ', b').
  • a strong rotational invariance is as follows: For any image I and its rotation ⁇ by any angle ⁇ about any point (a, b), and for any pixel P(n x , n y ) on I and the corresponding pixel P'(n' x , n' y ) on , the SFR magnitude at every (k x , k y ) in the k-space for P on I is equal to the SFR magnitude at (k' x , k' y ) for P' on ⁇ , where (k' x , k' y ) is the point obtained by rotating (k x , k y ) in the k-space by the same angle Accordingly, below a RIST* is introduced which is an alternative form of RIST, which roughly satisfies this strong requirement.
  • the SFR magnitude at every (k x , k y ) in the k-space for P on I is identical to that at same point (k x , k y ) for P x on I x .
  • An SFR possesses a "right-angle rotational invariance" property if the following is true: For any image I and its rotation by ⁇ 90° any point (a, b) and for any pixel P on I and the corresponding pixel P' on , the SFR magnitude at every (k x , k y ) in the k-space for P on I is equal to the SFR magnitude at the diagonally flipped point (k y , k x ) in the k-space for P' on .
  • an SFR that is right-angle rotationally invariant about a point (a, b) is also right-angle rotationally invariant about any other point ( ⁇ ', b').
  • RIST 2-dimensional Discrete Rotationally Invariant S-Transform
  • the magnitude of RIST has been defined in terms of the magnitudes of ST, without first defining the complex value of RIST, , itself.
  • relationship (7) can be expressed in words: For each x ' y ' in the k-space, the RIST
  • magnitude of an image I at pixel x ' y/ is equal to the arithmetic mean of the positive- discretization ST magnitude of the given image at that pixel and that of the flipped image I x at
  • Figure 3A illustrates 256 x 256 MRI image I with a white cross at pixel P(174, 176).
  • Figure 3B illustrates the image of Figure 3A flipped with a white cross at corresponding (81, 176).
  • relationship (7) satisfies the reflectional (and hence right-angle rotational) invariances defined in Section 3. From examples, relationship (7) roughly satisfies rotational invariance in general.
  • Figure 4A illustrates a 256 x 256 MRI image of a diseased brain, with a white cross at pixel P(174, 176).
  • Figure 4B illustrates a 256 x 256 MRI image of the diseased brain rotated by about -42° with a white cross at pixel P'(134, 68).
  • Figures 4C and 4D illustrate RIST magnitudes at P and P', with x and y frequency indices on the axes.
  • Figures 4E and 4F illustrate radial components at P and P', with a radius on a horizontal axis and radial ST magnitude on vertical axis.
  • Figure 4G illustrates radial components at P and P' put together for comparison.
  • Figures 4H-4L illustrates the same images as Figures 4C-4G, but using a FTFT-2D modified for RIST.
  • Figure 5A illustrates a 256 x 256 MRI image of a uniform line pattern with sinusoidal intensities inclined at 45° with a white cross at any point P.
  • Figure 5B illustrates a 256 x 256 MRI image of the uniform line pattern with same separation inclined at 22.5° with a white cross at any point P'.
  • Figures 5C and 5D illustrates RIST magnitudes of the two patterns, with x and y frequency indices on the axes.
  • Figures 5E and 5F illustrates radial components of the two patterns, with a radius on a horizontal axis and radial ST magnitude on vertical axis.
  • Figure 5G illustrates radial components of the two patterns put together for comparison.
  • relationship (8) is equivalent to relationship (7).
  • p may be used instead of p .
  • the second term is for reflection along y, so p réelle_ w
  • the FTFT-2D may be modified so that they compute RIST values fast and accurately. By “accurately”, it is meant that the results obtained are a reasonable approximation of relationship (7).
  • the flipped image I x is created and both images pre-processed. Then, to find the RIST value for a pixel P in I, the FTFT-
  • the time taken to find an RIST value by the new FTFT-2D is slightly more than double that to find ST, but is still very short.
  • Figures 4H-4K show the RIST magnitudes found by this new FTFT-2D, and they appear smoother than that by the exact relationship (7), thanks to the cropping operation inside FTFT-2D that helps remove the noise.
  • the process time is 0.039 seconds, while that using the FTFT-2D to find ST magnitude is 0.018 seconds.
  • RIST* an improved form of RIST, called RIST* will now be described. It differs from RIST in several ways. First, it is defined as a complex number, whereas with RIST only a magnitude is defined by relationship (7). Second, it allows the frequency indexes k x and k y to be signed, thus enabling a more comprehensive visualization and analysis of the spectral characteristics of the image. Third, it provides a more convincing demonstration of the rotational invariance of RIST.
  • the RIST* value at a point (n x , n y ) in an N x N square image may be defined as a complex number: ⁇
  • FIG. 6A illustrates 256 x 256 MRI image of a diseased brain with a white cross at pixel P(174, 176).
  • Figure 6B illustrates a 256 x 256 MRI image of the diseased brain rotated by about -42° with a white cross at pixel P'(134, 68).
  • Figures 6C and 6D illustrate ST magnitudes at P and P' obtained by RIST* with x and y frequency indices on the axes.
  • Figures 6E and 6F illustrate radial components at P and P' from RIST* with a radius on a horizontal axis and radial ST magnitude on vertical axis.
  • Figures 6A-6F show the RIST* magnitudes and texture curves for the example of Figures 4A-4F.
  • the semicircular of RIST* provides more spectral information than the quadrant of RIST.
  • the above may be provided by a FTFT- RIST tool that that displays the magnitude of RIST* in the semicircle, as well as the texture curve of RIST*. It also divides the semicircle into s equal sectors, where s is specified by the user. Then it finds the sector with the largest average RIST* magnitude and draws the texture curve for this major sector.
  • the texture curve in Figure 7(c) represents the radial variation of RIST* in all directions, while the major texture curve in Figure 7(d) is only for that major sector.
  • Figure 7 also provides evidence of the strong rotational invariance mentioned in Section 3.2: the semicircular RIST* diagram rotates with the image. As the strong condition implies the weak one, is demonstrates that RIST and RIST* are fairly rotationally invariant.
  • representations provide a very fast way to compute them for a pixel or for an ROI, using modified forms of the FTFT-2D tool. They are useful for spectral analysis of medical images.
  • FIG. 8 shows an exemplary computing environment in which example embodiments and aspects may be implemented.
  • the computing system environment is only one example of a suitable computing environment and is not intended to suggest any limitation as to the scope of use or functionality.
  • N umerous other general purpose or special purpose computing system environments or configurations may be used.
  • Examples of well known computing systems, environments, and/or configurations that may be suitable for use include, but are not limited to, personal computers, server computers, handheld or laptop devices, multiprocessor systems, microprocessor-based systems, network personal computers (PCs), minicomputers, mainframe computers, embedded systems, distributed computing environments that include any of the above systems or devices, and the like.
  • Computer-executable instructions such as program modules, being executed by a computer may be used.
  • program modules include routines, programs, objects, components, data structures, etc. that perform particular tasks or implement particular abstract data types.
  • Distributed computing environments may be used where tasks are performed by remote processing devices that are linked through a com munications network or other data transmission medium. I n a distributed computing environment, program modules and other data may be located in both local and remote computer storage media including memory storage devices.
  • an exemplary system for implementing aspects described herein includes an image processing device, such as computing device 800.
  • computing device 800 typically includes at least one processing unit 802 and memory 804.
  • memory 804 may be volatile (such as random access memory (RAM)), non-volatile (such as read-only memory (ROM), flash memory, etc.), or some combination of the two.
  • RAM random access memory
  • ROM read-only memory
  • flash memory etc.
  • Computing device 800 may have additional features/functionality.
  • computing device 800 may include additional storage (removable and/or nonremovable) including, but not limited to, magnetic or optical disks or tape. Such additional storage is illustrated in FIG. 8 by removable storage 808 and non-removable storage 810.
  • Computing device 800 typically includes a variety of computer readable media.
  • Computer readable media can be any available media that ca n be accessed by device 800 and includes both volatile and non-volatile media, removable and non-removable media.
  • Computer storage media include volatile and non-volatile, and removable and non-removable media implemented in any method or technology for storage of information such as computer readable instructions, data structures, program modules or other data.
  • Computer storage media include, but are not limited to, RAM, ROM, electrically erasable program read-only memory (EEPROM), flash memory or other memory technology, CD-ROM, digital versatile disks (DVD) or other optical storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other medium which can be used to store the desired information and which can be accessed by computing device 800. Any such computer storage media may be part of computing device 800.
  • Computing device 800 may contain communications connection(s) 812 that allow the device to communicate with other devices.
  • Computing device 800 may also have input device(s) 814 such as a keyboard, mouse, pen, voice input device, touch input device, etc.
  • Output device(s) 816 such as a display, speakers, printer, etc. may also be included. All these devices are well known in the art and need not be discussed at length here.
  • the computing device In the case of program code execution on programmable computers, the computing device generally includes a processor, a storage medium readable by the processor (including volatile and non-volatile memory and/or storage elements), at least one input device, and at least one output device.
  • One or more programs may implement or utilize the processes described in connection with the presently disclosed subject matter, e.g., through the use of an application programming interface (API), reusable controls, or the like.
  • API application programming interface
  • Such programs may be implemented in a high level procedural or object- oriented programming language to communicate with a computer system.
  • the program(s) can be implemented in assembly or machine language, if desired. In any case, the language may be a compiled or interpreted language and it may be combined with hardware implementations.

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Abstract

L'invention concerne un dispositif et des procédés de traitement d'images permettant d'effectuer une transformée S invariante en rotation (RIST) pour une image. Selon l'invention, un procédé donné à titre d'exemple permet de déterminer la magnitude de RIST au niveau d'un pixel. De plus, selon l'invention, un procédé donné à titre d'exemple permet de déterminer des magnitudes de RIST et des statistiques dans une zone d'intérêt.
PCT/US2012/066450 2004-04-15 2012-11-23 Procédé permettant de déterminer un spectre local au niveau d'un pixel au moyen d'une transformée s invariante en rotation (rist) WO2013078451A1 (fr)

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US14/360,294 US20150193671A1 (en) 2004-04-15 2012-11-23 Methods of determining local spectrum at a pixel using a rotationally invariant s-transform (rist)
US15/276,667 US9818187B2 (en) 2011-11-22 2016-09-26 Determining local spectrum at a pixel using a rotationally invariant S-transform (RIST)

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US201161562504P 2011-11-22 2011-11-22
US61/562,504 2011-11-22

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US15/276,667 Continuation-In-Part US9818187B2 (en) 2011-11-22 2016-09-26 Determining local spectrum at a pixel using a rotationally invariant S-transform (RIST)

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Cited By (2)

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CN110057321A (zh) * 2019-04-28 2019-07-26 西安理工大学 基于x-f-k变换快速实现频域解相的三维物体面形测量方法
CN110347970A (zh) * 2019-07-19 2019-10-18 成都理工大学 分数阶同步提取广义s变换时频分解与重构方法

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US20060083407A1 (en) * 2004-10-15 2006-04-20 Klaus Zimmermann Method for motion estimation
US20090161945A1 (en) * 2007-12-21 2009-06-25 Canon Kabushiki Kaisha Geometric parameter measurement of an imaging device
US20100008589A1 (en) * 2006-10-11 2010-01-14 Mitsubishi Electric Corporation Image descriptor for image recognition

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US6803919B1 (en) * 1999-07-09 2004-10-12 Electronics And Telecommunications Research Institute Extracting texture feature values of an image as texture descriptor in a texture description method and a texture-based retrieval method in frequency domain
US20060083407A1 (en) * 2004-10-15 2006-04-20 Klaus Zimmermann Method for motion estimation
US20100008589A1 (en) * 2006-10-11 2010-01-14 Mitsubishi Electric Corporation Image descriptor for image recognition
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Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110057321A (zh) * 2019-04-28 2019-07-26 西安理工大学 基于x-f-k变换快速实现频域解相的三维物体面形测量方法
CN110347970A (zh) * 2019-07-19 2019-10-18 成都理工大学 分数阶同步提取广义s变换时频分解与重构方法
CN110347970B (zh) * 2019-07-19 2023-03-28 成都理工大学 分数阶同步提取广义s变换时频分解与重构方法

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