WO1997009690A1

WO1997009690A1 - Data dimensional sieving and fuzzy connectivity for mri image analysis

Info

Publication number: WO1997009690A1
Application number: PCT/US1996/014500
Authority: WO
Inventors: Wolfgang Frederick Kraske
Original assignee: Northrop Grumman Corporation
Priority date: 1995-09-05
Filing date: 1996-09-05
Publication date: 1997-03-13
Also published as: TW357325B; AU6917496A

Abstract

In a method for isolating anatomical structures contained within a three-dimensional data set, a morphological skeleton (302) is first formed from the three-dimensional data set. Next, a seed data point (310) is selected from within the morphological skeleton. The seed data point is contained within a desired anatomical structure to be displayed and/or analyzed. Fuzzy connectivity (314) is utilized to define additional data points of the desired anatomical structure, so as to facilitate reconstruction of substantially only the desired anatomical structure. Such reconstruction of substantially only the desired anatomical structure facilitates viewing and analysis thereof by reducing complexity of the image and eliminating obstructing tissue.

Description

DATA DIMENSIONAL SIEVING AND FDZZY CONNECTIVITY

FOR MRI IMAGE ANALYSIS Field of the Invention

The present invention relates generally to medical imaging systems and digital signal processing. It relates more particularly to the use of data dimensional sieving and fuzzy connectivity to facilitate analysis and review of three-dimensional medical images such as those produced by magnetic resonance imaging (MRI) devices and the like.

Background of the Invention

Tomographic imaging techniques for use in medical applications are well known. Examples of such techniques include magnetic resonance imaging (MRI), computer aided tomography (CAT), and positron emission tomography (PET). In each of these techniques, a plurality of cross-sectional two-dimensional images, i.e., slices, of a body portion are generated and processed so as to provide a three-dimensional model of the imaged body portion.

To utilize such a three-dimensional model of a body portion, slices or images taken along planes of interest are generated and then images are printed or otherwise displayed for viewing. The slices viewed may be at various angles with respect to the three-dimensional model. They do not necessarily correspond to the angles of the slides from which the three-dimensional model was originally constructed. Thus, the medical diagnostition may review images taken along any desired plane within the three-dimensional model. This provides for a great deal of flexibility in the use of the three-dimensional model as a diagnostic tool.

As those skilled in the art will appreciate, such three-dimensional images provide a valuable tool to the medical diagnostition in a manner which is non-invasive, and which is therefore considered to be of very low risk to the patient.

However, although such three-dimensional imaging techniques have proven extremely useful for their intended purposes, they still possess inherent deficiencies which detract from their overall effectiveness. More particularly, it is frequently difficult to interpret the viewed two-dimensional slices or images when the anatomical structures of interest are surrounded by and/or intermixed with various other anatomical structures. The undesirable presence of such superfluous imagery only complicates the image, making it much more difficult to view and interpret the desired imagery.

For example, viewing delicate portions of the vascular system is typically difficult since veins, arteries, and capillaries are intermixed with surrounding tissue. This makes it very difficult to distinguish the desired portions of the vascular system from surrounding tissue. Often, only slight changes in the intensity of the image distinguish a desired anatomical structure from surrounding tissue.

Thus, it is desirable to provide a method for isolating anatomical structures of interest such that surrounding tissue is not displayed along therewith. In this manner, the medical diagnostition may view only the unobstructed anatomical structures of interest. This vastly reduces the complexity of the image and thus minimizes confusion as to precisely what portions of the image relate to the anatomical structure of interest. Summary of the Invention

In the analysis and review of three-dimensional medical imaging, it is of critical importance to be able to measure and analyze image features having various fractal dimensionalities from zero dimensions to three dimensions. For example, veins and arteries are characterized as one-dimensional curvilinear forms, while capillaries exhibit one plus fractal dimensions, typically exhibiting fractional fractal dimensionality. Tumors have three-dimensional fractal forms and exhibit smaller fractal dimensions if metastases are considered.

The present invention specifically addresses and alleviates the above-mentioned deficiencies with the prior art. More particularly, the present invention comprises a method for isolating anatomical structures contained within a three-dimensional data set, e.g., a three-dimensional model formed by MRI, a CAT scan, or a PET scan. The method comprises the steps of forming a morphological skeleton of the three-dimensional data set, selecting a seed data point within the morphological skeleton so as to identify a desired anatomical structure to be displayed or analyzed, and utilizing fuzzy connectivity to define additional data points of the desired anatomical structure so as to reconstruct substantially only the desired anatomical structure. Reconstruction of substantially only the desired anatomical structure facilitates the review and analysis of the anatomical structure.

For example, if it is desirable to obtain a three-dimensional data set containing only data points which are representative of the brain, then the patient's head may be imaged via MRI, CAT, PET scanning techniques or the like to provide a three-dimensional model of substantially the entire head. The three-dimensional data set which defines this model is then processed so as to form a morphological skeleton thereof. An operator then selects a seed data point within the morphological skeleton corresponding to the patient's brain. This is typically accomplished by viewing the morphological skeleton on a display such as a CRT. The morphological skeleton maintains all of the data available in the original three-dimensional data set. However, in the morphological skeleton, anatomical structures are separated from one another, based upon the fractal dimensionality thereof. Thus, anatomical structures having a fractal dimensionality of less than one dimension are separated from those having a fractal dimensionality of less than two dimensions and the anatomical structures are separated from those having a fractal dimensionality of less than three dimensions.

After selecting a seed data point within the brain, fuzzy connectivity is utilized to define the additional data points which are required to provide a substantially complete image of the brain. Reconstruction of the brain is simply the reverse of the process utilized to form the morphological skeleton. With the use of fuzzy connectivity to define the set of points defining the brain, it appears that all of the features thereof are substantially utilized in the reconstruction process. Reconstruction of the brain without the use of fuzzy connectivity would result in the loss of substantial surface details thereof. For example, the surface texture and even, to a lesser degree, the convolutions of the brain, would tend to be degraded or smoothed.

The morphological skeleton is formed by recursive opening and erosion of the three-dimensional data set so as to form a plurality of residuals which define the morphological skeleton. Reconstructing a desired anatomic structure from the morphological skeleton comprises performing the opposite procedure from that utilized to form the morphological skeleton. Thus, reconstruction comprises recursive dilation and closing of the morphological skeleton. As those skilled in the art are aware, each step of opening comprises an erosion followed by a dilation and each step of the closing comprises a dilation followed by an erosion.

The use of fuzzy connectivity during the reconstruction process assures that substantially all of the data points associated with the desired anatomical structure are utilized in the reconstruction process.

According to the preferred embodiment of the present invention, a generally spherical structuring element is utilized in both the formation of the morphological skeleton and the reconstruction process. However, those skilled in the art will appreciate that various other shapes of structuring elements are likewise suitable. Indeed, it has been found that various different shapes of structuring elements are particularly suited for use with various different dimensionalities or shapes of anatomical structures.

Generally, the seed data point is selected by positioning a cursor at a desired point on an image being displayed upon a monitor. Thus, the operator may simply visually identify and manually select a seed within the organ or anatomical structure of interest. However, as those skilled in the art will appreciate, various different computer algorithms may be utilized in the selection of such a seed. For example, the operator may simply initiate an algorithm which selects the largest organ within a given volume. Thus, if the operator desires to select the brain for reconstruction, the operator could merely select the largest organ within the head.

The use of fuzzy connectivity to define additional data points of the desired anatomical structure comprises defining connectivity based upon the size and shape of a structuring element utilizing a fuzzy generalization of mathematically defined distances between sets of data points as a criterion. This is accomplished based upon a modified Hausdorff metric.

Thus, separation of such anatomical features from one another according to the present invention is accomplished via dimensional sieving. Dimensional sieving results in the formation of a morphological skeleton utilizing the recursive opening and erosion processing according to well known principles. The opening and erosion processes are described in detail in "Morphological Systems for MultiDimensional Signal Processing" by Petros Maragos and Ronald W. Schafer, Proceeds of the IEEE, Volume 78, No. 4, April 1990; "Morphological Filters-Part I: Their Set-Theoretic Analysis and Relation to Linear Shift-Invariant Filters", by Petros Maragos and Ronald W. Schafer, IEEE Transactions on Acoustics, Speech, and Signal Processing, Volume ASSP-36, No. 8, August 1987; and "Morphological Filters, Part II: Their Relations to Median Order-Statistic, and Stack Filters", by Petros Maragos and Ronald W. Schafer, IEEE Transactions on Acoustics, Speech, and Signal Processing, Volume ASSP-35, No. 8, August 1987.

According to the present invention, a cascade of data dimensional sieving filters are used directly with a three-dimensional image from an MRI device or the like to isolate structures such as arteries and veins from surrounding tissue for unobstructed visualization. This cascade of data dimensional sieving filters comprises the use of a generally spherical structuring element, followed by the use of a two-dimensional surface structuring element, followed by the use of a curvilinear structuring element, followed by the use of a point structuring element.

Thus, to provide for the identification of desired dimensional features within the multi-dimensional data set provided by a tomographic imaging device, a data dimensional sieving algorithm separates the data based upon the dimensional characteristics of the anatomical structures contained therein. The algorithm utilizes filters which resemble geometric constructions such as lines, disks, and spheres, to sieve multi-dimensional features of curves, surfaces, and regions, as well as features of fractal dimensions in between.

A hierarchy of dimensional filters is thus utilized to first remove features of less than one fractal dimension, then to remove features of less than two fractal dimensions, and finally to remove features of less than three fractal dimensions from the original three-dimensional data set as the morphological skeleton is being formed. Thus, the cascade of filters is used directly with a tomographic image to isolate anatomical structures from surrounding tissues to facilitate analysis and review thereof.

By utilizing the residuals of morphological erosion and opening, the morphological skeleton is formed. This process is ideal for processing data with fractal dimensional components. For example, the recursive formation of the morphological skeleton utilizing alternating opening and erosion transforms a 3.4 dimensional form into .4 dimensional data when a spherical structuring element is utilized.

Once the morphological skeleton has been formed via recursive development utilizing alternating opening and erosion processes, then fuzzy connectivity is utilized in the reconstruction of those anatomical structures of interest. Reconstruction of anatomical structures without utilizing fuzzy connectivity results in the loss of significant features such as surface textures and roughness. These features must be reconstructed from the residuals defining the morphological skeleton utilizing fuzzy connectivity. The reconstruction of such anatomical features requires the satisfaction of a fuzzy connectivity criteria such that only those tissue features connected to the dimensional features isolated by the sieving process are utilized.

The final result of both the sieving and fuzzy connectivity processes is a classification and clear visualization of the anatomical structures of interest, e.g., tissues and/or tumor pathologies. Additionally, quantification of the volume of organs and tumors as well as other measurements of interest, such as the diameter of arteries and veins, are easily facilitated as a direct result of the use of dimensional sieving and fuzzy connectivity.

Connectivity is a mathematical concept which states that a set of points is connected if and only if every pair of points in the set can be connected by a line which is contained within the set. The algorithm described in this invention generalizes this concept of connectivity to the discrete topological grids utilized by a computer to store the digital image data by utilizing fuzzy set operators. A fuzzy set is itself a generalization of a discrete set by defining a function over a set representing degrees of membership such that membership varies from zero which indicates no membership to one which indicates complete membership.

To define connectivity, this algorithm utilizes a fuzzy generalization of mathematically defined distances between sets as a connectivity criterion. This criterion establishes that if two points or two sets of points are within a specified distance of one another, then they have membership to the same set of points.

The prior art attempted to isolate anatomical features from one another based solely upon the intensity of pixels within the three-dimensional data set. The present invention facilitates the distinguishing or isolation of anatomical features based upon such criteria such as size. shape, and intensity of the anatomical feature. Thus, more flexibility in designating those features to isolate is provided and improved accuracy of such isolation is attained.

These, as well as other advantages of the present invention will be more apparent from the following description and drawings. It is understood that changes in the specific structure shown and described may be made within the scope of the claims without departing from the spirit of the invention.

Brief Description of the Drawings

Figure 1 is an illustration of the recursive alternating opening and erosion processes for two dimensions utilized to define the residuals of which the morphological skeleton is constructed;

Figure 2 shows the two-dimensional structuring element utilized in the process for forming the morphological skeleton shown in Figure 1;

Figure 3 is a chart giving the results of utilizing structuring elements of different forms or dimensionalities upon images of different forms or dimensionalities;

Figure 4 shows a representative two-dimensional structuring element utilized in the fuzzy connectivity restructuring process wherein 2r is the major diameter thereof;

Figure 5 shows the use of the structuring element of Figure 4 to determine that two points belong to the same set, i.e., a set of data points defining a desired anatomical structure for reconstruction, the two points belong to the same set since when one of the points is located at the center of the structuring element, the other point falls within the bounds defined by the structuring element, wherein the dimension d defines the dimension between adjacent points such that the points fall within the set;

Figure 6 shows the use of the restructuring element of Figure 4 to iteratively determine that the set points illustrated are contained within a common set;

Figure 7 shows the set support function which defines the degree of fuzzy membership for a given pair of points, which is determined by the modified Hausdorff metric for those points.

Figure 8 is a block diagram of the conventional morphological data decomposition and reconstruction processes;

Figure 9 is a block diagram of the morphological data skeletonization process of the present invention;

Figure 10 is a block diagram of the morphological data decomposition and selective reconstruction processes of the present invention;

Figure 11 is a block diagram of the morphological data dimensional sieving decomposition and selective reconstruction processes utilizing a three-dimension example;

Figure 12 is a block diagram of the morphological data reconstruction from skeleton process of the present invention;

Figure 13 is a block diagram of the morphological data decomposition and selective reconstruction process of the present invention; and

Figure 14 is a block diagram of the fuzzy logic process of the present invention. Detailed Description of the Preferred Embodiment

The detailed description set forth below in connection with the appended drawings is intended as a description of the presently preferred embodiment of the invention, and is not intended to represent the only forms in which the present invention may be constructed or utilized. The description sets forth the functions and the sequence of steps for constructing and operating the invention in connection with the illustrated embodiment. It is to be understood, however, that the same or equivalent functions and sequences may be accomplished by different embodiments that are also intended to be encompassed within the spirit and scope of the invention.

The data dimensional sieving and connectivity methodology of the present invention is illustrated in Figures 1-14, which depict a presently preferred embodiment of the invention.

Referring now to Figure 1, the recursive development of a morphological skeleton utilizing alternating opening and erosion process is shown utilizing a two-dimensional geometric construction, i.e., a square, for purposes of illustration. Although a two-dimensional example is provided herein, for purposes as illustration, those skilled in the art will appreciate that use of the present invention in medical imaging typically requires the recursive use of a three-dimensional structuring element such as a sphere, a two-dimensional structuring element such as a surface, a one-dimensional structuring element such as a curve, and a zero-dimensional structuring element, i.e., a point.

After the first opening process, a square 101 having the corners removed therefrom is defined. An octagon 100, as shown in Figure 2, is utilized as the structural element for this example. The corners 102 are the residuals of the opening process for the original square. Each time an additional erosion and opening process is performed, progressively smaller squares 102, 103, and 104 is formed. After each recursive erosion and opening process, additional residuals 102 are defined. After the last erosion process is performed, the square is completely eliminated and the collection of residuals defines the desired morphological skeleton 106.

Dilation and erosion are defined as follows:

erosion,

(g⊖f_a)(x)=min{g(x+d)-(f_a(d)-f_a(0))},

d in E dilation,

(g⊕f_a)(x)=max{g(x+d)+(f_a(-d)-f_a(0))}

d in E

= - (- g ⊖ f_a)(r)

Structuring element, f, and image function, g, defined over domain of definition for f E

.

d=inf{ α| inf (X_αg)=sup(X_αg),αGℜ+}, αg - g(x/α),ℜ+ denotes the real numbers ≥0

Sε_α(g,X) = (X⊖αg)-(X⊖αg)_+εg, +0▂lim_ε↓0ε

Alternately for a black skeleton the extensive operations of dilation and closing are performed. ,

For digital raster formats of pixels or voxels, d is limited to the integer domain Z of the data and ∈ is equal to 1.

Σ

≤α≤ defined as a single dilation step followed by a single erosion step.

By decreasing the size of the structuring element 100, smaller residuals 102 are obtained and the resolution of the morphological skeleton is increased.

This morphological skeleton contains all of the information contained in the original image. The original image can be reconstructed from the morphological skeleton by reversing the recursive development process, i.e., by substituting dilation and closing for erosion and opening, respectively. Thus, by performing a series of dilations and closings, instead of the openings and erosions performed previously, the original three-dimensional data set is obtained from the morphological skeleton.

In forming the morphological skeleton 102, data dimensional sieving is performed such that anatomical structures having various dimensionalities are separated from one another in a manner which isolates them and makes them identifiable via computational methodology. Thus, according to the methodology of the present invention, those anatomical structures having a fractal dimensionality of less than one dimension are separated from those anatomical structures having a fractal dimensionality of less than two dimensions, both of which are separated from anatomical structures having a fractal dimensionality of less than three dimensions.

A desired anatomical structure which has been so isolated and identified can then be reconstructed by reversing the recursive morphological skeleton development sequence described above utilizing only the data points associated with the selected anatomical structure. However, merely reconstructing the desired anatomical structure results in the loss of significant features such as surface textures and roughness.

Thus, in order to preserve such significant features. it is necessary to utilize fuzzy connectivity during the reconstruction process. The use of fuzzy connectivity assures that all of the data points associated with the anatomical structure are utilized in the reconstruction process. According to the present invention, fuzzy connectivity defines the entire data set for the desired anatomical structure by utilizing a modified Hausdorff metric, wherein connectivity is defined by the size and shape of the structuring element.

For example, the structuring element is first centered upon a seed pixel by the operator. The seed pixel is one which the operator knows is a part of the anatomical structure for which reconstruction is desired. All other pixels contained within the volume defined by the structuring element are then considered to be a part of the anatomical structure being reconstructed. This process is then repeated for each new pixel within the data set until no additional new pixels are found. Although, as in the formation of the morphological skeleton, many different sizes and shapes of structuring elements are suitable, those generally spherical in configuration are preferred.

A series of different structuring elements may be utilized in either of the formation of the morphological skeleton or the reconstruction process, as desired, so as to achieve a desired effect.

As mentioned above, connectivity is a mathematical concept which states that a set of points is connected if and only if every pair of points in the set can be connected by a line contained in the set. The algorithm described in this invention generalizes this concept of connectivity to the discrete topological grids of computers and digital image data with fuzzy set operators. A fuzzy set is itself a generalization of a discrete set by defining a function over a set representing degrees of membership from no membership as represented by a zero to complete membership as represented by a one. This algorithm utilizes convex fuzzy membership, as shown in Figure 7, functions defined over convex set supports.

To define connectivity, this algorithm uses a fuzzy generalization of mathematically defined distances between sets as a connectivity criterion. This criterion establishes that if two points or two sets of points are within a specified distance of one another, then they have membership to the same set of points. To more precisely define this concept of connectivity, the neighborhood of points and the data must be defined.

As shown in Figure 7, convexity implies that a line fixed between any two points on the curve of the function must lie on or below the graph of the function:

λ f(a) + (1 - λ) f(b) ≤ f(λa + (1 - λ)b),

0≤λ≤1

erosion,

(g⊖f_a)(x)=min{g(x+d)-(f_a(d)-f_a(0))},

d in E dilation,

(g⊕f_a)(x)=max{g(x+d)+(f_a(-d)-f_a(0))}

d in E

= - (- g ⊖ f_a)(r)

Structuring element, f, and image function, g, defined over domain of definition for f, E,

.

Based on the previous definitions a measure of distance between sets or points g, h can be defined. This metric is used to define points or sets within this distance to be fuzzy connected.

2.4.1 Definition: Modified Hausdorff function metric .

Referring now to Figure 3, a chart showing the result of utilizing a structuring element of a particular form or dimensionality on an image of a particular form or dimensionality is shown. The chart includes structuring elements of point, segment, disk, and sphere form and images of point, curve, circles, and volume form. As shown in the chart, utilizing a structuring element defined by a point, for example, in the processing of a curve according to the methodology of the present invention, yields a curve. Similarly, utilizing a segment in the processing of a curve yields a curve and utilizing a disk or sphere in the processing of a curve provides a null product, since a two-dimensional disk or a three-dimensional sphere cannot be utilized to process a one-dimensional curve.

Referring now to Figures 4-6, the use of a two-dimensional example of a structuring element and the fuzzy connectivity reconstruction of a desired anatomical structure is shown. With particular reference to Figure 4, the structuring element 200 shown comprises an ellipse having a major diameter of 2r. Those skilled in the art will appreciate that various other shapes are likewise suitable for use as a structuring element.

Referring now to Figure 5, use of the structuring element to determine if two points are within a common set is shown. This is accomplished by placing the structuring element 202 around one of the points 210 of interest and then determining whether or not the second point of interest 212 lies within the boundary of the structuring element 202. As shown, the second point 212 does lie within the boundary of the first structuring element 202. In order to find additional points which are part of the common set of points, which define the anatomical structure of interest, this process is repeated by placing a structuring element 204 around the second point 212 in order to determine if any points lie within the boundary thereof.

With particular reference to Figure 6, this process is repeated so as to define all of the points which belong to a common set of data points which define the anatomical structure of interest. Structuring element 202 formed about point 210 defines point 212 as being included within the data set, structuring element 204 formed about point 212 similarly defines point 210 as belonging to the common data set, while structuring element 206 formed about point 212 defines point 214 as belonging to the common data set. Thus, all points which lie within the boundary of any structuring element at which a point within the data set is formed at the center thereof, also are members of the common data set.

Each point so defined to be within the data set is assigned a fuzzy membership number between zero and one, depending upon the distance between adjacent points, as discussed above.

Thus by utilizing fuzzy connectivity, the set of all data points defining a particular anatomical structure of interest are defined such that surface details of the anatomical structure, such as surface smoothness thereof, are maintained during the reconstruction process and are thus included in the reconstructive anatomical structure.

Referring now to Figure 8, an overview of the standard morphological decomposition and reconstruction process is shown. According to contemporary methodology, an input data array 300 is skeletonized 302 so as to form skeleton 304. Skeleton 304 is then reconstructed 306 so as to provide the original image 308. This process is used in various different data analysis, compression, and data signal processing applications.

Referring now to Figure 9, morphological data skeletonization according to the present invention is shown. Morphological data skeletonization is a recursive process wherein erode image n 320 subjected to erosion 322. The product of erosion is then subjected to dilation 323 and in parallel subjected to erosion 324. The product of erosion 324 is erode image n+1 326 which then becomes new erode image n 320 and is iteratively processed. The product of dilation 323 is subjected to subtraction 325 with respect to erode image in 320 so as to form skeleton 327 which is then subjected to addition with full skeleton 304.

Referring now to Figure 10, morphological data decomposition and selective reconstruction according to the present invention is shown. Input data array 300 is subjected to skeletonization so as to form skeleton 304. Skeleton 304 is used for the selection of a region of interest 310 so as to form edited skeleton 312. Fuzzy connectivity 314 is applied to the edited skeleton 312 to form the edited image 316.

Referring now to Figure 11, a three-dimensional example of the process of morphological data dimensional sieving, decomposition, and selective reconstruction is shown. Input data array 300 is skeletonized 342 wherein a three-dimensional kernel or structuring element configured as a sphere, for example, is utilized in the skeletonization process. The skeletonization 342 results in the formation of a skeleton 343 having less than three- dimensional features. This skeleton is then subjected to skeletonization 344 utilizing a two-dimensional kernel or structuring element configured as a facette. This two-dimensional skeletonization process 344 results in a skeleton having less than two-dimensional features 345. This skeleton having less than two-dimensional features 345 is then subjected to skeletonization utilizing a one-dimensional kernel or structuring element 346 so as to provide a skeleton having less than one-dimensional features 304.

Referring now to Figure 12, the process of morphological data reconstruction from a skeleton without the use of fuzzy connectivity is shown. As discussed above, such reconstruction results in the loss of substantial surface detail. Using reconstruction n

350, dilation 352 is performed so as to produce dilate image n 353, dilate image n 353 and skeleton n 354 are added 356 and the process is iterated by providing the added images as recon n 350.

Referring now to Figure 13, the process of morphological data decomposition and selective reconstruction of the present invention is shown. Recon n 360 is subjected to dilation 364 so as to produce dilate image n 368 and seed image n 366. Seed image n is subjected to fuzzy connectivity criteria 370 with skeleton n 362 so as to produce edited skeleton 378. Dilate image n 368 is combined 380 with edited skeleton 378 so as to produce a new recon n 360 and the process is iterated.

Referring now to Figure 14, the use of fuzzy connectivity according to the present invention is shown. A seed image n pixel 400 and the skeleton n 402 are operated upon by fuzzy logic 404 utilizing pixel fuzzy logic measure 406, i.e., the selective structuring element, so as to provide pixel fuzzy measure update 408 and set fuzzy connected pixels 410. The use of fuzzy logic in this manner is described in detail in "Analysis and Segmentation of Higher Dimensional Data Sets With Fuzzy Operators for Representation and Visualization" and published in Neuro and Fuzzy Systems: Emergent Science of Intelligent Computing, by Mitra, Gupta, and Kraske, published by SPIE Press, 1994, ISBN 0-8194-1566-9, provided herewith and forming a part of this patent application, the entire contents of which are hereby incorporated by reference.

Provided below is a list of the symbols utilized in the math equations in this patent application:

Provided below is a program listing utilized in the practice of the present invention upon a Pixor computer:

It is understood that the exemplary methodology described herein and shown in the drawings represents only a presently preferred embodiment of the invention. As those skilled in the art will appreciate, the present invention is suitable for use in a variety of different applications, other than medical imaging. For example, the present invention may be utilized in radar imaging, machine recognition, and various other imaging applications.

Indeed, various modifications and additions may be made to the described embodiment without departing from the spirit and scope of the invention. For example, various different shapes of structuring elements, other than those illustrated and described, may be utilized in either the morphological skeleton forming process or the reconstruction process. Additionally, various different criteria for defining the present membership of adjacent data points during reconstruction process are likewise suitable. Thus, these and other modifications and additions may be obvious to those skilled in the art and may be implemented to adapt to the present invention for use in a variety of different applications.

Claims

WHAT IS CLAIMED IS:

1. A method for isolating anatomical structures contained within a three-dimensional data set, the method comprising the steps of:

a) forming a morphological skeleton of the three-dimensional data set;

b) selecting a seed data point within the morphological skeleton, the seed data point being contained within the desired anatomical structure; and c) utilizing fuzzy connectivity to define additional data points of the desired anatomical structure so as to reconstruct substantially only the desired anatomical structure;

d) wherein reconstruction of substantially only the desired anatomical structure facilitates viewing and analysis thereof.

2. The method as recited in Claim 1 wherein the step of forming a morphological skeleton comprises recursive opening and erosion of the three-dimensional data set so as to form a plurality of residuals which define the morphological skeleton.

3. The method as recited in Claim 1 wherein the step of forming a morphological skeleton comprises utilizing a generally spherical structuring element in recursive opening and erosion of the three-dimensional data set.

4. The method as recited in Claim 1 wherein the step of selecting a seed data point comprises positioning a cursor at a desired point on an image being displayed on a monitor.

5. The method as recited in Claim 1 wherein the step of using fuzzy connectivity to define additional data points of the desired anatomical structure comprises defining connectivity based upon the size and shape of a structuring element utilizing a fuzzy generalization of mathematically defined distances between sets of data points as a criterion.

6. The method as recited in Claim 1 wherein the step of reconstructing substantially only the desired anatomical structure comprises recursive dilation and closing of a selected portion of the morphological skeleton.

7. The method as recited in Claim 1 wherein the step of utilizing fuzzy connectivity to define additional data points comprises defining connectivity based upon the use of a generally spherical structuring element for defining distances between adjacent data points.

8. The method as recited in Claim 1 wherein the three-dimensional data set comprises a data set generated by a device selected from the group consisting of:

a) a magnetic resonance imaging device;

b) a computer aid tomography device; and c) a positron emission tomography.

9. A method for facilitating analysis of three-dimensional medical images, the method comprising the steps of:

a) separating anatomical features from one another via dimensional filtering; and

b) storing desired separated features for analysis.

10. A method for facilitating analysis of three-dimensional medical images, the method comprising the steps of:

a) defining anatomical features having less than one dimension from the image via first dimensional filter and storing those features;

b) defining anatomical features having less than two dimensions from the image via a second dimensional filter and storing those features;

c) defining anatomical features having less than three dimensions from the image via a third dimensional filter and storing those features; and d) storing remaining features having three dimensions in a fourth memory;

e) wherein anatomical features of different dimensionalities are thus separated from one another so as to facilitate isolation of desired anatomical structures.

11. A method for reconstructing an anatomical structure from a morphological skeleton, the method comprising:

a) selecting a seed data point within the morphological skeleton, the seed data point being contained within the desired anatomical structure; and b) utilizing fuzzy connectivity to define additional data points of the desired anatomical structure so as to reconstruct substantially only the desired anatomical structure;

c) wherein the use of fuzzy connectivity results in reconstruction of substantially only the desired anatomical structure and substantially lacks surrounding tissue.