Provisional Application No. 60/099,329, filed September 8,1998, and U. S. Provisional Application No. 60/100,622, filed September 17,1998, both of which are incorporated herein by reference.

BACKGROUND OF THE INVENTION Throughout the specification, references are denoted by brackets and all of the references so denoted are hereby incorporated by reference. Prostate cancer is the most prevalent male malignancy and the second leading cause of death by cancer in American men [1]. In 1996, more than 40,000 deaths were predicted to be due to prostate cancer, and over the past 10 years the incidence of prostate cancer has increased with more than 300,000 newly diagnosed cases in 1996 [1]. Improved screening programs, utilization of the prostate-specific antigen (PSA) and digital rectal examination (DRE), along with a greater awareness of prostate cancer as a disease entity, have resulted in a dramatically increased overall detection rate, particularly for organ-confined tumors [1,8]. The key strategy to improve the prognosis and the quality of life for the patients with prostate cancer is to enhance early detection and accurate staging.

However, due to the highly variable behavior of prostate cancer and inadequate information obtained from the conventional diagnostic methodology, clinical decision making and treatment planning are unsatisfactory [18, 22], leading to the fact that the rate of patient call-

back for reassurance is too high and as many as 50% of radical prostatectomies are either unnecessary or ineffective [17,19]. This represents an enormous cost to an already overburdened health care system.

Currently, transrectal ultrasound (TRUS) provides a sensitive method for the detection of impalpable tumors [6,28]. TRUS is also considered to be a unique tool for improved accuracy of volume estimation of the prostate/tumor and the method of choice for biopsy guidance [6,9]. Previous studies have shown that many prostate cancers are undetected by TRUS, and the positive predictive values of lesions seen with TRUS and initially detected using DRE are 28% and 19%, respectively [5].

Fifty to sixty percent of cancers are bilateral despite a normal TRUS or DRE of the contralateral lobe. One limitation of conventional TRUS lies with the non- specificity of lesions detected, particularly hypoechoic abnormalities where only one third of these lesions prove to be cancer 1,6. Therefore, the only completely reliable method for the diagnosis of prostate cancer is through pathological examination of tissue samples if the PSA level is elevated, even in the absence of DRE or TRUS abnormalities [6]. However, clinical outcomes indicate that one out of five cancers will be missed in TRUS guided sextant biopsies [4,9], and the accuracy of the estimated findings with the existing biopsy protocols, such as tumor distribution, volume, and multicentricity, are insufficient [9].

The general consensus in prostate cancer diagnosis and staging is that detailed quantitative analysis of the extent and grade of cancer in systematic needle biopsy specimens provides useful prognostic information, especially when combined with standard clinical tests,

such as DRE, PSA, and PSA density [3]. The challenge, however, remains whether it is possible to improve prostate biopsy strategy to yield more representative samples of the cancer which accurately reflect biological potential prior to treatment.

Since the introduction of standard sextant core- needle biopsy technique in later 1980s 12, while technical enhancements have occurred in multiple test combination 14 and additional biopsy techniques 4, no major improvement has been made in optimization of biopsy protocols. In fact, most current prostate biopsy techniques take a fixed or pre-determined number of biopsies, normally six; and the biopsies are uniformly distributed. However, six biopsies may not be the optimal number, as tests show that at least 10% of cancer is undetected when compared to results obtained when eight to thirteen biopsies [4,9] are performed. Thus, the biopsy tissue samples are collected in a less selective fashion. Consequently, the ability to obtain clinically adequate samples of the disease that is present may be limited.

Also, although a significant correlation exists between total tumor volume, and total length of cancer on all biopsies, and the number of cores with cancer and percentage of cancer in all cores, only qualitative clinical uses of the corresponding outcomes have been proposed 23. In fact, recent simulation studies using 3-D reconstructed prostate models indicate that standard sextant protocol underestimates the presence of cancer where worst biopsy grade of poor differentiated cancers may be missed, and thus is inadequate to determine the best treatment plan [9,19,20,24].

Systematic biopsies are a useful and sensitive means to detect carcinoma of the prostate [3,12,14].

However, multiple biopsies pose a risk for detecting clinically insignificant cancers [16,25], yet may not be an adequate sampling to identify all patients with cancer at the earliest stage possible [4,9]. Particularly, with increased detection comes the risk of finding small, and highly or moderately differentiated cancers confined to the gland, which might best be left untreated, if they could be clearly identified.

The inventor has previously developed core technologies to reconstruct a 3-D graphic model of the prostate from excised prostates of previously imaged cancers [19,31], and to perform virtual simulation of various biopsy protocols [24,30]. This interactive environment has made it possible to study tumor patterns in locations that have previously been difficult to evaluate in true 3-D. The preliminary results have shown promising clinical potential in that the data from such studies provide major contributions to the understanding of the early natural history of prostate cancer including its pattern of growth and progression 16. The data can also lead to biopsy strategies and recommendations regarding the clinical management of patients based on biopsy findings [7]. The inventors also have correlated the findings in the simulated biopsies with the grade and volume of the cancer in the operative specimen of the entire prostate, and thereby have made it possible to study the intraprostatic location, multicentricity, and possible extraprostatic extension of a tumor, and subsequently determined the accuracy and pitfalls of currently used diagnosis and staging systems. It was found that 51% of the cases of prostate cancer were

multicentric, ranging from 2 to 5 tumors, and the present procedure leads to underestimation of both size and grade of prostate cancer, due to possible limitations of conventional protocols and misinterpretation of these lesions [19,24,27].

Many researchers have recently proposed various methods to improve prostate biopsy techniques [3,4,7,9,11,14,16]. Scardino et. al. 3 at Baylor College of Medicine have conducted research to assess the value of systematic biopsies for distinguishing clinically important from unimportant prostate cancers before treatment. These studies have focused on additional information that can be gained from a detailed quantitative assessment of grade and extent of cancer found in systematic needle biopsy specimens, since current available diagnosis and/or staging methods do not provide enough data to allow a reasonably accurate estimation of pathological stage and ultimate prognosis of the disease. They have also proposed to develop probability maps of cancer distribution so that new biopsy strategies can be developed. Whether these proposed probability maps were in 2-D or 3-D fashion is not evident from the reports, and it is not clear how to develop a better biopsy strategy based on those maps.

McCullough et. al. [4] at Bowman Gray School of Medicine have introduced a 5-region prostate biopsy protocol in which additional biopsies are taken in a systematic fashion in addition to sextant biopsies.

Their prospective study has shown a new method to be safe, effacious, and superior to the sextant method of biopsy in identifying prostate cancer at an early but significant stage. A 35% increase in diagnostic yield of prostate biopsy was observed in which 83% additional

cancers appear to be clinically significant with a Gleason score of six or more. This approach is indirectly and qualitatively supported by a mathematically derived hypothesis (using Bayesian theory) that demonstrates that for a fixed percent volume of prostate cancer the probability of finding cancer increases as the number of biopsies increases. Since no consideration of cancer distribution was incorporated into biopsy site selection, a major remaining question is whether the detection rate of 35% more cancers was simply due to doubling and tripling the number of prostate biopsies regardless of the regional area at which the detected clinically insignificant cancers may increase.

Miller et. al. [7,15,16] at University of Colorado Health Science Center have developed a computer model of the prostate to simulate the sextant random systematic core biopsy technique to verify its ability in detecting cancer in prostates with low-volume tumor. Various simulated biases for the angle of biopsy and the distribution of cancer foci were incorporated into the model. The results from this idealized model suggested that the distribution and growth patterns of cancerous foci can have a significant impact on the effectiveness of a given biopsy strategy. They have developed a 3-D model (only a 2-D simulation was reported in literature) of the prostate gland from its whole-mount histological maps and anticipated a continuing study towards realistic guidelines for improved biopsy techniques. However, one major limitation of their simulated model is that the shape of the simulated tumor foci (spherical) does not represent all the possible shapes of prostate cancer.

Busch et. al. 9 at University of Uppsala Hospital in Sweden have conducted a prospective study to evaluate

the sensitivity of the sextant biopsy protocol compared to a more extensive procedure for the detection of prostate cancer, and to define a biopsy model with a minimal number of biopsies while maintair. ing diagnostic specificity. Their conclusion suggests that the optimal number of samples to be taken and the clinical importance of isoechoic cancers have yet to be defined. More studies are needed to make the delicate trade off between gain in sensitivity and undesired side effects, such as patient discomfort and the risk of detecting clinically harmless cancers. Stamey et. al. [11,14] at Stanford University Medical Center have conducted an intensive clinical research on the evaluation of existing biopsy techniques and protocols, and the correlation of estimated findings to clinical significance for treatment of prostate cancer. The results from their work reveals important new information regarding the disease patterns of prostate cancer and provides very useful guidance for the further research in this domain. For example, a core cancer length of 3 mm or more on one or two needle biopsies reliable predicts cancer of clinically significant volume, and poorly differentiated cancer areas (with high grades) on biopsy should always be considered to represent clinically significant tumor.

Although the system of quantitation used is qualitative, the findings were generally consistent with those of the histological study.

Clearly, technical improvement is needed to recommend a more selective biopsy strategy with an optimized number of biopsies at locations with the highest probability of representative clinically significant cancer occurrence.

SUMMARY OF THE INVENTION Accordingly, it is an object of the invention to provide 3-D probability maps of the location of any tumor and of high grade cancer within the prostate based on analysis of digitally imaged surgical specimens, overlaid into transrectal ultrasound imaging features, so that optimal biopsy techniques can be developed (number and location of the biopsies will be optimized adaptively, statistically, and quantitatively, based on both 3-D probability maps and imaging featured likelihood) to substantially improve the accuracy of prostate cancer diagnosis and decrease clinical misstaging (i. e., to establish a more accurate Gleason grade and tumor volume estimate prior to prostatectomy), thus improving treatment planning [19,24,26,27,30,31]. In addition, by correlating the findings from computer simulation of biopsies with true tumor parameters, it is an object of the present invention to provide a more accurate algorithm to estimate tumor volume and other staging parameters. To the best of our knowledge, such a 3-D statistical modeling and multimodality visualization for prostate cancer research has not previously been done [3,9,16].

The originality and innovative nature of this research relies on the following: 1) 3-D statistical modeling of high grade cancer using standard finite mixture (SFM) distribution [45] and information theory [47] to guide the optimization of needle biopsy strategy that promises to increase positive predictive value for prostate cancer detection and a more accurate prediction of tumor volume; and 2) 3-D multimodality visualization of the master model 26 and imaging features 30 that can accurately define the pathways of needle biopsies,

prostate/tumor volume, and extent and distribution of tumor allowing on-line evaluation and guidance of biopsy protocols.

The present invention includes a method for conducting a tissue biopsy, which includes creating a plurality of three-dimensional graphic, electronic models of tumorous and non-tumorous individual patient tissue specimens from corresponding digitized cross-sectional sequences, where each of the sequences represents an actual patient tissue specimen. The digitized cross- sectional sequences consist of two-dimensional cross sectional slides. The slides represent slices of the tissue specimen at spaced intervals.

A three-dimensional graphic, electronic master model of a tissue specimen is then formed by mapping all of the graphic models of tumorous and non-tumorous individual patient tissue specimens. A three-dimensional statistical probability distribution is then incorporated into the master model, that designates positions of potential tumors to be found during the tissue biopsy, based on locations of actual tumors in the tumorous individual patient tissue specimens. The master model with the statistical probability distribution is then superimposed on a graphic, electronic patient's biopsy display during the tissue biopsy. The graphic, electronic patient's biopsy display can then be stored in a computer memory.

Although the tissue specimen is a prostate in the majority of the discussion of the invention, the method can be applied to other types of tissues as well. The tissue biopsy produces trans-rectal ultrasound images as said graphic, electronic patient's biopsy display.

Accordingly, the tissue biopsy includes the step of

directing a trans-rectal ultrasound probe to the positions of potential tumors designated by the three- dimensional statistical probability distribution and the master model.

Based on the tissue biopsy procedure, the method of the present invention also includes predicting a volume of a detected tumor using Bayesian theory principles, the three-dimensional statistical probability distribution, and neural network based algorithms.

The present invention also includes a method for determining ideal tissue biopsy procedures, which includes creating a plurality of three-dimensional graphic, electronic models of tumorous and non-tumorous individual patient tissue specimens from corresponding digitized cross-sectional sequences, where each of the sequences represents an actual patient tissue specimen.

A three-dimensional graphic, electronic model of a patient tissue specimen is then selected from a computer memory. A probe is then connected to a computer that includes the computer memory and from which the three- dimensional graphic, electronic model of a patient tissue specimen is displayed. An interactive simulation of a tissue biopsy is then performed on the three-dimensional graphic, electronic model of the patient tissue specimen, using the probe. A biopsy protocol is thus determined, including optimal probe shapes and pathways, based on the interactive simulation of a tissue biopsy.

The method can further include the steps of repeating the step of performing an interactive simulation of a tissue biopsy step on a plurality of three-dimensional graphic, electronic models of patient tissue specimens. Then, a statistical analysis can be

conducted to evaluate effectiveness of the biopsy protocol.

The method can further include the steps of forming a three-dimensional graphic, electronic master model of a tissue specimen by mapping all of the graphic models of tumorous and non-tumorous individual patient tissue specimens. Then, a three-dimensional statistical probability distribution can be incorporated into the master model. The probability distribution designates positions of potential tumors to be found during the tissue biopsy, based on locations of actual tumors in the tumorous individual patient tissue specimens. The master model, including the statistical probability distribution is then superimposed on the three-dimensional graphic, electronic model of a patient tissue specimen selected from the computer memory.

The interactive simulation of a tissue biopsy on the three-dimensional graphic, electronic model of a patient tissue specimen can be stored in a computer memory.

The interactive simulation of a tissue biopsy can include the step of directing the probe to the positions of potential tumors as designated by the three- dimensional statistical probability distribution, and by the master model.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. la shows digitally-imaged slides of a surgical prostate specimen, outlined slice by slice according to the present invention. FIG. lb shows the result of contour interpolation using non-linear formable modeling according to the present invention.

FIGs. 2 to 4 show an example of 3-D reconstruction of a computer model of a prostate using the surface-spine deformable model according to the present invention, with FIG. 2 showing an initial model, FIG. 3 showing the reconstruction after only 5 iterations, and FIG. 4 showing the final model after 20 iterations.

FIGs. 5a to 5d show how using a material editor, the surface of a prostate capsule can be adjusted into transparent format so the internal structures and any tumors can be viewed clearly using a multimodal view according to the present invention.

FIG. 6 shows a simulated TRUS guided needle biopsy based on the reconstructed prostate model of the present invention.

FIG. 7a shows the clinical setting of a TRUS guided prostate biopsy. FIG. 7b shows how a real ultrasound image of the prostate gland is given in a clinical setting based on the coordination of the biopsy needle.

FIGs. 8a to 8d show several views of a virtual environment for simulation of a TRUS guided prostate needle biopsy, where multimodality visualization enables accurate needle positioning according to the present invention.

FIGs. 9a and 9b show a table providing numerical results of a computerized needle biopsy performed according to the present invention.

FIGs. 10a and 10b show results from 3-D nonlinear matching using a surface-spine deformable model.

FIG. 11 shows a flow diagram outlining the data preparation procedure of the present invention.

FIG. 12 shows a flow diagram outlining 3-D object reconstruction of the process of the present invention.

FIG. 13 shows a flow diagram outlining the virtual environment formation process of the present invention.

FIG. 14 shows a flow diagram outlining the process of construction and quantification of 3-D probablity maps of the location of different cancer grades according to the present invention.

FIG. 15 shows a flow diagram outlining the process of superimposing and visualization of the master model with TRUS imaging features for on-line biopsy guidance according to the present invention.

FIG. 16 shows a graphical representation of statistical data mapping and clustering according to the present invention.

DESCRIPTION OF THE PREFERRED EMBODIMENT The statistical modeling and multimodality visualization of prostate cancer requires the acquisition of a clinically proven prostate cancer database (digitally imaged whole mount prostatectomy specimens), 3-D graphical reconstruction of the object of interest

(prostate structure and the tumors with different grades), a virtual environment for interactive simulation of TRUS guided needle biopsy, a graphics based cross object matching, and 3-D data mapping and statistical modeling. The modeling and visualization process of the present invention is organized into the following parts: 1) data preparation; 2) 3-D object reconstruction; 3) development of virtual environment; 4) interactive simulation of TRUS guided needle biopsy; 5) 3-D non- linear graphical matching, and 6) 3-D data mapping and statistical modeling.

Data Preparation The data preparation procedure of the present invention is outlined in FIG. 11. To study prostate cancer patterns, a statistically significant database 21 is used to provide ground"truth"of the disease when present. The database 21 includes digitized cross- sectional sequences 20 of hundreds of whole mount prostatectomy specimens, removed due to prostate cancer, and provided by the AFIP [26]. All necessary clinical information of these surgical specimen sequences 20 is complete including diagnostic, medical images [19]. Each of these sequences 20 consists of ten to fourteen slices that are 4 pm sections at 2.5 mm intervals. The corresponding digital images 25 of these slices are acquired at a resolution of 1500 dots per inch (dpi), and are shown in FIG. la. The contours of the regions of interest (ROI), including the prostate capsule, urethra, seminal vesicles, ejaculatory ducts, surgical margin, any localized tumor, prostate carcinoma with high grade, and areas of prostatic intraepitrelial neoplasia, are delineated using computer-aided methods, followed by a semi-automatic contour refining algorithm using a snake

model 69. A PC3DTM software program 22 is used to preview the possible outcomes in 3-D so that the data can be re-arranged 23 to avoid any misinterpretation about the shape and spatial distribution of the cancer when transferred from 2-D to 3-D [19]. The parameter setting for both focus and resolution of the digitizer is optimized 24 to assure high image quality.

3-D Object Reconstruction The 3-D object reconstruction of the process of the present invention is outlined in FIG. 12. Based on the original contours of the prostate and tumors (any kind or high grade), a 3-D surface of the object can be accurately and reliably reconstructed utilizing the elastic property of soft tissue deformation for mathematical implementation. The prostate specimens with localized tumors are used as the first target, which produces a total of eighty computerized prostate models after 3-D object reconstruction. For an accurate object reconstruction from 2-D contours, mathematical interpolation is required to fill the gaps between a start and a goal contour [7], and repeated for each of the contours. Instead of using linear or shape-based interpolation to create intermediate contours, a 3-D elastic contour model computes a 3-D force field between adjacent slices thus enabling a"pulling and pushing" metaphor to move the starting contour gradually to the final contour [31,55], as shown in FIG. ib. The non- linearity characteristics of the elastic contour model permits a meaningful interpolation result yielding a high quality representation of the realistic nature (soft tissue modeling) of the object surface.

Reconstruction of an object is to form 3-D surfaces based on the contours of successive 2-D slices. One

conventional way of doing this is to directly connect the contours by planar triangle elements where the reconstructed surfaces are usually coarse and static [7].

A physical-based deformable surface model is preferably used to perform 3-D object reconstruction. Two major operations are involved: (1) triangulated patches are tiled between adjacent contours with a criterion of minimizing the surface area, and (2) tiled triangulated patches are refined by using a deformable surface-spine model 26. The surface formation is governed by a second- order partial differential equation and is accomplished when the energy of the deformable surface model reaches its minimum [24,27,31]. The nonlinear property of the deformable surface model greatly improves the consistency of the reconstructed complex surface. FIGs. 2 to 4 show an example of 3-D reconstruction of a computer model of a prostate using the surface-spine deformable model according to the present invention, with FIG. 2 showing an initial model, FIG. 3 showing the reconstruction after only 5 iterations, and FIG. 4 showing the final model after 20 iterations. FIGs. 5a to 5d show how using a material editor, the surface of a prostate capsule can be adjusted into transparent format so the internal structures and any tumors can be viewed clearly using a multimodal view according to the present invention.

Following a pre-clinical evaluation by urology surgeons, pathologists, and radiologists, 3-D graphical model images 27 of the prostates that are reconstructed according to the above method have been shown to realistically represent actual shapes and distributions of prostate specimens and cancers, and have superior properties compared to known methods [7,9,16,19]. The computer algorithms are automatic in which several key

parameters can be easily controlled by the user through a human-computer interface. The shape information from high resolution medical images [28,43] 27 obtained as described above can be combined with other shape information so obtained to provide expanded views of prostate specimens, as well as other tissues. Since a realistic 3-D model can be reconstructed for any object and/or organ, other programs can be easily developed using the principles of the present invention to analyze many important cancer characteristics. Also, tumor growth and/or origins can be better defined using the above methods.

Development of Virtual Environment The virtual environment process of the present invention is outlined in FIG. 13. The use of the reconstructed 3-D computer models, in visualization and simulation of clinical procedures, can provide an off- line capability with which a large number of computerized "needle biopsies"can be taken from the models to address questions of sampling that simply are not amenable to study in the clinical setting. An interactive virtual environment is required to enable a reproducible computerized"needle biopsy"experiment. The results from the simulation provide reliable information that reflects the clinical reality. An interactive environment for visualizing the 3-D prostate models is created and displayed 30 according to the present invention, based on a state-of-the-art computer graphics toolkit 28 such as object-oriented Openlnventor, commercially available from Silicon Graphics, Inc.

[24,30]. With a sophisticated set 29 of various kinds of simulated lights, 3-D manipulators and viewers, including 3-D mouse and stereo glasses with on-line position

tracking capability, and color and material editors, the system of the present invention allows the user of the system to examine the prostate model in 3-D with any viewpoint, and dynamically walk through its internal structures to understand the spatial relationships among anatomical structures and the tumors present.

A force feedback system 31 can be further incorporated into the system to provide a tactile sensation to the user, using the PHANToM System for example. Equipped with hardware human-machine interface, the system developed as described above enables a full view of the 3-D surgical prostate model right in front of the user, e. g., a surgeon or a pathologist, for examination of the cancer pattern or performing surgical procedures. A typical system is shown in FIG. 6.

Interactive Simulation of TRUS Guided Needle Biopsy TRUS guided needle biopsy is considered a gold standard clinical procedure with its dual purposes of diagnosing and staging the prostate cancer. FIG. 7a shows a diagram of a transrectal biopsy procedure that is simulated by the system of the present invention.

Specifically, FIG. 7a shows the clinical setting of a TRUS guided prostate biopsy. FIG. 7b shows how a real ultrasound image of the prostate gland is given in a clinical setting based on the coordination of the biopsy needle. Under TRUS guidance, the needle is placed through the guide into the targeted lesion or location.

A two-step TRUS guided needle biopsy simulation is performed. First, various simulated TRUS probes are used to drive axially and/or longitudinally oriented sectional images, for an efficient planning of needle pathways.

Second, needles with or without triggers are constructed and simulated to perform an actual biopsy on the

reconstructed 3-D prostate models according to the planned needle pathways. This virtual system and process allows a surgeon to sit in front of the computer and simulate needle biopsies, plan optimal needle pathways when overlaid with TRUS imaging features, and further practice a designed biopsy procedure prior to actual clinical application to a patient. Furthermore, a statistical analysis can be conducted to evaluate the effectiveness of selected biopsy protocols based on sufficient large number of"virtual"biopsies, and, if necessary, recommend new biopsy techniques to improve prostate diagnostic accuracy.

The system of the present invention implements both sextant random core biopsy 12 and systematic 5-region biopsy techniques 4. Selected biopsy techniques have been performed based on dozens of reconstructed computer models of prostate specimens [24,30]. The simulation results are shown in FIGs. 8a to 8d, and the detection probability of each needle can be calculated to indicate its clinical importance. The analysis of estimated positive biopsy distribution (histogram) suggested that a spatial pattern of prostate cancer distribution exists.

More results are shown in FIGs. 9a and 9b, where the clinical stage with positive biopsies in these dozens of patients were used to distinguish clinically important and unimportant tumors. When the simulation is also recorded electronically, the results can be further analyzed to study various causes of hit or miss in each individual case. The grade of the tumor can also be incorporated into the system so that a spectrum of different cancer grade distribution can be investigated.

Furthermore, the physician that is practicing using the simulated prostate can use one or more biopsy needles

to practice planting a small piece of a radioisotope into a preselected location of a tumor during a virtual branchy therapy treatment, or, to practice directing a beam of radiant energy into a preselected location of a tumor during a virtual radiological onthology therapy treatment.

3-D Non-linear Graphical Matching Although 3-D computerized simulation of prostate biopsy provides useful information about the likelihood of clinically adequate sampling of the cancer, its utility in the statistical analysis can be problematic [4]. Mathematically, the simulation based on the each individual prostate model is a realization that only reflects a small piece of information regarding the whole ensemble if the deviation is high. For example, if all patients had identically sized prostate glands, and if there was a fixed percent volume of cancer in the prostate glands, finding the ideal number of biopsies to detect clinically significant cancer would be easy and consistent. However, the fact that there is significant variability among the sizes of prostate glands indicates a bias in the direct statistical analysis [3,4,9,16].

Some carcinomas detected in patients with small prostate glands can be undetected in patients with large prostate glands due to inadequate sampling of larger glands.

Accordingly, normalization of both prostate glands and tumors for all graphical models is a necessary step towards a correct statistical analysis result.

Such a normalization process can be achieved through 3-D object matching, which normally involves translation (i. e., positioning the origin), rotation (i. e., aligning the orientation), and scaling (i. e., adjusting the scale). Since most available image registration methods

are only valid for rigid objects, the challenge becomes how to incorporate soft tissue modeling of the prostate gland into the required 3-D object matching. To meet this challenge, the present invention incorporates a 3-D elastic matching method based on object reconstruction from 2-D contours [31]. Specifically, a 3-D nonlinear registration algorithm matches two surfaces by using a deformable surface-spine model. The advantage of the deformable surface-spine model lies in its ability to respond dynamically to applied external forces according to physical principles formalized in continuum mechanics as partial differential equations. The dynamic capability of this matching method is very effective to recover the non-rigid deformation between two surfaces, which is the case in the actual experimental setting 29. FIGs. 10a and 10b show the results of the 3-D nonlinear matching method incorporated in the present invention using a surface-spine deformable model.

The 3-D matching model of the present invention can be described as the following coupled dynamic system.

The initial spine is the axis of the surface determined from its contours. All the surface patches are contracted to the spine through expansion/compression forces radiating from the spine while the spine itself is also confined to the surfaces. The dynamics of the deformable surface-spine model are governed by the second-order partial differential equations from Lagrangian mechanics, and final shapes and relationship of the surface and spine are achieved when the energy of this dynamic system reaches its minimum [29]. Intensive experiments for optimizing the algorithm for the needs of the objects of the present invention have been performed.

In order to assure an efficient procedure and likely

global optimum, the present invention includes a 3-D principal axes algorithm to initially align two prostate glands [72]. Then, based on identified shift-invariant objects such as the prostate capsule, urethra, seminal vescles, and ejaculatory ducts, two sets of complex- structured tumor distributions are matched, with the tumor of one prostate correspondingly transformed to a new location, and with the tumor shape being modified according to the recovered nonlinear deformation, consistent with the deformed prostate capsule after registration.

3-D Data Mapping and Statistical Modeling In order to study prostate cancer patterns, a sophisticated mathematical model of probability maps of prostate cancer distribution was developed as a component of the present invention. As discussed above, computer simulation based on individual prostate models does not provide insight into the patterns of prostate cancer distribution in a statistical sense. In order to understand the spatial distribution of a tumor and its corresponding grade, a 3-D master model of the prostate showing probability maps of the location of any tumor and of high grade cancer is required. Thus, individual graphical models can be related to a global probability profile to determine an optimized biopsy technique 27.

Construction and Quantification of 3-D Probability Maps of the Location of Different Cancer Grades The system and process for construction and quantification of 3-D probablity maps of the location of different cancer grades is outlined in FIG. 14. In order to create a statistically significant master model hundreds of additional clinically proven surgical specimen sequences 32 of actual prostates are scanned

into an electronic database, to create a 3-D probability map of clinically significant and representative high grade cancer. Contour extraction 34 of key structures in these specimens is then conducted. Because this requires a large data storage capacity, high density CDROM and an on-line StorageTek robotic unit are examples of storage media that may be used with the present invention. Once again, the above-described 3-D object reconstruction method is used to generate the computer graphical models for these specimens.

Next, all the individual computer models are mapped 35 into a master model. The above-described method using jointly principal axes and the surface-spine deformable model produces very good results for 3-D object matching, and can be further enhanced using a blended deformable model. The results of the mapping process is a typical geometry for the master model that can preserve key aspects of each of the component shapes, so that each individual computer model is mapped to this standard base. This novel class of parameterized models is based on the linear interpolation of two parameterized shapes using a blending function [73]. The blended model is incorporated into previously discussed physics-based shape matching framework to use the dynamic deformation property while also providing abstraction of shape.

Based on the hundreds of normalized computer models, a 3-D is calculated 36. For each computer model, the voxels of localized prostate cancer are labeled"1", and the voxels of other internal structures are labeled"0", to generate a 3-D binary map of the prostate capsule and cancer, which is simply a mutually exclusive random sampling of the underlying spatial probability distribution of cancer occurrence. All these binary maps

are summed (geometrically normalized) together to obtain a 3-D histogram of the cancer distribution in which a mathematical normalization in the random space is required. Using previously developed mutual technology, this 3-D histogram is mathematically modeled by a standard finite generalized normal mixture (FGNM) distribution 45. In order to quantify this model, both an expectation-maximization (EM) algorithm 46 and a probabilistic self-organizing map (PSOM) algorithm are employed, thereby estimating the shape of the kernel, the number of the kernel, and the scaling factor in the mixture. As shown in previous studies [36,48], the method of the present invention will generate a statistical master model with K centers and a kernel shape such that the estimate of the spatial probability map achieves a minimum bias and variance at the same time. This advanced technology will establish an understanding of the spatial distribution of prostate cancer and corresponding grade.

For a given number of biopsies, the optimal location of the biopsy site is determined quantitatively based on the master model. A 3-D learning vector quantization method is applied to identify the best biopsy sites based on estimated probability maps [39]. Such a method provides an optimal solution in the sense of minimum mean squared error 47. Given this information, specific locations can be recommended for analysis, thereby developing more selective biopsy strategies.

Superimposing and Visualization of the Master Model with TRUS Imaging Features for On-line Biopsy Guidance Fig. 15 is a flow diagram that shows the process of superimposing and visualization of the master model with TRUS imaging features for on-line biopsy guidance

according to the present invention. In order to provide an on-line guidance for needle biopsies using both TRUS imaging features and the master model, the master model along with the spatial probability distribution pattern 41 is superimposed 39 on the TRUS image 40. Since the TRUS can only provide a gray scale image 40 in which key anatomical structures can not be directly identified, image segmentation is a key part of the present invention. A statistical model-based method 38 is employed for quantifying different tissue types and then segmenting major internal structures from TRUS images.

The model-based method 38 [35,36,37,38,41,43,44,48] has been applied to enable image segmentation from magnetic resonance (MR) brain images, computed tomography (CT) liver images, and computed radiography (CR) breast images.

Based on the segmented TRUS image 40 from the TRUS probe 43, the master model is superimposed over the on- line TRUS imaging. Since only 2-D images from TRUS may be available in the current clinical setting, a 3-D to 2- D registration is computed by the computer database/memory 21. The whole prostate gland is pre- scanned with two views to generate a sequence of image slices. Then, a matched filter is used to identify the most appropriate correspondence between the master model and a particular TRUS slice. After that, a multiple feature-based method is used to register the master model with the TRUS image. This method has shown a very robust performance when applied to PET and MRI brain image fusion [72]. Once again, soft tissue deformation needs to be considered, since the patient's body motion may be involved during the needle biopsy procedure.

Furthermore, the method can also incorporate advances

from site model based registration and mutual information maximization [71].

During the needle biopsy procedure 37 on the patient, the above process of superimposing and visualization of the master model with TRUS imaging features is useful to direct the one or more biopsy needles 44a. Specifically, together with the TRUS image 40 and master model including the spatial probability distribution pattern 41, the one or more biopsy needles 44a may be displayed 39 and viewed on a monitor, along with any medical equipment that may be necessary for a desired procedure. Such equipment may include a tool 44c for planting a small piece of a radioisotope into a preselected location of a tumor during a branchy therapy treatment, or, an emitter 44b for directing a beam of radiant energy into a preselected location of a tumor during a radiological onthology therapy treatment.

Simulation and Evaluation of Various Biopsy Protocols by Correlation of the Findings with True Tumor Parameters Based on an individual computer model, true tumor parameters will first be calculated. The key quantities are the tumor location, distribution, and representative volume. Assuming the reconstructed object-surface is accurate, true tumor volume is simply the interior volume confined by the tumor surface.

In order to simulate the actual clinical setting, a simulation of various biopsy protocols is conducted using two modes: purely computerized simulation and human controlled virtual biopsy. Various computer programs can be easily generated to perform a computerized biopsy in which clinical factors will be incorporated such as variability of needle angle and mispositioning. In a human controlled virtual biopsy, force feedback is

integrated into the routine practice and the error caused by human factor is also addressed.

The correlation of the findings in the simulated biopsies with the grade and volume of the cancer will answer many unknown questions through the analysis and measurements of the 3-D data and pathways of needle biopsies. Through these trials, statistical modeling and multimodality visualization can thus improve the biopsy technique in the diagnosis of prostate cancer.

Specifically, these trials can determine the likelihood of adequate tumor sampling using current standard transrectal sextant biopsy techniques [12]; spatial distribution, enumeration, symmetry, total tumor volume, and tumor volume as a fraction of prostrate volume; volume and distribution of extraprostatic tumors; spatial distribution of tumor foci; and distribution correlation of prostatic intraepithelial neoplasia and invasive tumors.

Derivation of an Algorithm to Estimate Tumor Volume and Other Staging Parameters Based on the above-described 3-D master model and computer simulation, statistical detection and estimation theory and neural network can be used to derive a more accurate algorithm to estimate tumor volume and other staging parameters from the outcomes of the novel biopsy technique. The precise relationship between the outcomes of sampled needle biopsies and the total tumor volume is complex. Current tumor volume estimation methods are problematic [6,10,13,14,20], and recent formulations have been proposed [23] to improve such estimations. An algorithm based on the 3-D SFM model and Bayesian theory as described above is successful in quantifying the mixture factor of the different tissue types [35,38].

The situation for estimating tumor volume differs in that the individual tumor volume must be estimated from limited samples in comparison to the large number of pixels in medical images, but the same methodology pertains: the tumor volume can be"predicted"based on Bayesian theory and the underlying probability maps.

Currently used protocols generally underestimate the tumor volume. This implies that traditional formulation may be augmented by newly developed machine learning approaches [3]. Neural networks can effectively learn the knowledge from large samples regarding the relationships among data, and have successfully developed various neural network based algorithms and fuzzy logic for robust clinical decision making, such as prostatron treatment planning for BPH and breast cancer diagnosis [42]. Therefore, a probabilistic modular neural network is applied according to the present invention to estimate total tumor volume directly from the outcomes of needle biopsy cores. This is advantageous as it provides a multi-dimensional non-linear mapping capability between the input (biopsy results, PSA, PSA density, size of prostate gland from TRUS, etc.) and the output (estimated tumor volume), without knowing the complicated mathematic relationships. Thus it can be demonstrated that machine learning can improve the accuracy of tumor volume estimation from the biopsies.

Since the probability maps are based on previously determined location of cancer, the likelihood of tumor volume given the outcomes of needle biopsies can be calculated, using a probability concentric onion like system together with Bayesian rule. Thus, the likelihood of tumor volume will decrease as the cancer-proven biopsy core moves layer by layer from the centrum toward the

periphery of the cancer foci. These layers are defined by the factorized standard deviations. This aspect of the invention further improves the ability to estimate the location of the detected cancer.

Having described an embodiment of the invention, it is to be understood that the invention is not limited to any of the precise embodiments described herein. Various changes and modifications could be effected by one skilled in the art without departing from the spirit or scope of the invention as defined in the appended claims.

Appendix Associated Literature 1 J. Catalona and W. W. Scott,"Carcinoma of the Prostate,"Campbell's Urology, P. C.

Walsh et. al., 1996.

[2] A. Chiarodo,"National Cancer Institute roundtable on prostate cancer: Future directions," Cancer Research 51: 2498-2505,1991.

[3] Y. Goto and P. T. Scardino et. al.,"Distinguishing clinically important from unimportant prostate cancers before treatment-Value of systematic biopsies,"1. Urol., Vol. 156, 1059-1063, September 1996.

[4] L. A. Eskew, R. L. Rare, and D. L. McCullough,"Systematic 5 region prostate biopsy is superior to sextant method for diagnosing carcinoma of the prostate,"1. Urol., Vol.

157,199-203, January 1997., [5] R. C. Flanigan et. al.,"Accuracy of digital rectal examination and transrectal ultrasonography in localizing prostate cancer,"'J. 1 liol., Vol. 152,1506-1509, November 1994.

[6] T. A. Stamey,"Diagnosis of Prostate Cancer: A Personal View,"1. Urol., Vol.

147,830-83Z March 1992.

[7] P. N. Werahera et. al.,"A 3-D Reconstruction Algorithm for Interpolation and Extrapolation of Plannar Cross Sectional Data,"IEEE Trans. Med. Imaging, Vol. 14, No. 4, December 1995.

[8] H. Lange,"The Next Era for Prostate Cancer,"JAMA, Vol. 269, No. 1, January 1993.

9 C. Busch, et. al., "Evaluation of transrectal ultrasound guided core biopsy strategies for the detection of prostate cancer: the sextant protocol underestimates the presence of cancer," (personal communications with the PD, Jan. 1997.

10 T. A. Stamey, et. al.,"Morphometric and clinical studies on 68 consecutive radical prostatectomies,"J. Urol., Vol. 139, pp. 1235-1241,1988.

11 J. E. McNeal, et. al.,"Zonal distribution of prostatic adenocarcinoma: Correlation with histologic pattern and direction of spread,"Am. J. Surg. Pathol., K. Vol. 1Z pp.

897-906,1988.

[12] K. K. Hodge, et. al.,"Random systematic versus directed ultrasound guided transrectal core biopsies of the prostate,"J. Urol., Vol. 142, pp. 71-74,1989.

[13] T. A. Stamey, et. al.,"Localized prostate cancer: Relationship of tumor volume to clinical significance for treatment of prostate cancer,"Cancer, Vol. 71, pp. 933-938,1993.

[14] T. A. Stamey,"Making the most out of six systematic sextant biopsies", Urol., vol. 45, no. 1, pp. 2-1Z Jan. 1995.

15 G. J. Miller and J. M. Cygan,"Diagnostic correlation with whole mount of radical prostatectomy specimens,"Monogr. Pathol., VoL 34, pp. 183-197,1992.

16 F. Daneshgari, et. al.,"Computer simulation of the probability of detecting low volume carcinoma of the prostate with six random systematic core biopsies,"Urology 45: 604-609,1995.

[17] J. H. Lynch,-Treatment of Advanced Prostate Cancer,"1. Family Practice, 35 (5), 488,1993.

[18] J. H. Lynch and C. W. Graham,"Management of Stage C Adenocarcinoma of the Prostate,"British J. Urol., 70, Suppl. 1,50-56,1992.

19 I. Sesterhenn et. al.,"Preliminary Results of Three-Dimensional Reconstruction of Previously Imaged Prostate,"Vie Prostate Supplement 4 : 33-41,1992.

[20] F. K. Mostofi, 1. A. Sesterhenn, and C. J. Davis,"Prostate carcinoma: Problems in the interpretation of prostate biopsies,"Hum. Pathol., 23: 223-241,1992.

[21] F. K. Mostofi, 1. A. Sesterhenn, and C. J. Davis,"A Pathologists's View of Prostate Carcinoma,"Cancer, 71: 906-932, Feb., 1993.

22 R. M.-Mordkin, W. S. Hayes, and J. H. Lynch,"The Management of Locally Advanced Prostate Cancer,"Oncology, 1996.

23 D. D. Dietrick, J. E. McNeal, and T. A. Stamey,"Core Cancer Length in Ultrasound-Guided Systematic Sextant Biopsies: A Preoperative Evaluation of Prostate Cancer Volume,"Urol., Vol. 45, No. 7, pp. 987-992, July, 1995.

[24] W. Hayes, 1. Sesterhenn, J. Xuan, Y. Wang. J. Lynch, and S. K. Mun,"Interactive 3-D Modeling of Localized Prostate Cancer and Computer Simulation of Needle Biopsy Techniques, ii Proc. Annual Meeting of Ame. Urology Society, New Orleans, 1997.

[25] M. K. Terris, J. E. McNeal, and T. A. Stamey,"Detection of Clinically Significant Prostate Cancer by Transrectal Ultrasound-Guided Systematic Biopsies,"J. Urol., Vol. 148, pp. 829-833, Sept. 1992.

[26] Y Wan& J. k6n, I. Sesterhenn, W. Hayes,'J. Lynch, and S. K. Mun,"Statistical Modeling and Multimodality Visualization of Prostate Cancer for Prostate Cancer Diagnosis and Stagin&"Technical Report, Georgetown University Medical Center, 1996.

[27] Y. Wang, J. Xuan, I. Sesterhenn, W. Hayes, D. Ebert, J. Lynch, and S. K. Mun, "Statistical Modeling and Visualization of Localized Prostate Cancer,"SPIE Medical Imaging, Newport Beach, California, Feb. 1997.

[28] M. L. Schiebler et. al.,"State-of-the-Art: Current Role of MR Imaging in the Staging of Adenocarcinoma of the Prostate,"Radiology, 189: 339-352,1993.

[29] J. Xuan, Y. Wang, T. Adah, Q. Zheng, W. Hayes, M. Freedman, and S. Mun,"A Deformable Surface-Spine Model for 3-D Object Registration,"to appear 4th IEEE ICIP, 1997.

[30] J. Xuan, Y. Wang, T. Adalt W. Hayes, J. Lynch, and S. K. Mun,"Virtual Simulation of Prostate Biopsies: 3D Modeling and Multimodality Visualization,"submitted to IEEE Trans.

Visualization and Computer Graphics, 1997.

31 J. Xuan, W. Hayes, Y. Wang, T. Adah, M. Freedman, S. K. Mun, and I. Sesterhenn, "Surface Reconstruction and Visualization of the Surgical Prostate Model,"SPIE Medical Imaging, Newport Beach, Feb. 1997.

[32] G. M. Nielson,"Challenges in Visualization Research,"IEEE Trans. Visualization and Computer Graphics, Vol. Z No. 2, pp. 97-99, June 1996.

[33] G. T. Herman,-3-D display: A survey from theory to applications,"Comput. Med.

Imag. Graph., Vol. 17, pp. 231-24Z 1993.

[34] M. L. Rhodes, Ed.,"Computer Graphics in Medicine,"IEEE Comput. Graph. Appl., Vol. 11, pp. 27-80,1991. [35] Y. Wang, T. Adah, C. M. Lau, and Z. Szabo,"Quantification of MR Brain Images by A Probabilistic Self-Organizing Map,"Radiology (Special Issue), Vol.

197 (P), pp. 25Z November 1995.

[36] Y. Wang,"Image Quantification and The Minimum Conditional Bias/Variance Criterion," (Invited Talk) Proc. 30th Conf. Info. Sci. Sys., pp. 1061-1064, Princeton, March 1996.

[37] Y. Wang and J. M. Morris,"On Numerical Verification of Time-Domain Moment Method in Ultrasound Tomography,"-SPIE Journal of Biomedical Optics, Vol., No. 3, pp.

21-26. July 1996.

[38] Y. Wang and T. Lei,"A New Stochastic Model-Based Image Segmentation Technique forMRImages,"inProc. FirstIEEEIntl. Conf. ImageProcessing, Austin, Texas 1994.

[39] Y. Wang, T. Adah, and S-C B. Lo,"Automatic Threshold Selection Using Histogram Quantization,"SPIE Journal of Biomedical Optics, Vol. ZNo. 3, pp. 211-219, April 1997.

40 Y. Wang and T. Lei,"A New Look at Finite Mixture Models in Medical Image Analysis,"Proc. IEEE Intl. Symp. Speech, Image Proc. & Neur. Net., April 14-16, Hong Kong 1994.

[41] Y. Wang and T. Adah,"Probabilistic neural networks for parameter quantification in medical image analysis,"Biomedical Engineering Recent Development, J. Vossoughi, Editor, 1994.

[42] Y. Wang, S-H. Lin, H. Li, and S-Y. Kung,"Data Mapping by Probabilistic Modular Networks and Information Theoretic Criteria,"in revision to IEEE Trans. Signal Processing, 1996.

[43] Y. Wang, T. Adah, S-Y. Kung, and Z. Szabo,"Quantification and Segmentation of Brain Tissues from MR Images: A Probabilistic Neural Network Approach,"submitted to IEEE Trans. Image Processing, 1997.

[44] Y. Wang, T. Adah, S-Y. Kung, and Z. Szabo,"Quantification and Segmentation of Brain Tissues from MR Images: A Probabilistic Neural Network Approach,"to appear J. VLSI Signal Processing & Tech.), 1997.

45 D. M. Titterington, A. F. M. Smith, and U. E. Markov, Statistical analysis of finite mixture distributions. New York: John Wiley, A85.

[46] R. A. Redner and N. M. Walker,"Mixture densities, maximum likelihood and the EM algorithm,"SIAM Rev., Vol. 26, pp. 195-239,1984.

[47] J. Rissanen,"Minimax entropy estimation of models for vector processes,"System Identification, pp.97119,1987.

[48] Y. Wang and T. Adah,"Efficient Learning of Finite Normal Mixtures for image Quantification,"Proc. IEEE Intl. Conf Acoust., Speech, and Signal Processing, Atlanta, Georgia, pp. 3422-3425,1996.

[49] N. Ayache,"Medical computer vision, virtual reality and robotics.."Image and Vision Computing, Vol. 13, No. 4, pp. 295-313, May. 1995.

[50] L. Cohen and 1. Cohen,--Finite, element methods for active contour models and balloons for 2-D and 3-D images", IEEE Trans. Pattern Ana. and Machine Intell., vol. 15, no. 11, pp.

1131-1147,1993.

51 S. Coquillart and P. Jancne,"Extended free-form deformations: A sculpturing tool for 3D geometric modeling", ACM Computer Graphics, vol. 24, No. 4, pp. 187-196,1990.

[52] F. P. Ferrie, J. Lagarde, and P. Whaite,"Darboux frames, snakes, and super-quadrics: Geometry from the bottom up", IEEE Trans. Patt. Anal. Machine Intell., vol. 15, pp.

771-783,1993.

[53] W. Grimson, From images to surfaces, MIT Press, Cambraidge, USA, 1981.

[54] M. Kass, A. Witkin, and D. Terzopoulos,"Snakes: active contour models,"Int. J.

Comput. Vision, Vol 1, No. 4, pp. 321-331,1988.

55 W. Lin, C. Liang, and C. Chen,"Dynamic elastic interpolation for 3-D medical image reconstruction from serial cross section", IEEE Trans. on Medical Imaging, vol. 7, No. 3, pp.

225-23Z Sep. 1988.1 [56] D. Ebert, et. al.,"Two-handed, interactive stereoscopic visualization,"Proc. IEEE Visualization, October 1996.

[57] R. Yagel, et. al.,"Grouping Volume Renderers for Enhanced Visualization in Fluid Dynamics,"IEEE Trans. Visual. Comput. Graph., Vol. 1, No. Z 1995.

[58] G. Celniker and D. Gossard,"Deformable Curve and Surface Finite-Elements for Free-Form Shape Design, U-Computer Graphics, Vol. 25, No. 4, pp. 257-266, July 1991.

[59] M. MoshfegK S. Ranganath, and K. Nawyn,"Three-Dimensional Elastic Matching of Volumes,"IEEE Trans. Image Processing, Vol. 3, No. 2, pp. 128-138, March 1994.

[60] Zienkiewicz, The Finite Element Method, The Third Edition, McGraw-Hill Book, 1967.

61 D. J. Buff,"A dynamic model for image registration,"Computer Graphics and Image Processing, vol. 15, pp. 102-11Z 1981.

62 L. Chang, H. Chen, and J. Ho,"Reconstruction of 3D medical images: A nonlinear interpolation technique for reconstruction of 3D medical images,"CVGIP; Graphical Models and Image Processing, vol. 53, no. 4, pp. 382391, July 1991.

[63] M. J. Herbert, C. B. Jones, and D. S. Tudhope,"Three-dimensional reconstruction of geoscientific objects from sections,"The Visual Computer, vol. I1, pp. 343-359,1995.

64 T. McInerney, and D. Terzopoulos,"Adynamicfinite element surface model for segmentation and tracking in multidimensional medical images with application to cardiac 4D image analysis,"Computerized Medical Imaging and Graphics, vol. 19, no. 1, pp.

69-83,1995.

[65] P. Metaxas, and D. Terzopoulos,"Dynamic deformation of solid primitives with constraints,"Computer Graphics, vol. 26, no. 2, pp. 309-312, July 1992.

[66] D. Metaxas, ai-d D. Terzopoulos,"Shape and non-rigid motion estimation through physics-based synthesis, IEEE Trans. Pattern Anal. Machine Intell., vol. 15. no. 6, pp.

580-591, June 1993.

[67] M. Moshfeghi,"Elastic matching of multimodality medical images,"CVGIP: Graphical Models and Image Processing, vol. 53, no. 3, pp. 271-28Z May 1991.

[68] M. Moshfeghi, and H. Rusinek,"Three-dimensional registration of multimodality medical images using the principle axes technique,"Philips J. Res., vol. 47, no. Z pp.

81-97,1992..

[69] D. Terzopoulos, and K. Fleischer,"Deformable Models", The Visual Computer, vol. 4, pp. 306-331,1988.

70 D. Terzopoulos, and A. Witkin,"Physically-based models with rigid and deformable components,"GrgphicsInterfdce'88, pp. 146-154, June 1988.

[71] Y. Wang,"Medical image registration: a review with recommendations,"Issues on Multimodality Medical Image Registration, National Technology Transfer Center Report, 1997.

[72] Y. Wang, C-M. Lau, T. Adah, and Q. Zheng,"PET/MRI image fusion of the brain by probabilistic image quantification and registration,"'to appear Proc. Intl. Conf Signal and Image Processing, New Orlearn, 1997.

[73] D. DeCarlo and D. Metaxas,"Blended deformable models,"IEEE Trans. Pattern Ana and Machine Intell., vol. 18, no. 4, pp. 443-448, April 1997.