GB2463906A - Identification of medical image objects using local dispersion and Hessian matrix parameters - Google Patents

Abstract

A computer-based method of identifying an object in a digital medical image comprises determining, at each of a plurality of points, the local dispersion of the image, and analysing the local dispersion along a direction of least variation or change to identify the object. The identified object may comprise regions within a predetermined value range. Dispersion may be determined using eigenvalues derived from a Hessian matrix (H, using image intensity functions, I); dispersion analysis may be performed using either the largest or smallest eigenvalue, and identification can be determined by eigenvalue thresholding. Also independently claimed is a method of identifying an object in a digital medical image that comprises calculating, at each of a plurality of points, the Hessian matrix for the image, and analysing the definiteness of the Hessian matrix for object identification; definiteness may be determined using the Sylvester condition or a Gaussian elimination condition. Processing to remove noise or enhance local structures, using a filter, may be performed. The methods have particular application to CT colonoscopy (CTC) imaging.

Description

I

I

Computer-implemented Lesion Detection Method and Apparatus The present invention relates to medical imaging and analysis. More particularly, the present invention relates to methods for detection of lesions in digital medical images.

Background to the Invention

Medical Imaging One example of such a digital medical image is a CT scan image. A CT scan image is a digital image comprising one or a series of CT image slices obtained from a CT scan of an area of a human or animal patient. Each slice is a 2-dimensional digital grey-scale image of the x-ray absorption of the scanned area. The properties of the slice depend on the CT scanner used; for example, a high-resolution multi-slice CT scanner may produce images with a resolution of 0.5 -1.0 rnmlpixel in the x and y directions (i.e. in the plane of the slice). Each pixel may have a 16-bit greyscale representation. The intensity value of each pixel may be expressed in Hounsfield units (HU). Sequential slices may be separated by a constant distance along the z direction (i.e. the scan separation axis); for example, by a distance of between 0.5-2.5 mm. Hence, the scan image may be a three-dimensional (3D) greyscale image, with an overall size depending on the area and number of slices scanned. Each pixel may then be a voxel in three-dimensional space. Alternatively, the scan image may comprise a single slice and therefore be a single two-dimensional (2D) greyscale image.

The CT scan may be obtained by any CT scanning technique, such as electron beam computed tomography (EBCT), multi-detector or spiral scan or any technique which produces as output a 2D or 3D image representing X-ray absorption.

CAD

Computer-assisted detection (CAD) is a computerized procedure in medical science that supports the medical team's interpretations and decisions. CAD uses information from a medical imaging modality such as CT, SPECT, PET, MRJ, Ultrasound, Electron microscopy, Fluoroscopy or optical tomography to detect suspicious lesions and masses.

During the past decade, the evolution of computer power and developments in computerized image analysis have impacted upon the interpretation stage of the medical imaging exam by providing a valuable second opinion to the radiologist, leading to better detection and early diagnosis of many aggressive diseases. Nowadays, computer-aided detection is used in many medical screening applications for various anatomies such as the colon, lung, breast, liver, prostate and brain.

In general, a CAD system consists of three main parts: the scanner I, the software 2, and the viewer 3 (see Figure 1). The scanner 1 is used for acquisition and digitisation.

Almost all scanners are already equipped with electronic devices that can provide digital acquisition data. The software 2 includes sophisticated computer programs that analyse the data captured and prompt the radiologist to review areas that may suggest a lesion. The viewer 3 is a graphical user interface (GUI) for image visualization and elaboration that provides the support for medical diagnosis.

The software in CAD uses automated or semi-automated algorithms for decision making and is composed, in principle, of five stages: pre-processing, segmentation, detection, feature extraction and classification (see Figure 2). The pre-processing step Si usually consists of artefact correction and noise removal. The segmentation step S2 separates the organ of interest (e.g.: lung or colon [4]) from the data. The detection step S3 is the core of the CAD as it aims to reduce the amount of data to process by selecting only the high probability candidate regions in the segmented organ by extraction and grouping of geometric features that characterize lesions (see Figure 3). Methods developed for this stage include the use of a volumetric shape index and curvedness, surface curvature with a rule-based filter, the Hough transform, and sphere fitting ([4] and references therein). Feature extraction step S4 characterises candidate regions by assessing which values are very similar for regions in the same category, and very different for regions in different categories. The last step, the classification S5, is based on statistical method of supervised classification or neural networks, and it seeks to distinguish features that are invariant.

CAD for CTC Colorectal cancer is a worldwide problem having global increases in the number of cases and deaths because of the expanding and aging population in both developing and developed countries. Computed Tomography Colonoscopy (CTC), or virtual Colonoscopy, is a promising screening tool for colon cancer. CTC is a non-invasive imaging modality that aims to image the colon and bowel, including polyps, diverticulitis and cancer. CTC uses x-rays to produce two-and three-dimensional images of the entire colon. CAD for CTC can detect the locations of suspicious lesions in CTC and assist radiologists in making their decisions. Colorectal cancer is believed to arise from elevated polyps that are potentially visible with CTC. Removing these elevated polyps presumably prevents the vast majority of cancers. However, there is growing recognition that some important polyps in the colon have complex structures or are not elevated. These types of polyps are very hard to detect. During the last few years CAD systems have substantially advanced CTC, and schemes for the detection of polyps has been established. However, CAD for CTC is still unable to detect some complex structures and the technology needs to be improved further to achieve a clinically satisfactory detection with high sensitivity and a low false-positive rate.

Conventional CAD scheme for CTC CAD schemes for CTC consist principally of the following four steps: 1. A pre-processing step Si that may include noise removal, faecal tagging effect minimization, or electronic colon-cleansing (ECC).

2. Segmentation S2 of the colon from extra colonic structures such as the small bowel, lung or stomach.

3. Detection S3 and segmentation of polyp candidates. Several methods have been developed, including the use of a volumetric shape index and curvedness, surface curvature with a rule-based filter, sphere fitting or an overlapping surface normal method. All these methods use shape-specific analysis that differentiates polyps from other structures. Unfortunately, as mentioned above, polyps do not have a unique shape and potential lesions may be missed.

4. Characterization and discrimination of false positives S4 using various internal features, such as volumetric texture or CT intensity.

5. A classification step S5 selects those candidates that belong to the polyp class and reports them as detected polyps by CAD.

Statement of the Invention

According to one aspect of the present invention, there is provided a computer-implemented method of identifying an object in a digital medical image of intensities at a plurality of points, the method comprising receiving medical image data representing said image; determining, at each of said points, the local dispersion of said intensities; and analysing said local dispersion along the direction of least variation to identify said object.

According to another aspect of the present invention, there is provided a computer-implemented method of identifying an object in a digital medical image of intensities at a plurality of points, the method comprising receiving medical image data representing said image; calculating, at each said point, the Hessian matrix of the image; determining, at each said point, the definiteness of the Hessian matrix; and analysing said definiteness of the Hessian matrix to identify said object.

In one embodiment, an automated detection method of normal and abnormal lesions from image data is presented. This method is based on local intensity dispersion analysis and can be used in many medical computed-aided detection (CAD) systems. A complete explanation is presented for a colon CAD system. Conventional CTC Colon CAD lesion detectors are often based on simple shape-specific methods and therefore they can miss some deformed lesions that have complex shapes.

Embodiments of the present invention extract highly probable lesions including and not limited to certain classes of shapes. They may comprise a fast and a robust method based on local intensity dispersion information provided by the Hessian matrix at each voxel. Furthermore, the processing requirements may be minimal, and the implementation simple in comparison to other methods known in the art.

Embodiments of the invention comprise a CAD scheme which relates to volumetric digital imagery, in particular a method that can be used for detection of normal and abnormal lesions. Instead of using shape analysis and distinction between each shape or a matching method to specific shape, 3D local intensity dispersion analysis is used to extract normal and abnormal lesions. The local intensity dispersion information is provided by the characteristics of the Hessian matrix at each voxel. The information

S

derived from the Hessian matrix allows location of normal and abnormal lesions that can be characterized as brighter regions with darker background.

Other extensions and advantages of the invention will be apparent to those skilled in the art from the following detailed description, the accompanying figures and the appended claims. The invention is not limited to CT scan images, but may be applied to other digital medical images, such as MRI, ultrasound or X-ray images. Conventional X-ray images may be developed on an X-ray film prior to being digitised.

Brief Description of the Drawings

Embodiments of the invention will now be described with reference to the drawings identified below.

Figure 1 is a CAD system diagram.

Figure 2 is a flow diagram of a known CAD scheme.

Figure 3 is a diagram of a known detection scheme.

Figure 4 is a flow diagram of calculation of eigenvalues in an embodiment of the invention.

Figure 5 illustrates two possible cases for lesion contrast in the embodiment.

Figure 6 illustrates characterization of the critical points in the embodiment.

Figure 7 is a schematic diagram showing a medical imaging device and a remote computer for processing image data from the medical imaging device.

Figure 8 is a more detailed diagram of the remote computer.

Detailed Description of the Embodiments

In the interest of clarity, the following description focuses on the use of the suggested methodology for the case of colorectal cancer, in the form of lesions (polyps) on the Colon. Similarly, the specific embodiment is particularly illustrated with reference to data generated by Computed Tomography Colonoscopy (CTC). The present invention is not limited to one application or one medical modality. As will be apparent, it can likewise be extended to other CAD applications and can be adapted to any other medical modality, including data generated by PET/SPECT, MRI, OT, US, EM, and the like.

CAD scheme for CTC The CAD scheme of the present embodiment colligates well to CTC, particularly the segmentation and the detection steps. Instead of using shape analysis to distinguish between each shape, a local intensity dispersion analysis is used to extract normal and abnormal lesions. The local intensity dispersion uses information only from the largest eigenvalue of the Hessian. If the data is processed without ECC, two eigenvalues are needed, the largest and the smallest eigenvalues as seen in the description below.

First, there is presented a reliable tool used for the detection of normal and abnormal anatomical structures in the colon. CT values in a 3D CTC image can be considered to be a 3D intensity function I(x, y, z). The Hessian matrix at each point of the image I can be used. The Hessian matrix denoted as H is the matrix of second derivatives of the intensity function I with respect to geometry. The Hessian matrix H is a 3-by-3 symmetric matrix that describes the second-order structures of local intensity variation of the original intensity I at each point. It is a good structure descriptor that can provide the local intensity dispersion information through a simple partial derivative test.

Calculation of the second derivatives of the intensity function I is important for the quality of the Hessian. In practice, images are usually accompanied with high frequency noise; thus, a denoising filter is necessary. There are many strategies to attenuate the noise and acquire an accurate Hessian. One can categorize these methods into different filtering classes: isotropic diffusion and anisotropic diffusion [2, 31 and references therein. The use of robust statistics in anisotropic diffusion [3] is very promising and has not been used in the field of CAD. For convenience, only isotropic diffusion is presented as it is the most commonly used method in the field. The isotropic diffusion filtering can be seen as a Gaussian filter.

For fast implementation, one method to calculate the derivatives for the Hessian using isotropic diffusion is a serial cascade of causal and anti-causal Gaussian filters [1]. This is normally less costly than other alternative strategies. This recursive Gaussian filter is also called an infinite-impulse-response (IIR) approximation to Gaussian filtering.

Because the Hessian matrix has 3-by-3 symmetry, only six components are calculated.

Also, it is important to note that that the Gaussian function is separable. Therefore, the multi-dimensional Gaussian filter can be separated into one-dimensional Gaussians along its main axes making it more efficiently computed. The one-dimensional Gaussian function and its first and second derivatives can be expressed by: = j!. I = p1.. rj (1) where the derivatives g' are with respect to t and a is a noise scale that makes the detector ignore details smaller that 0(a), also called high frequencies. As the Gaussian function is separable, the three-dimensional Gaussian derivatives filter masks are composed of a multiplication of the one-dimensional Gaussian function in each direction. The Gaussian filter mask corresponding to g, g' and g" are denoted by G0, G, and G2. The second derivatives computation may be expressed by: = I*(C2(x).Go(j').G0(")) = J * ((; (.) . G2 (,) . Ga (z)) = 1*((;0(x).Go(,).G2(z)) (2) I = I(G1().G1(j)G0(z)) = It(G1(x).Go(,).G1()) I = The asterisk "*" represents the convolution operator. The subscript notation represents the partial derivatives with respect to spatial coordinates x, y, and z. Thus, the symmetric Hessian matrix is given by: jc JO. 1 t IIy = Y ** (3) To. Jo. Jo.

32i a2z where partial second derivatives of I are represented as I = , I, etc. axax ôxÔy This matrix is symmetric and thus has real eigenvalues. Each eigenvalue describes the local intensity dispersion in the corresponding eigendirection (oriented by its eigenvector). To obtain reliable orientation estimates for flowlike structures of these three directions and to focus only on studying the regions with appropriate size, one can average the orientations by applying a component-wise convolution with a Gaussian G, where p is an integration scale. The convolution implementation can be done using a recursive strategy as above.

1: !r: JJ JJr 1'..:i " ;(: 1::: (4) L 1: I: ] where the indices p and a are dropped from the Hessian components for clarity.

The eigenvalues of H, (X1 �=X2 �=X3) integrate the variation of the intensities within a neighbourhood of size O(p). They describe the average contrast in their corresponding eigendirections. The integration scale p reflects the characteristic size of the texture. X1 �=X2 �=X3 are invariant under orthonormal transformations. A multidimensional space can be defined whose axes correspond to these invariant measurements.

A fast and robust way to compute the eigenvalues of H is to solve a cubic equation analytically [6] yielded from the characteristic matrix equation: H-)tIHO (5) In the vicinity of a stationary point h0 = (xo, yo, zo) (minimum, maximum or saddle), the intensity function I (h = (x, y, z)) can be approximated by: II0+-i_hTHh (6) As H is a symmetric matrix, it can then be shown that all its eigenvalues are real numbers and eigenvectors associated with different eigenvalues are orthogonal. It is then possible to construct an orthonormal coordinate system from the eigenvectors of H, called the principal axes. By the principal axis theorem, one can construct an orthogonal matrix P whose columns are the eigenvectors of H, and PHPT = D, a diagonal matrix whose diagonal are the cigenvalues of H. Thus, the previous equation becomes: I I +!(ph)TD(ph) 2 (7) +1(21k1 �27k +3k) where k= (Ph)1, i = 1,2, 3.

Hence, one can characterize the local structures by the corresponding critical point property using the eigenvalues of H (see also Figure 6): * If all eigenvalues of H are strictly positive (H positive definite), the critical point is a relative (or local) minimum.

* If all eigenvalues of H are strictly negative (H negative definite), the critical point is a relative (or local) maximum.

* If H has both positive and negative eigenvalues (H indefinite), the critical point is a saddle point.

* Further analysis is necessary in the case where H is positive semi-definite or negative semi-definite.

An alternative to using an eigenvalue-based method to characterize the critical point is to check the Sylvester condition for the positive or negative definiteness of the real symmetric Hessian matrix H: * If H is positive definite, the critical point is a relative (or local) minimum.

* If H is negative definite, the critical point is a relative (or local) maximum.

* Further analysis is necessary in the case where H is positive semi-definite or negative semi-definite.

The Sylvester condition for the positive definiteness of the real symmetric Hessian matrix H is defined as follows: The real symmetric Hessian matrix H is positive definite f and only f all the determinants (&; i 1, 2, 3) of the upper left corner sub-matrices of H are positive.

:j,r: : -- -/ i i p (8) The Sylvester condition for the negative definiteness of the real symmetric Hessian matrix H is given by replacing the ">" symbols with "<" symbols in Equation 8.

Using the determinant properties and Sylvester condition, one can develop a practical and fast criterion based on the Gauss elimination type algorithm. This algorithm uses the sign-preserving row operation property of the determinant and can lead to the following [7]: The real symmetric Hessian matrix H is positive definite f and only f H can be reduced to an upper triangular matrix where all diagonal elements are positive, by using only inner sign-preserving row operations.

Reduction of the Hessian matrix H to an upper triangular matrix is given by: IJr 1;:

I I I

I j [ , i

_______ I

-I -+ ] where r,, i 1, 2, 3 represents the ith row of the original or the resulted matrix.

Another way to study local properties of an analytical shape is through its local Gaussian and mean curvatures (K, and K2) that come from the differential geometry framework [5]. This approach is based on the following 2D formulation, called also Monge-representation of the surface patch: z(u,v)K1u2 +ic,v2 (9) This approach is different to the proposed approach as it is based on the surface shape representation and in the embodiment uses information from the whole 3D volumetric image.

Note that the proposed methodology is not restricted to 3D digital images only, but could be extended to any dimension. For example, in some applications, the detection of normal or abnormal tissue (lesion or objects) can be distinguished from 2D input digital images. In these applications, the suggested methodology could be easily implemented. The eigenvalues criterion, the Sylvester criterion method and the Gauss elimination type criterion could be applied using the same principles as described in the 3D case.

In the case of Colon CAD, lesions (also called colorectal polyps) are fleshy growths occurring on the lining of the colon or rectum. Polyps are sac-like bodies composed of layers of cells and are either pedunculated (attached to the intestinal wall by a stalk) or sessile (grow directly from the wall) and may have different shapes. Colorectal polyps can be recognized in the CTC scan by their shape, but also by their appearance in the mass of soft tissue with high Hounsfield unit (bright intensity) compared to the air or other adjacent tissues. Thus a local intensity dispersion analysis can extract these colorectal polyps.

An important step in embodiments of the invention is the detection algorithm for the extraction of potential polyp candidates. Because polyps are masses of soft tissue and in order to recognize them in CTC scans, it is sufficient to find regions that are compact and have brighter contrast compared to the surrounding neighbourhoods (colonic wall).

Thus, regions with X3 << 0 are potential polyp candidates in the colon wall. It is not necessary to characterize the structural shape of these lesions because they are the only mass of soft tissue on the colon wall. Note that X3 <<0 is the largest eigenvalue (X1 �=X2 �=X3 << 0), and it is also the minimum absolute eigenvalue. This condition prevents the detection of saddle-like structures such as folds (saddle point case), that normally have less variation in the one direction and mathematically the Hessian is indefinite. In some cases, colorectal polyps emerge in fluid that has been tagged using a contrast agent that is brighter than soft tissue. In this instance, the condition can be similarly specified for the case where the contrast is reversed, that is where Xi >> 0 (see Figure 5).

Two non-limiting schemes exemplify the use of the algorithm for polyp detection: Scheme 1: with ECC pre-processing 1. Pre-processing step: Electronic colon-cleansing.

2. Segmentation: Extraction of a colon strip containing the inner and outer colon wall: * Lumen segmentation: lumen binary mask * Apply a morphological dilation to the lumen to create a dilated lumen mask.

* Taking out the lumen from the morphologically dilated mask 3. Detection of potential polyps on the soft tissue in the lumen strip: local intensity dispersion analysis is performed along the largest eigendirection that corresponds to X3 <<0 (for example, X3 �=T, where T is a threshold) and only regions within the range of soft tissue on the Hounsfield scale (HU) are considered.

4. False positive reduction: * Apply conditional erosion and dilation on the potential regions to eliminate all small regions without changing soft tissue voxels.

* Eliminate regions that do not adjoin with air.

5. Classification and reporting detected polyps to the CAD.

Scheme 2: without ECC pre-processing 1. Segmentation: Extraction of colon strip as in the above scheme.

2. Detection of potential polyps on the soft tissue in the Lumen strip: local intensity dispersion analysis is performed on the largest and the smallest eigendirection that correspond to X3 <<0 and X1 >> 0 (for example, X3 �=T, where T is a threshold) and only regions within the range of soft tissue in the Hounsfield scale are considered.

3. False positive reduction: process as on the above scheme.

4. Classification and reporting detected polyps to the CAD.

Computer System As shown in Figure 7, the scan image may be created by a computer 104, which receives scan data from a scanner 102 and constructs the scan image. The scan image is saved as an electronic file or a series of files, which are stored on a storage medium 106, such as a fixed or removable disc. The scan image may include metadata associated with the scan image. The scan image may be analysed by the computer 104, or the scan image may be transferred to another computer 108 which runs software for processing the scan image, for example as described below. The software may be stored on a carrier, such as a removable disc or a solid-state memory, or downloaded over a network such as a local area network (LAN), wide-area network (WAN), an internet or the hiternet.

The computers described herein may be computer systems 200 as shown in Figure 8.

Embodiments of the present invention may be implemented as programmable code for execution by the computer system 200. Various embodiments of the invention are described in terms of this example computer system 200. After reading this description, it will become apparent to a person skilled in the art how to implement the invention using other computer systems and/or computer architectures.

Computer system 200 includes one or more processors, such as processor 204.

Processor 204 may be any type of processor, including but not limited to a special purpose or a general-purpose digital signal processor. Processor 204 is connected to a communication infrastructure 206 (for example, a bus or network). Various software implementations are described in terms of this exemplary computer system. After reading this description, it will become apparent to a person skilled in the art how to implement the invention using other computer systems and/or computer architectures.

Computer system 200 also includes a main memory 208, preferably random access memory (RAM), and may also include a secondary memory 210. Secondary memory 210 may include, for example, a hard disk drive 212 and/or a removable storage drive 214, representing a floppy disk drive, a magnetic tape drive, an optical disk drive, etc. Removable storage drive 214 reads from and/or writes to a removable storage unit 218 in a well-known manner, Removable storage unit 218 represents a floppy disk, magnetic tape, optical disk, etc., which is read by and written to by removable storage drive 214. As will be appreciated, removable storage unit 218 includes a computer usable storage medium having stored therein computer software andlor data.

In alternative implementations, secondary memory 210 may include other similar means for allowing computer programs or other instructions to be loaded into computer system 200. Such means may include, for example, a removable storage unit 222 and an interface 220. Examples of such means may include a program cartridge and cartridge interface (such as that previously found in video game devices), a removable memory chip (such as an EPROM, or PROM, or flash memory) and associated socket, and other removable storage units 222 and interfaces 220 which allow software and data to be transferred from removable storage unit 222 to computer system 200. Alternatively, the program may be executed andfor the data accessed from the removable storage unit 222, using the processor 204 of the computer system 200.

Computer system 200 may also include a communication interface 224.

Communication interface 224 allows software and data to be transferred between computer system 200 and external devices. Examples of communication interface 224 may include a modem, a network interface (such as an Ethernet card), a communication port, a Personal Computer Memory Card International Association (PCMCIA) slot and card, etc. Software and data transferred via communication interface 224 are in the form of signals 228, which may be electronic, electromagnetic, optical, or other signals capable of being received by communication interface 224. These signals 228 are provided to communication interface 224 via a communication path 226.

Communication path 226 carries signals 228 and may be implemented using wire or cable, fibre optics, a phone line, a wireless link, a cellular phone link, a radio frequency link, or any other suitable communication chaimel. For instance, communication path 226 may be implemented using a combination of channels.

In this application, the terms "computer program medium" and "computer usable medium" are used generally to refer to media such as removable storage drive 214, a hard disk installed in hard disk drive 212, and signals 228. These computer program products are means for providing software to computer system 200.

Computer programs (also called computer control logic) are stored in main memory 208 andlor secondary memory 210. Computer programs may also be received via communication interface 224. Such computer programs, when executed, enable computer system 200 to implement the present invention as discussed herein.

Accordingly, such computer programs represent controllers of computer system 200.

Where the invention is implemented using software, the software may be stored in a computer program product and loaded into computer system 200 using removable storage drive 214, hard disk drive 212, or communication interface 224, to provide

some examples.

In alternative embodiments, the invention can be implemented as control logic in hardware, firmware, or software or any combination thereof.

Except where specified otherwise, it will be appreciated that the methods described herein may be implemented in software in a computer system such as the computer system 200. References to a step being performed automatically' may encompass performance by such software, preferably without user intervention.

Alternative Embodiments The present invention may be applied to different types of lesions, such as lung nodules, liver lesions, mammographic masses, and brain lesions. Segmentation techniques appropriate to the required lesion type may be used.

The application of the invention is not limited to CT scans; for example, aspects of the invention may be applied to MRI, PET or X-ray images.

Although the above embodiments are described with reference to a medical image comprising intensity values, the image could be pre-processed so that each pixel or voxel no longer represents an intensity as measured by the scan that produced the image. For example, the pre-processing could alter the local or global contrast of the image. Alternatively or additionally, the image could be pre-processed to produce spatial data representing other properties, such as connectivity.

Alternative embodiments of the invention may be apparent from reading the above description. Such alternative embodiments may nevertheless fall within the scope of the present invention.

References [1] I. T. Young, and L. J. van Vliet. Recursive implementation of the Gaussian filter.

Signal Proc., (1995), 44(2), 139-151.

[2] T. Chan Ct al. High-order total variation-based image restoration. SIAM J. Sci. Comput., (2000), 22(2), 503-5 16.

[3] A. Douiri et a!. Local diffusion regularization method for optical tomography reconstruction by using robust statistics. Opt. Lett., (2005), 30, 2439-2441.

[4] H. Yoshida and J. Nappi. CAD in CT colonography without and with oral contrast agents: Progress and challenges. Conip. Med. Imag. and Graphics, (2007), 31, 267-284.

[5] J. J. Koenderink Solid Shape. MIT press, Cambridge, MA (1990) [6] G. Cardano Ars Magna or The Rules of Algebra, (1545).

[7] W. Li. Practical criteria for positive-definite matrix, M-matrix and Hurwitz matrix.

App. Math. and Comput., (2007), 185(1), 397-401.

[8] US 6,345,112 Bi (Summers et al.) [9] US 7,236,620 Bi (Gurcan)

Claims (42)

1. Claims 1. A computer-implemented method of identifying an object in a digital medical image of values at a plurality of points, said method comprising: a. receiving medical image data representing said image; b. determining, at each of said points, the local dispersion of said values; and c. analyzing said local dispersion along the direction of least variation to identify said object.
2. 2. The method of claim 1, wherein said identified object comprises regions within a predetermined value range.
3. 3. The method of claim I or 2, wherein determination of said dispersion is performed using a Hessian matrix.
4. 4. The method of claim 3, wherein a plurality of eigenvalues are derived from said Hessian matrix.
5. 5. The method of claim 4, wherein said eigenvalues are derived by an analytical method.
6. 6. The method of claim 4 or 5, wherein said dispersion analysis is performed using only the largest of said eigenvalue.
7. 7. The method of claim 6, wherein said identification is determined by thresholding the largest cigenvalue.
8. 8. The method of claim 4, wherein said identification is determined using the smallest eigenvalue.
9. 9. The method of claim 8, wherein said identification is determined by thresholding the smallest eigenvalue.
10. 10. A computer-implemented method of identifying an object in a digital medical image of values at a plurality of points, said method comprising: a. receiving medical image data representing said image; b. calculating, at each said point, the Hessian matrix of the image; c. determining, at each said point, the definiteness of the Hessian matrix; and d. analyzing said definiteness of the Hessian matrix to identify said object.
11. 11. The method of claim 10, wherein said definiteness is determined using the Sylvester condition.
12. 12. The method of claim 10, wherein said definiteness is determined using a Gaussian elimination criterion.
13. 13. The method of any one of claims 10 to 12, wherein said identification is applied to the Hessian matrices that are negative definite.
14. 14. The method of any one of claims 10 to 13, wherein said identification is determined by thresholding the definiteness values of the Hessian matrices.
15. 15. The method of any preceding claim, wherein said image is pre-processed.
16. 16. The method of claim 15, wherein said image is pre-processed to remove noise.
17. 17. The method of claim 15 or 16, wherein said pre-processing enhances local structures in the image.
18. 18. The method of any one of claims 15 to 17, wherein said pre-processing is performed using an isotropic denoising filter.
19. 19. The method of any preceding claim, wherein derivatives of the image are determined by convolving with a derivative of a Gaussian filter with a standard deviation corresponding to the size of the object to be identified.
20. 20. The method of any preceding claim, wherein said identification includes false positive reduction.
21. 211. The method of claim 20, wherein said false positive reduction is performed using conditional morphology.
22. 22. The method of claim 20, wherein said false positive reduction is achieved using a classifier.
23. 23. The method of any preceding claim, wherein the medical image comprises an image of at least part of a colon.
24. 24. The method of claim 23, wherein said object is a lesion in a colon.
25. 25. The method of claim 23 or 23, wherein said image is pre-processed to electronically cleanse the colon of faecal tagging material.
26. 26. The method of any one of claims 23 to 25, wherein said points correspond to a band around the colon lumen.
27. 27. The method of claim 26, wherein said band is a region offset from a segmentation of the colon.
28. 28. The method of any one of claims 20 to 22, wherein said false positive reduction eliminates regions that do not adjoin with air.
29. 29. The method of any one of claims 1 to 22, wherein the medical image comprises an image of at least part of a brain, a lung, a liver or a breast.
30. 30. The method of any preceding claim, wherein said image is two dimensional.
31. 31. The method of any one of claims 1 to 28, wherein said image is three dimensional.
32. 32. The method of any preceding claim, wherein said values are image intensity values.
33. 33. The method of any preceding claim, wherein said medical image is a CT image.
34. 34. The method of any one of claims I to 32, wherein said medical image is an MR image.
35. 35. The method of any one of claims I to 32, wherein said medical image is a X-ray image.
36. 36. The method of any one of claims I to 32, wherein said medical image is an ultrasound image.
37. 37. The method of any one of claims 1 to 32, wherein said medical image is a microscopic image.
38. 38. A computer program comprising program code means arranged to perform the method of any preceding claim when executed by a suitably arranged processor.
39. 39. A computer program product comprising the computer program of claim 38.
40. 40. Apparatus arranged to perform the method of any one of claims 1 to 37.
41. 41. A method substantially as herein described with reference to the accompanying drawings.
42. 42. Apparatus substantially as herein described with reference to the accompanying drawings.