Automatic Determination of the Curved Axis of a 3-D Tube-Shaped Object in Image Volume

1. Field of the Invention

The present invention concerns a method for automatically determining the true curved axis of three dimensional tube-like shaped objects in a three dimensional image volume.

2. Description of the Prior Art

Medical related diagnoses and some industrial non-destructive inspections are often based on viewing image slices derived by known imaging techniques such as computed tomography (CT), magnetic resonance imaging (MRI), positron emission tomography (PET) or single photon emission computed tomography (SPECT). Computed tomography is a particular x-ray tomography method which produces axial transverse tomograms, i.e. images of body layers which are essentially perpendicular to the longitudinal axis of the body in medical related diagnosis. A computer tomograph computes a two dimensional (2-D) distribution of attenuation of a pencil thin x-ray beam moved linearly in the slice plane of the object. The numerical matrix of the 2-D attenuation distribution is converted into a black and white or color television image in which each image point (pixel) corresponds to a matrix element and different gray or color tones are assigned to different attenuation values.

With a computer tomogram, an object detail exactly corresponds to an image detail and not to a large number of object elements lying behind each other in the direction of radiation. Classical x-ray techniques, which produce a photographic recording of a two dimensional projection image of a three dimensional object area projected by the radiation cone into the image plane, suffer from blurred images of structures superimposed from different object depths. Computed tomography, however, avoids this superposition effect by only processing information on the layer, i.e. slice, of interest to the image.

Within the field of nuclear medicine imaging diagnostics, emission forms of computed tomography (ECT) provide slice images of the organ and tissue function, regional blood flow and regional metabolism by measuring emitted radiation in the areas of interest and generating an image corresponding to the emitted radiation measured. ECT with positron emitting isotopes is known as positron emission tomography (PET), and ECT with gamma photon emitting isotopes is known as single photon emission computed tomography.

The cuts from the image volume to produce the image slices are derived in part from a determined transverse image slice of the particular object. Traditional techniques resort to straight line or piece-wise straight line approximations to describe the curved axis of tube-like shaped objects such as human organs or body parts. Current medical related inspections and diagnoses of these tube-like shaped human body parts or organs, such as the head left ventricle, lung airways and blood vessels, are often made upon viewing image slices produced from a curve axis determined according to such traditional techniques. Consequently, traditional, straight line approximations for curved axis based image slices introduce undesirable inaccuracy and error into inspections and diagnoses from viewing such approximated image slices.

Detecting the center point of the cross section of an object or body part under conventional center of mass based methods are difficult where the intensity of the object's developed image is relied upon as an indication of mass. This method works where the intensity of the object in the image appears to be symmetric. In many imaging applications, however, the image of the object is often not symmetric or the intensity is not uniformly distributed along the circle. Moreover, the object of interest in the image may be partially missing or mixing with the surrounding background structures in the image because of defects, diseases, imperfect imaging conditions, or imperfect segmentation algorithms. All of these defects make the task of detecting the center point of the cross section even more difficult by using conventional center of mass approximation methods. Consequently, there is a need for an improved method for finding the center point of a near circular shaped cross section of an object or body part under the above mentioned real-world constraints.

Hence, it is an object of the present invention to provide a method for automatically defining the curved axis for curved tube-like shaped objects. More specifically, it is an object of the present invention to provide a method of automatic determination of the center and the radius of each cross section of a tube-liked shaped object which may be irregular or incomplete.

The present method provides determination of a curved axis of a tube-like shaped object inside an image volume which consists of a set of initial transverse image slices sliced in a direction perpendicular to the long axis of the volume. The initial transverse image slices have image intensity patterns which indicate the structure of the three dimensional tube-like shaped object in the image volume. Initially the image volume is divided into multiple piece-wise volume segments in the direction of the long axis of the image volume. A long axis of a transverse image of one of the piece-wise volume segments is detected for cutting the piece-wise volume segment along this long axis and obtaining a piece-wise longitudinal plane of the piece-wise volume segment. The new transverse image slices of the three dimensional tube-like shaped object are obtained by reslicing the image volume perpendicular to the straight line axis defined by straight center lines of a longitudinal cut of the piece-wise volume segments. The center point of the cross section of the tube-like shaped object revealed in the image intensity pattern of the transverse image slice is determined with an average intensity function defined as (1/(2.PI.r)) .SIGMA..sub.m I.sub.m. A hypothetical center point is varied for a varying radius to determine average intensity for various hypothetical center points and various radius values. The hypothetical center point and radius where the average intensity function is an overall maximum indicates the location of the center point for the cross section of the three dimensional tube-like shaped object as shown by the transverse image slice.

The center point is located with the average intensity function for consecutive cross sections of the three dimensional tube-like shaped object for multiple transverse image slices. The consecutively determined center points define the curved axis of the three dimensional tube-like shaped object. The curved axis is used as a spatial reference for more accurate slicing of the three dimensional tube-like shaped object for inspections and diagnoses. The present method may be applied to three dimensional tube-like shaped human organs such as a heart left ventricle, lung airways or blood vessels.

The present method by determining centers of consecutive cross sections of the three dimensional tube-like shaped object for defining the curved axis provides greater accuracy than conventional linear approximation methods for determining the curved axis. The accuracy of the present method can be increased by generating thinner or more transverse image slices, thereby decreasing the distance between consecutive center points and defining the curved axis with more center points.

FIGS. 1-2 are flow charts of steps in accordance with the present method.

FIGS. 3a-3d illustrate geometric details for obtaining the cross section from an image volume and a reference point according to the present method.

FIG. 4 is a graph demonstrating the variation of the average intensity function F over a varying radius r.

FIG. 5 is a 3-D plot of the average intensity function F varying with the position of the center points within a 9.times.9 neighborhood area.

FIG. 6 is a cross section of the left ventricle of the human heart showing a center point of the cross section determined in accordance with the present method.

FIG. 7 is a drawing illustrating the average intensity function F being derived for a cross section of a geometric object.

Although the present invention can be used in many different applications where finding the true axis and radius of cross sections of tube-like shaped objects is useful, the present invention is especially suited for use with medical related imaging techniques such as computed tomography (CT), magnetic resonance imaging (MRI), photon emission tomography (PET) and single photon emission computed tomography (SPECT). Accordingly, the present invention will be described in conjunction with obtaining the true curved axis of tube-like shaped human organs or body parts from a 3-D transverse image volume.

Current straight line based approximation methods for determining the true axis of tube-like shaped human organs or body parts impart undesirable inaccuracies and errors into medical related inspections and diagnoses based on viewing image slices derived from such approximations. Moreover, conventional center of mass methods of searching for the center point of near circular shaped cross sections of human organs or body parts are limited, in part, due to existing medical imaging techniques producing imperfect image intensities distribution. Current imaging techniques produce images which often are not symmetric, the intensity is not uniformly distributed along the circle, or the image of the object may be partially missing or mixing with surrounding background structures because of defects, diseases, imperfect imaging conditions, or imperfect segmentation techniques. Consequently, an improved method for determining the true axis of tube-like shaped objects such as human organs or body parts will improve the accuracy of medical related inspections and diagnoses based on image slices determined from the true axis.

The present method reduces the problem of finding the true axis of a tube-like shaped object to defining a 3-D curve connecting the center points of cross sections of the tube-like shaped object. This new method searches for the center of a cross section by maximizing (where the object is bright) or minimizing (where the object is dark) a specially designed correlation function about a reference point. This new method is efficient and reliable even for images that reveal only part of a full circular-shaped object, namely a sector or a number of disconnected arcs of the circular shaped cross section. The direct applications of the present method in the medical field include positron emission tomography (PET) or single photon emission computed tomography (SPECT) myocardial perfusion studies, curved determination for lung airway related diagnosis, and blood flow studies from 3-D vessel images using computed tomography (CT) or magnetic resonance imaging (MRI).

The steps for automatically determining the true axis and radius of cross sections of tube-like shaped objects are shown in the flow charts of FIGS. 1 and 2. The first step is to obtain cross sections from a 3-D image volume and to provide the starting searching point of each slice for the curved axis determination. Initially, the entire image volume is divided into several piece-wise volume segments in the direction of the long axis of the image volume 101. The number of segments or fragments developed will vary with different applications. The overall computation time can increase significantly with an increase in the number of piece wise volume segments. As an illustration, FIG. 3a shows a cylindrical shaped, transverse image volume 301 and a curved, tube-like shaped portion inside the image volume for which a curved axis is to be determined.

The long axis of the middle transverse image of each individual segment is detected 102. Piece-wise longitudinal planes 103 are obtained by cutting the volume segments along this long axis. Then the straight center lines 104 of the longitudinal cuts are determined. These steps are detailed in FIGS. 3b and 3c. When the center axis of the segment 302 to be divided is not aligned parallel to the direction of the long axis of the transverse image volume 301, the transverse image of the tube-like shaped object can appear as an elliptical or horseshoe like image 307.

The next step 105 requires defining the straight-line axis of one piece-wise segment by the straight center line 306 of the longitudinal cut 305 of the piece-wise segment 303. The cross section or transverse image slice is acquired by slicing the 3-D image volume perpendicular to the straight-line axis 106. The point where the straight-line axis and the transverse image slice intersects is used as a starting point for obtaining the radius and the center point of the transverse image slice. These steps are repeated for each transverse image (cross section) 201 to determine the radius or center points for defining the curve axis.

Determination of the radius or center point of the sliced, transverse images or cross sections requires consideration of present day imaging characteristics. Under most practical situations, the image of a circular object is separated from its background by intensity or the image is already segmented out from its background. For purposes of the present method, an average intensity F of the pixels (produced by known imaging techniques) along an arbitrary circle of radius r centered around two dimensional coordinates (x,y) is defined as F((x,y),r)=(1(2.PI.r)) .SIGMA..sub.m I.sub.m, where the summation of the intensity I is over all the points m along the circle. If the hypothetical center (x,y) and the radius r approach those of the image circle (x.sub.o, Y.sub.o) and r.sub.o, the average intensity function F will have a distinct signature with a maximum or a minimum. For example, the graph of FIG. 4 shows a distinct average intensity function F having a maximum 401 at a radius approaching 10. At a radius less then 10 or above 10, the average intensity function decreases from a maximum to indicate that the test circle defined by the center point (x,y) and radius r chosen do not provide the best image intensity fit with the imaged cross section. Consequently, the center and the radius of the circular object can be found by maximizing where the object is bright and minimizing where the object is dark with this intensity function F with respect to r 202 and (x,y) 203. Shown in FIG. 7 is a detail of the searching direction along radius r 703 about a selected neighborhood area (x,y) 702 for a cross section of an object 701. Due to the isotropic nature of the intensity function F, i.e. does not vary with direction, the searching result will not be biased by the non-uniformity of the intensity along the image circle. FIG. 7 illustrates that as the center point (x,y) 701 approaches the center point of the object 701 and the radius r approaches the radius of the object 701, the image area defined by (x,y) will match the cross section area of the object: the average intensity function F will be a distinct overall maximum.

Given a reasonable starting point of cross sections from the 3-D image volume, as discussed with respect to steps 101 through 102, the average intensity function F will generally yield an accurate determination of the center and the radius of the circle. For each hypothetical center point, the intensity function F is first maximized/minimized again with respect to the position of the center points within the user defined neighborhood of the reference point as shown in FIG. 5, where the selected neighborhood area is a 9.times.9 area. The true center point of the image is determined to be the one which results in the overall maximum value in F, shown in FIG. 5 to be the highest point 501 of the 3-D graph. Illustrated in FIG. 6 is a cross section of the left ventricle of a heart, where the hot spot in the center represents the center point of the cross section detected by the maximum of the intensity function F.

The center point determined for a preceding cross section or transverse slice is preferably used as the starting point (x,y) for the succeeding transverse slice to find the centers of a sequence of transverse slices of a tube-like shaped object. The radius r and center point (x,y) values which produce the maximum intensity function F value are recorded for each transverse slice 204. When all the slices 205 have been maximized with respect to the intensity function F, the series of center points of the consecutive transverse slices are connected to generate a curve axis for the tube-like shaped object of interest 206. The generated curve axis is then used for re-slicing the image volume of the object of interest for accurate diagnosis or inspection.

It is assumed that all processing steps in the description above are carried out automatically, by using a computer (not shown). Persons skilled in the art know how to program a computer to perform the required steps.

It should be understood that the embodiment described herein is merely exemplary and that a person skilled in the art may make many variations and modifications to this embodiment utilizing elements functionally equivalent to those described herein. Any and all such variations or modifications as well as others which may become apparent to those skilled in the art, are intended to be included within the scope of the invention as defined by the appended claims.