Neural network based auto-windowing system for MR images

An adaptive hierarchical neural network based system with online adaptation capabilities has been developed to automatically adjust the display window width and center for MR images. Our windowing system possesses the online training capabilities that make the adaptation of the optimal display parameters to personal preference as well as different viewing conditions possible. The online adaptation capabilities are primarily due to the use of the hierarchical neural networks and the development of a new width/center mapping system. The large training image set is hierarchically organized for efficient user interaction and effective re-mapping of the width/center settings in the training data set. The width/center values are modified in the training data through a width/center mapping function, which is estimated from the new width/center values of some representative images adjusted by the user. The width/center mapping process consists of a global spline mapping for the entire training images as well as a first-order polynomial sequence mapping for the image sequences selected in the user's new adjustment procedure.

BACKGROUND OF THE INVENTION
 1. Field of the Invention
 The present invention relates to Magnetic Resonance (MR) image displays,
 and more particularly, to an auto-windowing system for MR images capable
 of adapting to optimal display parameters, personal preferences and
 different viewing conditions while online.
 2. Prior Art
 Adaptive and automatic adjustment of the display window parameters for
 Magnetic Resonance (MR) images under different viewing conditions is a
 very difficult and challenging problem in medical image perception. There
 are several factors that make this problem difficult, namely, the function
 describing a human expert's adjustment of display window parameters for a
 wide variety of MR images is extremely complicated, the adjustment result
 is subjective and substantially depends on personal preference, the
 adjustment function varies with the viewing conditions, etc. The viewing
 conditions are generally the condition of the monitor and the exterior
 viewing environment, such as the illumination condition. It is almost
 impossible to account for all these issues in a single universal
 algorithm.
 The display windowing process is primarily used in the mapping of 12-bit MR
 image intensity values into 8-bit gray levels for displaying MR images on
 a common 8-bit computer monitor. The display window consists of a width
 parameter and a center parameter. The windowing process maps the image
 intensity values linearly from [center-width/2, center+width/2] to the
 nearest integer in [0,255]. For the MR image intensity values below
 (center-width/2), they are mapped to 0. Similarly, the image intensity
 values greater than (center+width/2) are mapped to 255. Apparently, these
 two parameters can greatly influence the appearance of the image to be
 displayed. In other words, the brightness and the contrast of an image is
 determined by these two parameters. Inadequate adjustment of these
 parameters can lead to degradation of image quality, and in severe cases
 to loss of valuable diagnostic information of the images.
 Most previous methods for the adjustment of display window parameters are
 either very restricted to certain types of MR images or perform very
 differently from the human adjustment. R. E. Wendt III, "Automatic
 adjustment of contrast and brightness of magnetic resonance images",
 Journal of Digital Imaging, Vol. 7m No. 2, pp 95-97, 1994. Wendt III has
 proposed a method which first determines the type of an MR image by
 reading the image header information, and then computes the display
 parameters depending on the type of the image. Unfortunately, different
 rules must be set for different types and orientations of MR images in
 this method. This makes the algorithm impractical, since new rules need to
 be added in the program to reflect any new changes in the MR image
 acquisition process, such as, for example, the use of new coils or new
 pulse sequences. Ohhashi et al. has developed a neural network based
 method for the automatic adjustment of the display window. A. Ohhashi, S.
 Yamada, K Haruki, H. Hatano, Y Fujii, K Yamaguchi and H Ogata, "Automatic
 adjustment of display window for MR images using a neural network",
 Proceeding of SPIE, Vol. 1444, Omage Capture, Formatting and Display, pp.
 63-74, 1991. This method is still a pure histogram based method, and as
 such, there is a potential problem of very different adjustments for
 images with very different spatial distributions but very similar
 histograms. In addition, this method only uses a single neural network for
 approximating the human adjustment, which is too complicated for a wide
 range of MR images to be sufficiently approximated with good
 generalization power by a single neural network.
 Recently, the inventors proposed a comprehensive hierarchical neural
 networks (HNN) based algorithm for automatic and robust adjustment of the
 display window, which is the subject of U.S. patent application Ser. No.
 08/885,080 entitled "Robust and Automatic Adjustment of Display Window
 Width and Center for MR Images" filed on Jun. 30, 1997, now U.S. Pat. No.
 5,995,644, the entire disclosure of which is incorporated herein by
 reference. This algorithm is based on the principle of learning from
 examples, (i.e. a large set of MR images associated with the window
 width/center values adjusted by human experts). This HNN based algorithm
 uses both wavelet histogram features and spatial statistical information
 of MR images for feature generation, which overcomes the problem of using
 pure histogram information only. A hierarchical neural network was
 developed to decompose the very complicated function approximation problem
 into several simple subproblems. The hierarchical neural Rtworks are
 comprised of a modified competitive layer neural network for clustering
 any input image into a certain number of clusters, and the Radial Basis
 Function (RBF) and the Bi-modal Linear Estimation (BLE) networks for each
 class to provide good estimation results. Finally, a data fusion step is
 used to intelligently combine the multiple estimates from the RBF and BLE
 networks to provide accurate and robust estimation results.
 All the above methods lack the capabilities of adapting the window
 width/center adjustment to different personal preferences or different
 viewing conditions as described above. The automatic display window width
 and center adjustment by using all the previous methods can only be
 optimized for a particular personal taste and for a particular viewing
 condition. The demand for an adaptive and automatic windowing system is
 very common since the automatic windowing system needs to be used by many
 persons with different personal preferences and in different viewing
 conditions.
 SUMMARY OF THE INVENTION
 The present invention is based on the inventors previously described HNN
 based display window width/center estimation algorithm, the entire
 disclosure of which is incorporated herein by reference. Due to the basic
 learning-from-examples principle of the HNN algorithm, the training data
 set is organized into categories as well as sequences with some
 representative images selected from each sequence. By re-adjusting some
 representative images of the sequences in some categories selected by the
 user, the width/center values of the entire training data are mapped
 through a global mapping function and a sequence mapping process to adapt
 the width/center settings of the training data set to the user's
 preference and the viewing conditions. The global mapping function used is
 a linear spline function that is obtained by fitting the data of all the
 re-adjusted representative images. This is used to capture the general
 personal preference and account for the effect of the viewing condition.
 The sequence mapping process involves fitting the baseline width/center
 values in a sequence with low-order polynomial functions and setting the
 new width/center values in one sequence with the new baseline polynomial
 function. The sequence mapping is applied after the global mapping and
 only to the sequence with representative frames selected by the user for
 re-adjustment. After the above mapping process, the hierarchical neural
 networks are re-trained with the new training data, thus the re-trained
 HNN algorithm is adapted to the user's personal preference as well as the
 viewing condition.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS
 Referring to FIG. 1, in the HNN algorithm of the prior art, the feature
 generator 12 extracts two types of features from MR images as the input to
 the HNN, namely, the wavelet histogram feares and spatial statistical
 features. The selection of these features resolves in most cases the
 conflicting situations where the display window settings are very
 different although the histograms of the images are very similar. The
 wavelet transform is used to compress the histogram information into a
 much smaller size for efficient training of neural networks. For
 distinguishing different types of MR images, a neural network based
 clustering algorithm 14 is employed to cluster any input image into
 multiple clusters. The neural network based clustering algorithm 14 uses
 two totally different and independent estimation methods in each class to
 achieve good estimation performance. Once the input images are classified
 by classifier 16, radial basis function (RBF) networks 18 are used for
 accurate estimation for known (trained) MR images, while bimodal linear
 (BLE) networks 20 provide robust and reasonable estimation for a wide
 range of images, that may not be included in the training data'set.
 The use of hierarchical neural networks significantly simplifies the
 approximation of the complicated display window adjustment function by
 decomposing a large and complex problem into a number of small and simple
 sub-problems. The last step in the HNN algorithm is a data fusion process
 22 that intelligently combines the multiple estimates supplied by the RBF
 and BLE networks in the assigned clusters based on a consistency measure.
 Hierarchy of the Training Data
 The HNN algorithm is based on learning from examples. The training data set
 consists of a very large number (i.e., thousands) of feature vectors
 extracted from the MR images along with the associated width/center values
 adjusted by human experts. It is not necessary to store the original MR
 images in the training data, since only the compact feature vectors and
 the width/center values are required in the training of the HNN. This
 overcomes the problem of saving and transmitting an enormous amount of
 training image data. The online training system of the present invention
 changes the existing window width/center values in the training data to
 adapt to the personal preference and viewing environment through some user
 interaction. The user interaction involves the re-adjustment of the window
 width/center for some representative images in the training data set. It
 is impractical and unnecessary for the user to re-adjust a very large
 number of MR images in the training data set. Thus, the representative
 images are used to simplify the user interaction process and make the
 mapping of the re-adjustment to the entire data set effective. According
 to an embodiment of the invention, the representative images are selected
 based on a hierarchical organization of the entire training data. This
 hierarchical organization facilitates efficient user interaction as well
 as effective mapping of the training data according to the new
 re-adjustments by the user for adaptive online training.
 The hierarchy of the training data organization is shown in FIG. 2. The
 entire training images are first classified into a few major categories
 according to the types and studies of MR images. For example, the MR
 images in our training data set are categorized into head, body, heart,
 spine, neck, periphery, angiography and miscellaneous categories. Other
 implementations can use different categories without departing from the
 scope of this disclosure. This categorization depends on the training
 image set, and allows additions of new categories or deletions of existing
 categories based on the changes in the training data set. By carefully
 examining the training images of each category, the MR images can be
 grouped into the same sequence together with an appropriate order and
 assign a category to each sequence. For example, the MR images in category
 1 are grouped into sequences Seql-Seq N.sub.1. Thus, there are many MR
 sequences in each category in an organized order. Representative frames
 are then selected in each sequence for the user re-adjustment. In the
 present implementation, two or three representative frames are selected,
 however, any suitable number of representative frames can be selected for
 the desired application. The representative frames should be chosen such
 that their locations in their sequence are well separated. For example,
 one can choose the representative frames separately from the beginning
 portion, the ending portion, and the middle portion of a sequence.
 In addition to the feature vectors and the width/center values of all the
 training images, the online training data set needs to store all the
 representative images for the user re-adjustment. The number of
 representative images in each sequence should be as small as possible for
 saving the storage space for the online training data as well as making
 the user interaction efficient. Note that it is not required for the user
 to go through all the representative images in the online training set.
 The user can simply select a few sequences in some categories of interest
 to re-adjust the display window width/center of the corresponding
 representative frames.
 Mapping of Width/Center Settings
 Two types of the width/center mapping have been developed for modifying the
 training data from the user's re-adjustment of some representative images
 to adapt the HNN algorithm to the personal preference and viewing
 environment. The first type is a global mapping process which is applied
 to the entire data set to account for the general personal preference and
 the viewing condition. The other is a sequence mapping procedure that is
 only limited to each individual sequence with representative frames being
 re-adjusted by the user. The sequence mapping is used to enforce the
 change of the width/center setting for the sequence according to the
 user's new adjustment. The details of these two types of mapping are
 addressed subsequently.
 Global Mapping
 The global mapping function is a transformation of the original
 width/center values to the new width/center values. The global mapping
 transformation is denoted by .function. (w, c) with .function. (w,
 c)=.function..sub.w (w)w,.function.,(c)c), where w and c are the original
 width and center values, and .function..sub.w (w) and .function..sub.c (c)
 are the scaling factors for generating new width/center values,
 respectively. Each of the functions .function..sub.w and .function..sub.c
 are represented by a spline function with non-uniform nodes. The spline
 function is a piecewise polynomial with some continuity conditions, which
 is constituted by several polynomials with each polynomial assigned to an
 interval determined by two neighboring nodes. Assume there are n nodes,
 x.sub.i, for i=1, . . . , n, chosen in order between 0 and 4095, i.e.
 0&lt;x.sub.1 &lt;x.sub.2 &lt;. . . &lt;x.sub.n &lt;4095, and two fixed nodes x.sub.0 =0
 and x.sub.n+1 =4095 for the spline. A spline function .function.(x) can be
 written as
 ##EQU1##
 where each P.sub.i (x) is a polynomial inside the interval [x.sub.i,
 x.sub.i+1 ] and is zero outside the interval. The spline can usually be
 represented by the values of the function and the necessary function
 derivatives at the nodal points. The present invention uses the linear
 spline for the global mapping function. The linear spline function can be
 simply defined from the nodal values .function..sub.i, i=1, . . . , n,
 with the boundary condition .function.(x.sub.0)=.function..sub.0 and
 .function.(x.sub.n+1)=.function..sub.n+1 as follows
 ##EQU2##
 where B.sub.i (x) are the basis functions that are nonzero in a small
 interval determined by the nodal locations. Note that the first and the
 last terms are from the boundary condition. These basis functions are
 defined as follows:
 For B.sub.0 (x),
 ##EQU3##
 For B.sub.i (x), i=1, . . . , n
 ##EQU4##
 B.sub.i (x)=0 elsewhere
 For B.sub.n+1 (x),
 ##EQU5##
 After introducing the linear spline model for the global mapping function,
 we now describe how we fit the linear spline functions to the
 re-adjustment data. Let the data points from the re-adjustment of N
 selected representative images be given by (a.sub.k, b.sub.k), k=1, . . .
 N, where a.sub.k is the original width or center value, and b.sub.k is the
 ratio of the re-adjusted width or center value to the original value
 a.sub.k. The boundary condition is .function..sub.0 =.function..sub.n+1
 =1. The linear spline fitting problem is to find the unknown nodal values,
 .function..sub.1, . . . , .function..sub.n, such that the fitting errors
 between the spline and the data points are minimized. In addition, we can
 impose a smoothness constraint on the spline to achieve robust fitting.
 Thus, the linear spline fitting can be accomplished by minimizing the
 energy function E(.function..sub.1, . . . .function..sub.n) defined as
 follows
 ##EQU6##
 where .lambda. is a regularization parameter that controls the smoothness
 of the spline. This parameter has been set to 1.0 in our implementation.
 The energy function E(.function..sub.1, . . . , .function..sub.n) consists
 of the data compatibility energy in the first summation and the smoothness
 energy in the second summation. This energy function is a quadratic and
 convex function of the coefficient vector u=(.function..sub.1, . . . ,
 .function..sub.n).sup.T. The solution to this least square problem can be
 obtained by solving the system Au=y, where A is an n.times.n matrix and y
 is an n.times.1 vector, which is derived from the energy function E(u). To
 be more specific, the (i,j)-th entry in the matrix A can be written as
 ##EQU7##
 where .delta.(i) is the delta function that takes the value 1 when i=0 and
 the value 0 elsewhere. The i-th entry of the vector y is given by
 ##EQU8##
 Note that the matrix A is a tridiagonal and symmetric positive defmnite
 (SPD) matrix. (See. G. H. Golub and C. F. Van Loan, Matrix Computations,
 2.sup.nd Edition, The Johns Hopkins University Press, 1989). This linear
 system can be solved simply by Gaussian elimination. After applying the
 above linear spline fitting procedure to obtain both the width and center
 global mapping functions, the width/center global mapping transforms are
 applied to all the original width/center values in the training data set
 to generate the new width/center settings for the new training data set.
 Thus the retrained HNN algorithm is accommodated to the user's general
 personal preference and the environments viewing condition.
 FIGS. 3a and 3b show an example of the global spline mapping function
 computed by fitting a linear spline to the user re-adjustment data
 separately for width and center, respectively. The circles in the figure
 represent the data points.
 Sequence Mapping
 Unlike the global mapping that is applied to the entire training data set,
 the sequence mapping is only applied to each individual sequence that
 contains representative frames re-adjusted by the user. The sequence
 mapping function is performed after the global mapping process. The
 sequence mapping is used to enforce the new width/center settings of all
 the images in the same sequence to comply to the user's re-adjustments.
 The idea behind the sequence mapping procedure is to use a baseline curve
 to represent very general width or center settings in an ordered sequence.
 This baseline curve is a function of the image index in a sequence, and is
 obtained by fitting a low-order polynomial, usually up to first order, to
 the width or center values at locations of the representative frames. The
 procedure involves fitting the baseline polynomials to the width/center
 values of the representative frames from the user re-adjustment and to
 those after the global mapping process. Then, the new baseline curve is
 enforced by adding the difference between these two baseline curves at the
 corresponding image index to the width/center value of each image in the
 sequence. The details of this procedure are now described.
 Let the ordered images in a sequence be indexed from 1 to m and the
 associated width/center values obtained after the global mapping process
 be denoted by w.sub.i /c.sub.i for i=1, . . . , m. The re-adjusted
 representative frames in the same sequence are indexed by r.sub.j with
 1.ltoreq.r.sub.j.ltoreq.m for j=1, . . . , m' and the associated
 re-adjusted width/center values are denoted by w.sub.j '/c.sub.j ', where
 m' is the number of representative frames in the sequence selected in the
 re-adjustment. Two baseline curves represented by low-order polynomials
 p.sub.w (i) (or p.sub.c (i)) and p.sub.c '(i) (or p.sub.c '(i)) are fitted
 to the width (or center) values of the representative frames obtained
 after the global mapping and re-adjusted by the user, respectively. To
 enforce the baseline curve to the width/center setting from the user's
 re-adjustments, we perform the following sequence mapping to all the
 width/center values in this sequence to generate the new training data,
EQU (w.sub.i,c.sub.i).fwdarw.(w.sub.i +p.sub.w '(i)-p.sub.w (i), c.sub.i
 +p.sub.c '(i)-p.sub.c (i))
 Note that this sequence mapping procedure is only performed for the
 sequence with its representative frames being selected in the user
 re-adjustment process. The order of the polynomials used in the baseline
 curve fitting depends on the number of re-adjusted frames in this sequence
 and is generally less than 1. More complex computations for higher orders
 of polynomials can also be employed.
 Examples of an MR sequence with its width/center settings after the global
 mapping process and the sequence mapping procedure described in this
 section are shown in FIGS. 4a and 4b. In the examples, two representative
 frames are selected for the user re-adjustment. Their re-adjusted
 width/center values are marked using a star (*) in the figures. The
 sequence mapping enforces the baseline of the new width/center settings in
 the sequence using the user's re-adjusted values of the representative
 frames in the sequence.
 Training of the Hierarchical Neural Networks
 In this section, we briefly discuss the training of the hierarchical neural
 networks [Lai&Fang, 1997] used in our system. As shown in FIG. 1, the
 hierarchical neural networks consist of a modified
 competitive-layer-neural network for clustering, a number of RBF networks
 and BLE networks for window width/center estimation. In the training of
 the HNN, we first train the modified competitive layer neural network.
 Then, the entire training data set is clustered into different classes
 through the trained modified competitive layer neural network. For each
 class, the associated RBF and BLE networks are trained using the training
 data assigned to this class. Each training component in the HNN is
 described below.
 Modified Competitive Layer NN
 The training of the modified competitive layer neural network is an
 unsupervised learning process. As illustrated in FIG. 5, the network
 contains n classes with each class represented by a centroid vector u, and
 a bias b, where 1&lt;i&lt;n and i is the index for the class. The main
 difference between the modified competitive layer NN and the standard one
 (see, T. Kohonen, Self-Organization and Associative Memory, 2.sup.nd
 Edition, Springer-Verlag, Berlin, 1987) is that the former assigns m
 (1.ltoreq.m.ltoreq.n) classes for each input vector while the latter
 assigns only one class for each input vector. In invention uses a modified
 version of the Kohonen's learning rule to train this network. The
 modification is according to the use of soft clustering. The training
 procedure is listed below.
 1. Randomly initialize the centroid vectors u.sub.i according to the sample
 mean and variance of the entire training data set; set the running
 averages z.sub.i to 1/n and the biases b.sub.i to c/z.sub.i, where the
 constant c is set to 0.0054, and set k=0.
 2. Randomly select a input vector from the training data set and increment
 k by 1.
 3. Compute the values -.parallel..nu.-u.sub.i.parallel.+b.sub.i for
 1.ltoreq.i.ltoreq.n and select the m classes with the smallest values as
 the output. Note that the symbol .parallel..parallel. denotes the
 Euclidean distance.
 4. Update the centroid vectors, the running averages and the biases of all
 the assigned classes computed in the previous step as follows:
EQU u.sub.i.sup.(new) =u.sub.i.sup.(old) +.mu.(v-u.sup.(old))
EQU z.sub.i.sup.(new) =z.sub.i.sup.(old).times.bc+(1-bc)

##EQU9##
 where .mu. is the learning rate and bc is the bias time constant with a
 positive value slightly less than 1. In the exemplary implementation, the
 learning rate is set to 0.01 and the bias time constant is set to 0.999.
 5. Return to step 2 when k is less than the maximum number of iterations,
 otherwise the training is finished.
 In the present invention of the adaptive display window width and center
 adjustment system, the total number of clusters (n) in the HNN is set to
 120 and the number of clusters (m) assigned to each input vector is set to
 4.
 RBF Networks
 The structure of the radial basis function (RBF) networks is shown in FIG.
 6. The RBF networks consist of M nodes and a bias b with each node
 containing a centroid vector x.sub.j, a weight W.sub.j, and a space
 constant .sigma..sub.j. Note that the space constant is set to the same
 value .sigma. in our system. The output value of an RBF network for an
 input vector v can be written as
 ##EQU10##
 The coefficients x.sub.j, W.sub.j and b for each RBF network are computed
 through a supervised training algorithm. (S. Chen, C. F. N. Cowan, and P.
 M. Grant, "Orthogonal least squares learning algorithm for radial basis
 function networks", IEEE Trans. Neural Networks, Vol. 2, No. 2, pp.
 302-309, 1991). The training data for each class is obtained after the
 soft clustering of the training data accomplished by the modified
 competitive layer neural networks. The RBF training is performed in an
 incremental fashion, i.e. the total number of nodes used in the RBF, M, is
 added one by one until the RBF networks achieve the error goal of fitting
 the training data. The centroid vector x.sub.j of each node is selected to
 be the available feature vector in the training data with the largest
 fitting error using the existing RBF network. Note that the feature vector
 is unavailable once it was chosen to be a centroid in the RBF training
 process. The weights W.sub.j and the bias b are computed by solving the
 following minimization problem
 ##EQU11##
 where (v.sub.i, d.sub.i) is the i-th feature vector and the corresponding
 normalized width/center value in the training data for this class, and
 .omega..sub.i is the weighting associated to the i-th data sample. The
 solution to this least square problem is equivalent to solve the following
 linear system
 ##EQU12##
 Since we always set the number of nodes M to be less than the total number
 of data samples for this cluster N, this is an over-constrained linear
 system and can be robustly solved by the singular value decomposition
 (SVD) method (See., Chen et al., 1991; and W. H. Press, S. A. Teukolsky,
 W. T. Vetterling and B. P. Flannery, Numerical Recipes in C. 2.sup.nd
 Edition, Cambridge University Press, 1992). The present invention requires
 the maximum number of nodes used in the RBF training to be less than the
 number of data samples N and also less than a fixed number, which is set
 to 40 in the exemplary implementation to provide good generalization
 power. The weighs .omega..sub.i are used to assign different weighting for
 different training samples that can be specified in the user interaction
 process. A larger weight is given for the image sequences that were
 selected in the user re-adjustment than those not selected to enforce the
 trained HNN to comply to the new user's window width/center adjustment.
 BLE Networks
 The bi-modal linear estimation (BLE) networks is primarily used to provide
 the two mean values in the mixture of two Gaussian distributions for the
 width or center in each cluster, thus supplying a consistency measure for
 the estimation from the corresponding RBF networks in the same cluster. As
 shown in FIGS. 7a and 7b, the width and center BLE network contains only
 two scaling coefficients, K.sub.w0 and K.sub.w1 and K.sub.c0 and K.sub.c1,
 respectively, for generating the two mean values. Note that the inputs to
 the BLE networks are the reference width and center values determined from
 the image histogram analysis. Similar to the training of the RBF networks,
 a supervised training procedure for the BLE networks is also emplyed. The
 training data for each cluster is obtained from the soft clustering of the
 entire training data set that is accomplished by the modified competitive
 layer networks. In each cluster, the ratios of the width/center values in
 the training data to the reference width/center values are divided into
 two groups with each group representing samples from a Gaussian
 distribution. Then we can simply compute the sample mean for each group to
 be the corresponding scaling coefficient. The division into two groups is
 through a thresholding process with the threshold empirically set to 1.0
 for both the width and center BLE networks and for all the clusters.
 Implementation Results
 In the exemplary implementation of the adaptive window width/center
 adjustment system of the present invention, a training data set containing
 a wide variety of 2436 MR images is used. These images were first manually
 grouped into sequences and then divided into eight categories namely,
 head, body, heart, spine, neck, periphery, angiography and miscellaneous
 categories. In each sequence, two representative frames are manually
 selected roughly from the beginning and the end of the sequence
 respectively. In the global mapping process, the smoothing splines model
 the global width/center transformation function. In addition to the
 boundary conditions at the width/center values of 0 and 4095, the nodes of
 the spline are non-uniformly chosen at the values of 125, 250, 500, 750,
 1000, 1500, 2000 and 3000. The distribution of these nodes is denser in
 the period of low width/center values and coarser in the period of high
 width/center values. This selection takes into consideration the higher
 sensitivity of the global width/center transformation for low width/center
 values than that for high values. For the sequence mapping, the order of
 the polynomial for modeling the baseline of the width/center settings in
 the sequence is set to 0 or 1 depending on the number of representative
 frames selected in the re-adjustment process.
 After the global mapping and sequence mapping processes, the new training
 data set adapted to the re-adjusted width/center values of some
 representative images is generated. The HNN is re-trained using this new
 training data set using previously described training procedures. In the
 training of the RBF networks, larger weights are assigned to the training
 samples in the sequences selected for re-adjustment to enforce the HNN
 training to comply to the user's adjustment. In the exemplary
 implementation, we assign 6.0 for the weights of the samples in the
 selected sequences and 1.0 for others. Other weights can be assigned
 without departing from the scope of this disclosure.
 In the exemplary implementation, 120 clusters are used in the HNN for the
 entire training data set with each cluster containing the RBF and BLE
 networks for width and center estimation. Each input vector to the HNN is
 assigned to 4 clusters and the width/center estimates from these 4
 clusters are integrated to provide the final HNN estimation. The total
 execution time for the width/center mapping process and the HNN
 re-training takes about 47.54 seconds on a SUN Ultra-SC workstation or
 276.53 seconds on a SUN SC-10 workstation. FIGS. 8a-8d depict a head MR
 image selected in the re-adjustment process and displayed with different
 width/center settings. FIG. 8a shows the original width/center setting in
 the training data set (w=1524, c=882) as made by a human expert. FIG. 8b
 shows the MR image with the newly re-adjusted width/center setting
 (w=1222, c=707). FIG. 8c shows the original HNN width/center estimate
 (w=1355, c=737), and FIG. 8d shows the MR image of the head with the newly
 re-trained HNN width/center estimate (w=1189, c=708). Thus, it can be seen
 that the re-trained HNN estimate of FIG. 8d is adapted to the re-adjusted
 width/center setting shown in FIG. 8b.
 Another example on a spine MR image is shown in FIG. 9, where FIG. 9a is a
 spine MR image displayed with the original width/center setting (w=718,
 c=289) by a human expert. FIG. 9b is the spine MR image with the newly
 re-adjusted width/center setting (w=574, c=231). FIG. 9c is the spine MR
 image of the original HNN width/center estimate (w=758, c=335), and FIG.
 9d is the spine MR image with the newly re-trained HNN width/center
 estimate (w=602, c=240).
 It should be understood that the present invention is not limited to the
 particular embodiment disclosed herein as the best mode contemplated for
 carrying out the present invention, but rather that the present invention
 is not limited to the specific embodiments described in this specification
 except as defined in the appended claims.