Patent Publication Number: US-6342889-B1

Title: Method and system for selecting at least one optimal view of a three dimensional image

Description:
This application is a continuation-in-part of 09/200,706 filed Nov. 27, 1998. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates generally to the analysis of computer-generated images, and more particularly to a method and system for selecting at least one optimal view of a three dimensional image. 
     BACKGROUND OF THE INVENTION 
     Computer-generated images are used in many different industries to model surfaces and solids. In the medical fields, computer imaging is used in combination with ultrasound imaging, magnetic resonance imaging or other medical imaging technology, to display, analyze and organize the data these medical imaging technologies provide. For example, ultrasound machines use ultrasonic wave, i.e. sonar, to scan a patient&#39;s body. The data thus obtained is then analyzed by physicians to assist the physicians in their diagnosis and treatment of patients. Ultrasound can be used to view a fetus, blood-flow patterns in arteries, or to scan organs for irregularities such as cysts, etc. 
     Typically, a three dimensional image is displayed to a user by being projected on a two dimensional surface such as a screen or a print out. Computer systems have been devised that permit the user to take different cross-sectional views of the image, thereby enabling a user to view a portion of the three dimensional image by choosing one or more cross-sectional views. Some computer systems permit the user to geometrically transform the image by rotating, translating and scaling the image, and also permit the user to take cross-sectional views at different orientations, such that the user can sequentially view the three-dimensional image using a series of oblique planes. Other computer systems take a different approach instead of showing a cross-section of the three dimensional image, they “render” the image by making part of the image transparent or translucent such that points under those parts are revealed. In a maximum intensity display, for example, the highest intensity points along a line parallel to the sight of the user are shown, similar to an x-ray picture of a foot. 
     While three dimensional images provide a wealth of information, filtering out the information that is of interest from irrelevant information can be very time-consuming. There may be many different cross-sectional views of interest in a single three dimensional image. Each of these different cross-sectional views may contain only one point of interest. If all of these cross-sectional views must be stored and subsequently reviewed, then resources may be wasted in that a great deal of irrelevant information is being stored and must be filtered out again when the cross-sectional views are again reviewed. It may also be necessary to keep track of many different cross-sectional views of the three dimensional image in order to keep track of all of the points of interest in that three dimensional image. 
     Accordingly, there is a need for a system and method of analyzing computer-generated images in order to filter out as much irrelevant information as possible from the cross-sectional views used to display the information of interest. 
     BRIEF SUMMARY OF THE INVENTION 
     An object of one aspect of the present inventions to provide a method of analyzing a computer-generated three dimensional image and of selecting at least one view of the three dimensional image that maximizes the relevant information as compared to alternative views of the three dimensional image. 
     According to one aspect of the present invention there is provided a method of selecting at least one optimal surface of a three dimensional image such that the at least one optimal surface includes at least two spatial coordinates of interest. The three dimensional image is generated in a coordinate space by an image-defining array consisting of ordered image properties. Each ordered image property in the image-defining array has a unique associated spatial coordinate in the coordinate space such that each ordered image property is mappable to the unique associated spatial coordinate. 
     The three dimensional image also has a plurality of surfaces. Each surface has an associated image-defining subarray in the image-defining array such that each surface of the plurality of surfaces is generated by mapping each ordered image property of the associated image-defining subarray onto the unique associated spatial coordinate. This plurality of surfaces includes a selected visible surface shown in a display divided tip into a plurality of display coordinates. The display selectably displays views such that a series of distinct selected visible surfaces of the plurality of surfaces of the three dimensional image are viewable on the display. The display includes an associated one-to-one projection means for projecting each selected visible surface of the three dimension image onto the display, such that a view-specific one-to-one correspondence exists between each display coordinate and the spatial coordinate projected. 
     The method is implemented using a data processor having a memory, a coordinate space modeling means, a user interface means, a mapping means. The memory has access to the image-defining array. The coordinate space modeling means is loaded in memory and models and manipulates the coordinate space. The coordinate space modeling means responds to a group of commands to rotate the coordinate space, translate a selected visible surface of the coordinate space, and, pivot a selected visible surface about an arbitrary axis on the selected visible surface. The user interface means permits commands to be selected from the group of commands, and communicates with the coordinate space modeling means in order to relay selected commands to the coordinate space modeling means. 
     The mapping means is operable for each visible surface of the three dimensional image to map each ordered image property of the associated image-defining subarray for each visible surface onto the unique associated spatial coordinate in the coordinate space to generate the visible surface of the three dimensional image. 
     The method comprises the following steps. (1) The user interacts with the coordinate space via the user interface means and the coordinate space modeling means to generate a series of views of the three dimensional image in the display. Each view includes at least one selected visible surface of the three dimensional image. (2) The user then selects a plurality of spatial coordinates of interest from the series of views. Each spatial coordinate of interest in the plurality of spatial coordinates of interest is selected by selecting a display coordinate in an associated view in the series of views using the user interface means. The spatial coordinate of interest is then determined based on the associated view and the view-specific one-to-one correspondence between the selected display coordinate and the spatial coordinate of interest mapped on the selected display coordinate. (3) Next, the coordinate space is manipulated by the coordinate space modeling means to orient a selected visible surface of the coordinate space, such that the selected visible surface of the coordinate space corresponds to the at least one optimal surface. 
     In preferred versions of the above-described method, step 3 is executed automatically on user command after selection of at least two or three coordinates of interest. 
     In another preferred version of the above-described method, when at least three coordinates of interest are selected, step 3 includes the following steps. (1) Calculating a first vector by subtracting a first coordinate of interest selected from the at least three coordinates of interest from a second coordinate of interest selected from the at least three coordinates of interest. (2) Calculating a second vector by subtracting the first coordinate of interest from a third coordinate of interest selected from the at least three coordinates of interest. (3) Automatically applying the group of commands to (I) rotate the coordinate space; (ii) translate a selected visible surface of the coordinate space; and, (iii) pivot a selected visible surface about an arbitrary spatial coordinate on the selected visible surface such that an optimal plane defined by the first vector, the second vector and any one of the at least three coordinates of interest is a visible surface. 
     In preferred versions of the above described method, the three dimensional image includes a selected sub-image of interest and the step of interacting with the coordinate space via the user interface means and the coordinate space modeling means that generates a series of sub-image views of the selected sub-image in the display. The plurality of spatial coordinates of interest are then selected from this series of sub-image views. Conveniently, the plurality of selection points are selected automatically. 
     When the selected sub-image of interest is a blood vessel, each of the series of sub-image views is preferably a cross-sectional view of the blood vessel, and the plurality of spatial coordinates of interest are selected to define a line extending lengthwise within the blood vessel. Preferably, the at least one optimal surface generated includes two orthogonal optimal surfaces; and the coordinate space is manipulated via the coordinate space modeling means to orient two selected visible surfaces of the coordinate space to be aligned with the two orthogonal optimal surfaces. Conveniently, these two orthogonal optimal surfaces are concurrently projected onto the display. 
     In additional preferred versions of the above-described method, the coordinate space modeling means orients a sequence of selected contiguous surfaces of the coordinate space into alignment with the at least one optimal surface. Each of the sequence of selected contiguous surfaces is projected onto the display in succession to provide a moving view along the length of the blood vessel. 
     in accordance with another aspect of the present invention there is provided a method of selecting at least one optimal view from a plurality of views of a three dimensional image. The plurality of views is generated from an image-defining array using a data processor having a coordinate space modeling means for modeling and manipulating a coordinate space. The data processor also includes a display for showing the plurality of views of the coordinate space. 
     The image-defining array has a plurality of ordered image properties. Each ordered image property in the plurality of ordered image properties has a unique associated coordinate in the coordinate space such that the three dimensional image is generated in the coordinate space by mapping each ordered image property in the plurality of ordered image properties onto the unique associated coordinate in the coordinate space. Each view in the plurality of views has an associated view-defining subarray in the image-defining array, such that each view in the plurality of views is shown on the display by being generated in the coordinate space by mapping each ordered image property in the associated view-defining subarray onto the associated coordinate in the coordinate space and by being projected from the coordinated space onto the display. 
     The method includes the following steps: 
     (1) selecting a plurality of coordinates of interest in the coordinate space; 
     (2) determining the at least one optimal view in order to contain the plurality of coordinates in a minimum number of views; 
     (3) showing the at least one optimal view on the display. 
     In accordance with an embodiment of the present invention, there is provided a system for selecting at least one optimal surface of a three-dimensional image such that the at least one optimal surface includes at least two spatial coordinates of interest. The three dimensional image is generated in a coordinate space by an image-defining array having a plurality of ordered image properties, each ordered image property in the image-defining array having a unique associated spatial coordinate in the coordinate space such that each ordered image property is mappable to the unique associated spatial coordinate. The three dimensional image has a plurality of surfaces, each surface of the plurality of surfaces having an associated image-defining subarray in the image-defining array such that each surface of the plurality of surfaces is generated by mapping each ordered image property of the associated image-defining subarray onto the unique associated spatial coordinate. The plurality of surfaces includes a selected visible surface shown in a display. 
     The display is divided up into a plurality of display coordinates, and selectably displays views such that a series of distinct selected visible surfaces of the plurality of surfaces of the three dimensional image are viewable thereon. The display has an associated one-to-one projection means for projecting each selected visible surface of the three dimensional image onto the display, such that a view-specific one-to-one correspondence exists between each display coordinate and the spatial coordinate projected thereon. 
     The three dimensional image is generated using a data processor having a memory, a coordinate space modeling means, a user interface means, a mapping means. The memory has access to the image-defining array. The coordinate space modeling means is loaded in memory and models and manipulates the coordinate space. The coordinate space modeling means responds to a group of commands to rotate the coordinate space, translate a selected visible surface of the coordinate space, and, pivot a selected visible surface about an arbitrary axis on the selected visible surface. The user interface means permits commands to be selected from the group of commands, and communicates with the coordinate space modeling means in order to relay selected commands to the coordinate space modeling means. 
     The mapping means is operable for each visible surface of the three dimensional image to map each ordered image property of the associated image-defining subarray for each visible surface onto the unique associated spatial coordinate in the coordinate space to generate the visible surface of the three dimensional image. 
     The system includes coordinate selection means operable to select a plurality of spatial coordinates of interest from a series of views generated using user interface means and the coordinate space modeling means, each view including at least one selected visible surface of the three dimensional image. Each spatial coordinate of interest in the plurality of spatial coordinates of interest is selected by selecting a display coordinate in an associated view in the series of views using the user interface means, and by determining the spatial coordinate of interest based on the associated view and the view-specific one-to-one correspondence between the selected display coordinate and the spatial coordinate of interest mapped thereon. The system also includes an optimal surface generation means operable to manipulate the coordinate space via the coordinate space modeling means to orient a selected visible surface of the coordinate space, such that the selected visible surface of the coordinate space corresponds to the at least one optimal surface. 
     Preferably, the three dimensional image includes a selected sub-image of interest, and the user interface means and the coordinate space modeling means of the system are operable to generate a series of sub-image views of the selected sub-image. The coordinate selection means is operable to select the plurality of spatial coordinates of interest from the series of sub-image views. Where the selected sub-image of interest is a blood vessel, the user interface means and the coordinate space modeling means are operable to generate the series of sub-image views as a plurality of cross-sectional views of the blood vessel, and the plurality of spatial coordinates of interest are selected to define a line extending lengthwise within the blood vessel. 
     Preferably, the at least one optimal surface generated by the system includes two orthogonal optimal surfaces, and the optimal surface generation means is operable to manipulate the coordinate space via the coordinate space modeling means to orient two selected visible surfaces of the coordinate space to be aligned with the two orthogonal optimal surfaces. Conveniently, the display and the associated one-to-one projection means are operable to concurrently project the two orthogonal optimal surfaces onto the display. 
     Preferably, the coordinate space modeling means of the system is operable to orient a sequence of selected contiguous surfaces of the coordinate space into alignment with the at least one optimal surface, and the one-to-one projection means of the system is operable to successively project each of the sequence of selected contiguous surfaces onto the display to provide a moving view along the length of the blood vessel. 
     In a further preferred embodiment of the invention, the system includes recognition means for recognizing the sub-image of interest, and automatic point selection means for automatically selecting the plurality of selection points. 
     In accordance with another embodiment of the present invention there is provided a system for viewing at least one coordinate of interest in a three dimensional image generated on a data processor having a coordinate space modeling means for modeling and manipulating a coordinate space and a display for simultaneously showing at least three views of the three dimensional image. The system includes point selection means for selecting an arbitrary coordinate of interest from a first view in the plurality of views, and also includes orthogonal view generation means for generating two mutually orthogonal views on the display. Both of the two mutually orthogonal views on the display are orthogonal to the first view and intersect with the first view at the arbitrary coordinate of interest such that the arbitrary coordinate of interest can be viewed from three orthogonal directions simultaneously. 
     In accordance with a further aspect of the present invention, there is provided a method of selecting at least one optimal view of a selected sub-image of a three dimensional image. The three dimensional image is generated from an image-defining array using a data processor having a coordinate space modeling means for modeling and manipulating a coordinate space, and a display for showing a plurality of views of the coordinate space. 
     The image-defining array has a plurality of ordered image properties and each ordered image property in the plurality of ordered image properties has a unique associated coordinate in the coordinate space such that the three dimensional image is generated in the coordinate space by mapping each ordered image property in the plurality of ordered image properties onto the unique associated coordinate in the coordinate space. Each view in the plurality of views has an associated view-defining subarray in the image-defining array, such that each view in the plurality of views is shown on the display by being generated in the coordinate space by mapping each ordered image property in the associated view-defining subarray onto the associated coordinate in the coordinate space and by being projected from the coordinated space onto the display. 
     The method includes the following steps: 
     (1) selecting a plurality of selection points in the sub-image of interest from the plurality of views; 
     (2) determining the at least one optimal view in order to contain a maximum number of said plurality of selection points; 
     (3) showing the at least one optimal view on the display. 
     In accordance with a further embodiment of the invention, there is provided a system for selecting at least one optimal view of a selected sub-image of a three dimensional image generated from an image-defining array using a data processor having a coordinate space modeling means for modeling and manipulating a coordinate space. The system also includes a display for showing a plurality of views of the coordinate space. 
     The image-defining array has a plurality of ordered image properties, each ordered image property in the plurality of ordered image properties has a unique associated coordinate in the coordinate space such that the three dimensional image is generated in the coordinate space by mapping each ordered image property in the plurality of ordered image properties onto the unique associated coordinate in the coordinate space. Each view in the plurality of views has an associated view-defining subarray in the image-defining array, such that each view in the plurality of views is shown on the display by being generated in the coordinate space by mapping each ordered image property in the associated view-defining subarray onto the associated coordinate in the coordinate space and by being projected from the coordinate space onto the display 
     The system comprises 
     (1) selection means for selecting a plurality of selection points in the sub-image of interest from the plurality of views; and, 
     (2) optimal view generation means for generating the at least one optimal view to contain a maximum number of the plurality of selection points. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     Reference will now be made, by way of example, to the accompanying drawings, which show preferred aspects of the present invention, and in which 
     FIG. 1 is a block diagram showing an optimal view selection system according to an aspect of the present invention; 
     FIG. 2 is a pseudo code listing of the logic steps to be executed in an optimal view selection method according to the present invention, 
     FIG. 3 is a pseudo code listing of the logic steps required to determine an optimal plane in accordance with step  13  of FIG. 2; and, 
     FIG. 4 is a block diagram showing an optimal view selection system according to a further aspect of the present invention. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS OF THE INVENTION 
     Referring to FIG. 1 there is illustrated a block diagram of a computer system  22  for analyzing computer-generated three dimensional images in accordance with a preferred embodiment of the invention. As shown in FIG. 1, the computer  22  is connected to a monitor  24  having a 640 by 480 screen, an input device  30  such as a manually operated mouse  30 , and an ultrasound image data source  32  such as an ultrasound archive system that stores retrievable ultrasound image data. 
     When scanning a patient, an ultrasound operator passes a probe over a portion of the patient&#39;s body. The probe emits and receives a series of ultrasonic waves. Based on the difference between the ultrasonic waves that are emitted and those that are received, a frame of data representing a cross-sectional view of the patient&#39;s body is obtained along the path of the probe. The probes generates, say, 150 frames of data in a typical pass over the scanned portion of the patient&#39;s body. Each frame of data represents a cross-section of the part of the patient&#39;s body that is scanned using ultrasonic waves. Each frame is typically 640 by 480 pixels, but only the region of interest, which is typically about 250 by 250 pixels, is stored. Accordingly, the image data in the ultrasound image data source  32  for a single image would consist of about 150 frames, each frame being about 250 by 250 pixels. 
     The image data source  32  communicates with the computer  22  and provides image data to a data submodule  28  of the imaging software (not represented in the block diagram of FIG. 1) on the computer  22 . The data submodule  28  orders the image data in an image data array, such that each ordered image property in the image data array has associated spatial coordinates. The x and y spatial coordinates are determined by the location of the data the 250 by 250 frame while the z spatial coordinate is assigned to the data by the data submodule  28  based on the frame in which the data is found. 
     In order to form three dimensional images based on the ultrasound data for image data received from the ultrasound image data source  32 , the computer  22  includes a conventional polytope submodule  34  for generating a coordinate space. Preferably, the coordinate space takes the form of a right-angled parallelepiped, which will be referred to as modelPoly (where “poly” is an abbreviation of “polyhedron”). The modelPoly is defined around the origin of a left-handed xyz coordinate system. 
     The polytope submodule  24  handles all of the geometry involved in rotating, translating and scaling modelPoly. The calculations involved in geometrically transforming the coordinate space are more easily performed when modelPoly remains located about the origin. Accordingly, all of the geometry involved in rotating, translating and scaling modelPoly is recorded in a rotation matrix R, a translation matrix T and a scaling matrix S, while modelPoly itself remains located about the origin. ModelPoly is rotated, translated and scaled by the matrices R T and S to form a winPoly. It is winPoly as projected on the screen of the monitor  24  that the user sees. Initially, the matrices R, T, and S is do not specify any rotation, translation or scaling of winPoly as compared to modelPoly. Then the user gradually adds information to each of R, T and S by performing sequences of geometrical transformations on winPoly. Say, for example, that the user rotates winPoly, thereby changing the visible face of winPoly (by convention, visible faces are defined by a line of sight that is parallel to the z coordinate axis and is negative). This rotation information is recorded in R 1  by multiplying R 0  by a matrix representing the rotation of winPoly (R 1  in this case—R n  is the rotation matrix after n distinct rotations have been applied to modelPoly). Subsequently, winPoly is rotated again; this information is recorded in R 1  by multiplying R 1  by a matrix representing this second rotation of winPoly (the matrix generated by R 1   −1 *R 1  in this case) 
     Some operations such as slicing and pivoting are recorded on modelPoly itself and not in the matrices that transform modelPoly to winPoly. These operations determine the clip state of modelPoly, that is, these operations determine all of current surfaces of modelPoly. Initially, this clip state includes the six faces and eight vertices of the parallelepiped. A new surface can then be added by slicing in from one of the original six plants along the normal of such original face to generate a new surface parallel to such original face. Then this first-added surface can be discarded by cutting in from the first-added surface, or by pivoting about an arbitrary axis on the first-added surface to generate a second-added surface. After this second operation, the clip state would include the six initial faces and the second-added surface, but not the first-added surface, which has been discarded. 
     After modelPoly is rotated, translated and scaled by the matrices R, T and S to form winPoly the coordinates of the visible faces of winPoly are projected to a two-dimensional image with lines connecting adjacent coordinates. The two-dimensional projection of winPoly is then sent to a raster submodule  38  (FIG.  1 ). The raster submodule  38  maps image data onto the two-dimensional image of each visible faces of winPoly by, for each ordered image property of the image data array that has associated coordinates on a visible surface, mapping such ordered image property onto such associated coordinates. First, the projected face is broken up into contiguous, 2 dimensional triangles. Next, each triangle is filled by first identifying the minimum y value and the maximum y value that lie in the triangle. Then, for these two points, and for each y value falling between these two points, a line segment is determined. One end of this line segment is a point having the smallest x integer value falling inside the triangle, while the other end is a point having the largest x integer value falling inside the triangle. The ordered image properties having associated spatial coordinates corresponding to this line segment are then mapped onto the line segment by the raster submodule. 
     The projected two dimensional image of winPoly is projected onto the screen of the monitor  24  where it can be seen by the user. Using the input device  30 , the user can send commands to a ser interface submodule  40 , where these commands are interpreted and transmitted to the polytope module  34 . These commands include translate, rotate or scale, winPoly, in which case the polytope submodule  34  updates the matrices T, R and S as required. Alternatively, these commands include slice or pivot surfaces of modelPoly, in order to add new surfaces to modelPoly. These new surfaces of modelPoly will also appear in winPoly, after being rotated, translated and scaled by R, T and S, and from winPoly will be projected onto a two dimensional surface to be displayed on the monitor  24 . 
     The above-described geometrical manipulation as well as surface generation using slicing and pivoting are well known to those skilled in the art of medical imaging and are widely used. Accordingly, no farther detail regarding these imaging techniques will be provided herein. Using the above-described computer system, users can generate a series of sectional views, which may be parallel to one of the originally six faces or may be oblique sectional views. These sectional views can then be reviewed by a physician or other suitably skilled person to identity points of interest. Those sectional views that include points of interest will typically be retained by the physician, who will use them to help make a diagnosis. 
     When reviewing image date using the computer  22 , a user interacts with winPoly as displayed on the monitor  24 , by translating, rotating and scaling winPoly, and by slicing or pivoting surfaces of modelPoly, which sliced and pivoted surfaces are automatically mapped onto winPoly. When the user finds a point of interest in a particular viewed surface, the user presses an “Optimal Surface” button and using the input device  30  selects the point of interest, thereby specifying the display coordinates of the point of interest on the monitor  24 . This sends a message to an optimal view submodule  36  via input device  30  and user interface submodule  40  that a point of interest is at the display coordinates specified. The optimal view submodule  36  then determines the spatial coordinates on the visible surface of winPoly that correspond to the display coordinates of the point of interest on the monitor  24  as well as the corresponding modelPoly spatial coordinates, which are determined using the matrices R, T and S. These spatial coordinates of interest are then stored in memory  26 . The user can then continue to interact with winPoly and to select new points of interest. 
     After two or more points of interest have been selected, and their corresponding modelPoly spatial coordinates have been stored, the user can elect to generate an optimal surface including at least two spatial coordinates of interest. If only two points are selected, then an optimal plane can be generated including both these points. The optimal plane is definable by either one of the two selected points, and by two vectors, one of which is the vector obtained by subtracting modelPoly spatial coordinates corresponding to one of the selected points from modelPoly spatial coordinates corresponding to the other of the selected points. The second vector used to define the plane can then be selected arbitrarily, provided, of course, that the second vector is not parallel to the first vector. For simplicity, the optimal view submodule sets the second vector equal to (0,Y,0), Y&gt;0. The normal to the optimal plane thus generated is calculated by taking the cross product of the two vectors. This normal will lie in the xz plane. 
     If three or more points of interest have been selected and their corresponding modelPoly spatial coordinates have been stored, the user can elect to generate an optimal surface including at least three spatial coordinates of interest. If only three points are selected, then an optimal plane is generated including these three points. The optimal plane is definable by any one of the three modelPoly spatial coordinates corresponding to the three selected points, and by two vectors. These two vectors are defined by the three modelPoly spatial coordinates corresponding to the selected three points. Specifically, a first vector is determined by subtracting a first one of the three modelPoly spatial coordinates from a second one of the three modelPoly spatial coordinates, while a second vector is determined by subtracting the first one of the three modelPoly spatial coordinates from a third one of the three modelPoly spatial coordinates. The normal of the plane defined by these two vectors and any one of modelPoly spatial coordinates corresponding to the three selected points is determined by taking the cross-product of these two vectors. FIG. 3 sets out in pseudo code the above-described steps for generating an optimal plane. 
     Once an optimal viewing plane has been defined, such plane is displayed on the monitor  24  by first rotating winPoly such that the optimal viewing plane will be visible when exposed (assuming that the above-stated convention holds, that the user&#39;s line of sight is parallel to the z axis and in a negative direction, then the rotation should result in the vector defining the normal of the optimal viewing plane having a positive z component; preferably, the z component should also be large relative to the x and y components of the vector). Then a visible surface is sliced and pivoted as required to obtain the optimal viewing plane. The optimal view submodule  36  is integrated into the polytope submodule  34  and automatically performs these transformations to generate the optimal viewing plane as a visible face. 
     If more than three points of interest are selected, then multiple optimal planes may be generated according to the above-described steps, and winPoly sequentially transformed to show each of these optimal planes as a visible face in turn. Alternatively, more complicated viewing surfaces may be generated that encompass more than three coordinates. A plane in an xyz coordinate system is defined by an equation of the form Ax+By−Cz=D. However, where four or more points are selected, and these four or more points cannot all be contained in a single plane—which will usually be the case—then a suitable surface may be defined by a higher order equation or interpolating polynomial. This interpolating polynomial can be determined using the interpolation techniques discussed below. 
     Example of how an Optimal Curved Surface can be Displayed 
     Consider a block of data of dimensions DimX, DimY and DimZ Each data point within the block of data is characterized by an integer triple (x,y,z) such that x is between 0 and DimX, y is between 0 and DimY and z is between 0 and DimZ. The set of data points in the block is named D(dimX, dimY, dimZ). The voxel intensity map V (for greyscale data), maps the set D(dimX, dimY, dimZ) onto the integers from 0 to 256. 
     B(dimX, dimY, dimZ) is the set of real triples satisfying the three conditions that (1) x is between 0 and dimX, (2) y is between 0 and dimY, and (3) z is between 0 and dimZ. Consider a curved surface in three dimensions that is described by the equation F(x,y,z)=0. Assume that F is continuous and has continuous partial derivatives with respect to x, y and z. Then the desired surface is the surface D(F) that intersects with the set B(dimX, dimY, dimZ) such that F(x,y,z)=0 for (x,y,z) in B(dimX dimY, dimZ). 
     S is digitized to be made up of integer points by a rounding algorithm to yield SD(F). SD remains a surface in the sense that a ray moving through D(dimX, dimY, dimZ) cannot pass through SD. Accordingly, SD is modified to ensure that no ray can pass through SD. 
     Once SD is generated a mask function is required that indicates when a data point is on SD. There is a function VM that maps D(dimX, dimY dimZ) to the set {0,1} such that VM(x)=1 if x is in SD, and VM(x)=0 if x is not in SD. The operation of this function creates a second data set equal to the dimensions of the first data set. For each point in the original data set there is a corresponding point in the new set whose value is one if the original point is in SD, or zero if the original point is not in SD. 
     Given winPoly generated by user interaction as described above, the view created by the mask function can be displayed by using a modified form of ray tracing. This is done by starting at each point pRinit on the surface of the winPoly, and by moving in constant increments along a ray moving into the screen. For each point pR along the ray, including the first pRinit, one maps back to a data point pD in data set and then calculates VM(pD), which is the mask value at that point on the ray. The first point pD on the ray such that VM(pD) is equal to one is the point on the digitized surface SD. Then the voxel intensity V(pD) is displayed at The point pRinit (in actuality, given that the display is two dimensional, the voxel intensity V(pD) is displayed at the projection of the point pRinit onto the XY plane). 
     Preferably, the optimal view submodule  36  is integrated with the polytope submodule  34  such that on the user electing to display an optimal surface, these submodules automatically determine the plane that will contain the selected coordinates of interest and then manipulate modelPoly and winPoly to render such plane visible. Alternatively, however, the user can suitably manipulate modelPoly and winPoly manually to render visible a plane containing multiple points of interest without calculating the vectors defining the plane. 
     The optimal view submodule  36  enables a user to select a point of interest by freezing such point. As a consequence of so doing, the user will then be restricted to manipulating winPoly and modelPoly such that all visible surfaces displayed must include such point. This is possible as the polytope submodule  34  permits arbitrary pivoting about an arbitrary point, and not just about an arbitrary axis, on the visible surface. When the user, having frozen one point of interest already, finds a second point, then an optimal plane has been rendered visible. The user can then elect to freeze the second point as well. At that point, the user will still be able to generate new planes as the two frozen points of interest will together define an axis of rotation about which new planes can be chosen. If and when a third point of interest is located and frozen, the plane will be fixed, unless the third point fails on the axis of rotation defined by the first and second points. 
     In FIG. 2, a pseudo code listing shows the steps of a method of selecting at least one optimal view of a three dimensional image in accordance with a preferred aspect of the invention. The method is preferably implemented using the above-described three dimensional imaging system. 
     The first step of the method, after starting, is to initialize all of the data structures employed as indicated in line  2 . The modelPoly, generated in model coordinates, is transformed by the rotation matrix R, the scaling matrix S and the translation matrix T to generate winPoly in window coordinates. All of these matrices are initialized so as to not rotate, scale or translate modelPoly when generating winPoly (i.e. S specifies 1:1 mapping such that there is no scaling). The ordered image properties of the image-defining array is mappable onto winPoly to generate projected visible surfaces of winPoly on the monitor  24  (although winPoly has not yet been generated). When viewing these projected visible surfaces of modelPoly, a user may decide to select a point of interest; the coordinate corresponding to this point of interest is then added to the set of interesting coordinates. Initially however, the set of interesting coordinates is empty. 
     ModelPoly has a clip state consisting of the six initial faces and the eight initial vertices of modelPoly&#39;s initially parallelepiped form; these six initial faces always remain in the clip state. New surfaces are added to the clip state when parts of modelPoly are cut away to expose these new surfaces; formerly new surfaces may be removed from the clip state at this point if such former new surfaces are part of the portion of modelPoly that must be cut away to expose the new surface. 
     Next, in line  3 , the R, S and T matrices multiply each modelPoly coordinate to generate winPoly coordinates. Initially, there is no rotating, scaling or translation of modelPoly to generate winPoly. However, each time one or more of R, S and T are changed in subsequent steps, each coordinate in modelPoly is multiplied by the relevant matrix to change winPoly. These transformation techniques are well known to those skilled in the art. After step  3  has been executed, the next step, line  4 , is to project winPoly onto the x-y coordinates. This projection must be a one-to-one projection. After projecting winPoly onto the x-y coordinates, the raster and data submodules fill all the visible surfaces by mapping the ordered image property specified by the image-defining array for each coordinate on the visible surface, “visible surfaces” are surfaces of winPoly that have been projected onto the x-y coordinates. 
     After winPoly has been projected on the x-y coordinates, this projection is displayed on a screen. Then the user can choose from a number of options, including an exit option, by suitably manipulating the mouse. The user can rotate winPoly, which is mathematically represented by multiplying the current matrix R n  (R n  is the rotation matrix after n rotation operations) by a rotation transformation matrix R D  to yield R n−1 , R n+1  is then multiplied to each coordinate of modelPoly to yield each new coordinate of winPoly after the rotation represented by R 1 . This sequence of steps is represented in FIG. 2 by the following loop: step  5  to step  6  to step  3  to step  4  to step  5 . Analogous loops are defined by the pseudo code of FIG. 2 for scaling (step  5  to step  7  to step  3  to step  4  to step  5 ) and for translation (step  5  to step  8  to step  3  to step  4  to step  5 ). 
     The slicing and pivoting options of step  5  are different from the rotation, scaling and translation options of step  5  in that these modify modelPoly itself and its clip state, instead of merely modifying the matrices R, S and T used to generate winPoly from modelPoly. Before any slicing or cutting is performed, it will be one to three of the initial six faces of winPoly that are projected to the x-y plane, rasterized (image data is mapped to the visible surfaces by the raster submodule) and displayed. These original faces are then pivoted or sliced by cutting away part of the modelPoly to expose a new surface. If a new surface is modified by slicing or pivoting, then that formerly new surface is deleted from the clip state and the current new surface is added. If, however, one of the initial 6 surfaces is cut away by slicing or pivoting, then such initial surface remains in the clip state. After slicing or pivoting, the clip state and modelPoly are suitably modified, as set out in step  14 , and then the matrices R, S and T transform the modelPoly to yield a winPoly with new surfaces exposed. This new winPoly is then projected, one-to-one onto the x-y plane, and is displayed on a screen. The slicing loop shown in FIG. 2 is step  5  to step  9  to step  13  to step  3  to step  4  to step  5  and the pivoting loop is step  5  to step  10  to step  13  to step  3  to step  4  to step  5 . 
     If the user opts to select a point of interest, then the user locates the cursor as close to such point as possible and clicks an “Optimal Surface” button. The screen coordinate, (x-y coordinate) closest to such point is then determined. As there is a one-to-one correspondence between such x-y coordinate and the winPoly coordinates, the corresponding winPoly coordinates can be located. Then by multiplying such coordinates by the product of R −1 , S −1  and T −1 , the corresponding modelPoly coordinates can be determined. These modelPoly coordinates are then designated coordinates of interest and are stored in memory. If there is only one coordinate of interest, then the user returns to step  5 , thus, the loop in that case is step  5  to step  11  to step  5 . 
     If two or more coordinates of interest have been determined, then the user may elect at that time to generate an optimal plane. Assuming the user so elects, the rotation matrix R is modified so as to point the normal of the optimal plane in winPoly in a direction substantially parallel to the z axis, and having a positive sense. Then the surfaces of modelPoly are sliced and pivoted, and the clip state changed, as required, to expose the optimal surface. The loop specified by FIG. 2 is as follows: step  5  to step  11  to step  12  to step  13  to step  14  to step  5 . Step  13  automatically goes to step  5  and executes the rotating, slicing and pivoting loops as required to render the optimal plane visible. FIG. 3 sets out pseudo code for calculating an optimal plane. 
     While the subject invention has been described such that the coordinates of interest are selected from displayed surfaces of the three dimensional image, it will be appreciated by those skilled in the art that the surfaces need not be viewed in order to select coordinates of interest. For example, selection of the points of interest may be automated, such that no views of the three dimensional image are projected before the optimal view is generated. In the case of the scan of a liver, for example, the image would, in the case of a healthy liver, be expected to be fairly uniform, reflecting the relative homogeneity of the liver. In such case, the selection of coordinates associated with image properties that do not reflect this uniformity might well be automated. 
     Alternatively, coordinates may be selected from views that are not views of surfaces. For example, the raster submodule  38  may perform a rendering mapping that shows the interior of winPoly. One example of a volume rendering mapping is to show winPoly as a series of rays parallel to the z coordinate axis. Then, of all of the ordered image properties having associated coordinates on one such ray, only the ordered image property of highest intensity is mapped to such ray. Thus, the resulting image shows coordinates at varying depths, and indicates these depths by the distance of such coordinates along its ray. 
     Referring to FIG. 4, a block diagram for a computer system  122  is shown in accordance with a further aspect of the invention in which the points of interests are selected from a sub-image of the three-dimensional image. A common example of such a sub-image is a blood vessel (the scope of the term “blood vessel” in the context of this specification includes arteries, capillaries and veins, although the sub-image of interest would most typically be an artery). Using the above-described steps, the user can rotate, slice and pivot winPoly at will until a point that lies in the sub-image of interest appears on the display. The user can then rotate winPoly to show more of the sub-image of interest. These further rotations of winPoly are effected, as described above, by multiplying the current rotation matrix R n  by a rotation transformation matrix R T  to obtain R n−1 . Alternatively, the user can slice or pivot to change the clip state of modelPoly so as to provide a better display of the sub-image of interest. 
     When the sub-image of interest is a blood vessel, the user would typically rotate winPoly in order to obtain a cross-section of the blood vessel. Then the user selects a point of interest, as described above, by locating the cursor as close to this point as possible and clicking the “optimal surface button”. Afterwards, the user further slices the blood vessel so that a series of cross-sectional views are taken along the length of the blood vessel. At each cross-sectional view, a point of interest can be selected. Once the user has selected points of interests along the entire length of the blood vessel that is of interest, then an optimal surface is generated along the length of the vein that encompasses as many of these points of interests as possible. This optimal viewing surface can then be displayed by suitably rotating, slicing, and pivoting winPoly to make this optimal viewing surface visible on the display. 
     Preferably, two orthogonal viewing surfaces that extend longitudinally relative to the blood vessel are generated; these two viewing surfaces intersect and are orthogonal at the points of interest selected. The display shows both of these orthogonal viewing surfaces simultaneously in order to show the blood vessel from two different perspectives. 
     These aspects of the invention can also be automated such that the user need only identify a single point of interest in the sub-image of interest such as a blood vessel. Specifically, the imaging software includes an image recognition sub-module  142  that, in the cast of a blood vessel of example, tracks the ring of color representing the blood vessel from frame to frame. Specifically, by selecting a point of interest the user is, in effect, selecting both spatial coordinates associated with such point, and image properties in the image data array that are associated with the selected spatial coordinates. Specifically, once a point is selected, the image recognition submodule  42  collates the selected spatial coordinates and the selected image properties associated with such point. The image recognition submodule  42  then maps out the sub-image of interest by identifying spatial coordinates that neighbor the selected spatial coordinate and then collating the image properties of the neighboring coordinates. Once collated, the image properties of the neighboring coordinates are compared with the selected image properties to filter out those neighboring coordinates that do not have relevant image properties. Those coordinates corresponding to image properties that are not filtered out, are, in turn, selected. 
     Using the points selected in this way, the optimal view submodule defines a viewing surface that encompasses as many of the selected points as possible to provide a viewing surface that extends lengthwise through the blood vessel. This viewing surface is then displayed on the monitor. Optionally, two orthogonal optimal viewing surfaces are defined and displayed for viewing the blood vessel along its length. 
     A still further aspect of the present invention involves generating optimal views of a single point of interest. Consider a selected face on modelPoly. Select an arbitrary point on this face. Then, two planes can be generated that are perpendicular (orthogonal) to the selected plane, and that are also orthogonal to each other. The three planes intersect at the selected point ch plane corresponds to a face (ortho-Face) inside the cube, generated by clipping the original 6-sided modelPoly against the new plane. 
     At this point, three faces are displayed; the selected face and the two orthoFaces. There is a symmetry about these 3 faces: each face is cut by the other two orthoFaces at right angles. Now, the intersection of two faces determines a line segment, so for a particular face there are two lines segments where each of the other two orthoFaces intersect with it. When these line segments are displayed, they resemble cross-hairs. 
     The selected face and its two orthoFaces are displayed separately, as if the user were viewing them face-on. Also, the user can see the selected face on the original cube, if it is visible. When cross-hairs are turned on, cross-hairs appear on the three separately displayed face views, and also on the original winPoly. 
     The user can shift the intersection point in any of the 4 displayed cross-hair faces, and see the corresponding two updated orthoFaces displayed in their respective areas on the screen. The user can also select one of the faces and rotate the two corresponding orthoFaces about the axis of intersection. 
     After an optimal viewing plane is generated from 3 user-selected point of interest, the cross-hair point of intersection can be chosen as one of the user-selected points, and the two ortho can be generated and displayed. The user can then turn the cross-hairs on and interrogate the region around the selected point by rotating the corresponding orthoFaces. 
     Accordingly, it will be apparent that the present invention may be implemented in other specific forms without departing from the spirit or the essential characteristics thereof. In particular, while the invention has been described in the context of medical imaging generally, and ultrasound imaging in particular, it will be apparent to those skilled in the art that the invention is applicable in other imaging contexts. The presently discussed embodiments are considered to be illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than the foregoing description, and all changes that come within the meaning and range of the claims are therefore intended to be embraced.