Abstract:
A method and apparatus for reducing noise in a three dimensional rectilinear parallelepiped data point array includes both erosion and dilation processes for each array point value. The erosion process includes the steps of determining gradients along all three axis which pass through a data point and modifying the point value as a function of the gradients to generate an updated point value. The dilation process includes the steps of using point values from the updated array, determining gradients along all three axis which pass through the point, and modifying the updated point value as a function of the gradients to generate a final and revised point value.

Description:
BACKGROUND OF THE INVENTION 
     The field of this invention is nuclear magnetic resonance imaging methods and systems. More particularly, the invention relates to a method and apparatus for reducing noise in a three dimensional data array generated using magnetic resonance imaging techniques. 
     Any nucleus which possesses a magnetic moment attempts to align itself with the direction of the magnetic field in which it is located. In doing so, however, the nucleus precesses around this direction at a characteristic angular frequency (Larmor frequency) which is dependent on the strength of the magnetic field and on the properties of the specific nuclear species (the magnetogyric constant γ of the nucleus). Nuclei which exhibit this phenomena are referred to herein as “spins”. 
     While many different tissue samples and various bodies may be examined using NMR imaging, in order to further simplify this explanation the invention is described in the context of an exemplary transaxial volume through a patient&#39;s body wherein the volume includes the patient&#39;s heart and the volume will be referred to as a region of interest. In addition, it will be assumed that an NMR imaging system includes a three dimensional imaging area having Cartesian coordinate x, y and z axes and that the patient is positioned within the imaging area with the patient&#39;s height (i.e. from head to feet) defining an axis along the z axis. 
     When the region of interest is subjected to a uniform magnetic field (polarizing field B 0 ), the individual magnetic moments of the nuclear spins in the region attempt to align with the polarizing field, but precess about the direction of the field in random order at their characteristic angular or Larmor frequencies, producing a net magnetic moment M z  in the direction of the polarizing field. 
     If the region of interest is subjected to a magnetic field (excitation field B 1 ) which is in the x-y plane and which is near the Larmor frequency, the net aligned moment M z  may be “tipped” into the x-y plane to produce a net transverse magnetic moment which is rotating or spinning in the xy plane at the Larmor frequency. 
     The NMR signal which is emitted by the excited spins after the excitation signal B 1  is terminated is a function of physical properties of the spin which generates the signal. These emitted NMR signals are digitized and processed to generate an NMR data set. 
     To determine the point of origin of an NMR signal, each NMR signal is encoded with spatial information, such as by the “spin-warp” technique, discussed by W. A. Edelstein et al. in “Spin Warp NMR Imaging and Applications to Human Whole-Body Imaging”,  Physics in Medicine and Biology,  Vol. 25, pp. 751-756 (1980) which is incorporated herein by reference. 
     According to the spin-warp scheme, spatial encoding is accomplished by employing three magnetic gradient fields (G x , G y , and G z ) which have the same direction as polarizing field B 0  and which have gradients along the x, y and z axes, respectively. By controlling the strength of these gradients during each NMR cycle, the spatial distribution of spin excitation can be controlled and the point of origin of the resulting NMR signals can be identified. 
     A useful acquisition technique is the slice or two dimensional technique wherein NMR data are acquired for a single transaxial slice of a region of interest at one time. The invention is described in the context of slice imaging wherein several slices are acquired consecutively and are “stacked” to form a three dimensional data set. 
     To determine the z-axis origin of a signal during slice data acquisition, signal generation is limited to a specific transaxial slice of the region of interest using gradient field G z . To this end, the Larmor frequency F of a spin can be expressed as: 
     
       
           F =( B   0   +B   z )γ  (1) 
       
     
     where B z  is essentially the strength of gradient G z  within a specific transaxial slice of the region of interest and is the magnetogyric constant of the nucleus of the material in which the field is generated. Because the gradient field strength varies along the z-axis, each z-axis slice has a different Larmor frequency F. When the excitation signal B 0  is provided at a specific excitation frequency, only spins within the “selected” z-axis slice which are at the excitation frequency are tipped. Therefore, when the excitation signal B 0  is turned off, only spins within the selected z-axis slice generate NMR signals. 
     To spatially encode NMR signals along the x axis, excitation signal B 0  is provided at a small range of frequencies. The x axis gradient G x  is small enough that all of the spins along the x axis have Larmor frequencies within the small range of excitation signal frequencies and therefore each of the spins along the x axis generates an NMR signal when the excitation signal is turned off, each x-axis signal having a unique and identifiable frequency. Hence, x-axis position can be determined by identifying the frequency of each NMR signal received during an acquisition. This type of encoding is commonly referred to as frequency encoding. 
     To encode y axis position within NMR signals, the y axis gradient G y  is employed to cause spins along the y axis to have different phases; therefore, resulting NMR signals from spins along the y axis have different phases which can be used to determine y axis position. Because y axis position is encoded using signal phase, this type of encoding is commonly referred to as phase encoding. 
     After data have been acquired for one region of interest slice, the acquisition process is repeated for adjacent region of interest slices until data have been acquired for every slice within the region of interest. After digitizing and processing, the slice data are combined to provide a three dimensional data point (TDDP) array. The TDDP array includes a plurality of data points distributed at regular parallelepiped positions in a three dimensional lattice within the region of interest, at least one value (Vxyz) being characteristic of a physical property of the region of interest associated with each respective one of the lattice positions. Each cubically adjacent set of eight such positions defines a cubic volume referred to hereinafter as a “voxel”, a physical property value being specified for each of the eight voxel vertices. 
     After a complete TDDP array has been acquired and stored, the array can be used to form an image of the region of interest using one of many well known reconstruction techniques. 
     For the purposes of this explanation, signals which are generated by spins and are characteristic of the property of the region of interest being detected will be referred to as “true” signals, signal components which are randomly generated within a region of interest will be referred to generally as “noise” and the combination of true signals and noise will be referred to as a “combined” signal. 
     While extreme measures are taken when designing an NMR system to minimize stray and random magnetic fields and signals within the region of interest during a data acquisition period, noise often occurs in two forms: first, as a background distortion exhibiting a low and relatively constant amplitude throughout a region of interest, and second, with appreciable amplitude caused by localized magnetic fields within the region of interest. The latter type of noise, being localized, will be referred to hereinafter as “localized noise”. 
     Unfortunately, extremely sensitive sensing coils required to detect low amplitude true signals also detect an appreciable amount of background noise from within the region of interest during an acquisition period. Therefore, after a data acquisition period, each TDDP array data point typically includes both a true signal component and a noise component (i.e each data point value constitutes a combined signal). In addition, some data points are dominated by a localized noise component. 
     While an image can be generated using combined signals, the noise components reduce image clarity and minimize diagnostic usefulness of the image. In addition, localized noise causes artifacts within a resulting image. For this reason, to the extent possible, noise must be eliminated from the TDDP array prior to generating an image therefrom. 
     Various filtering techniques have been devised for reducing image noise. These filtering techniques can generally be divided into two different types, thresholding and morphological filtering. According to an exemplary thresholding technique, each combined signal within the TDDP array is compared to a threshold value. The threshold value is selected such that, below the threshold value most signals are generally known to be dominated by a background noise component (i.e. the true signal component is relatively small). Where a combined signal value is less than the threshold value, the combined signal value is set equal to zero. Where a combined signal value is equal to or greater than the threshold value, the combined signal value is maintained in the TDDP array. 
     While thresholding eliminates isolated low amplitude noise (i.e. where the true signal component is relatively small compared to the noise component), such techniques fail to reduce noise within a combined signal where a true signal component is appreciable. In addition, thresholding techniques fail to eliminate localized noise where noise amplitude is relatively high. 
     Morphological filters may be categorized as either binary or gray level. Binary filters use an eroding and dilating protocol to reduce image noise. To this end, an exemplary binary filter first uses the thresholding technique to reduce background noise and generate a binary TDDP array. In the present context, binary indicates that any data point value above the threshold is set equal to a normalized one value while any data point value below the threshold value is set equal to zero. Next, with the binary array formed, an erosion process is performed on the array wherein structures within the array are identified, a structure being any one separate data point, or a set of two or more adjacent data points, each having a value of one. An exemplary structure may include a sphere which has a diameter of 100 points, each point within the sphere having a one value. To erode the array, data points which have one values and are associated with the outer boundaries of each structure are changed to zero values. In effect the “outer layer” of each structure within the array is “peeled” away. For example, after a signal erosion process, the spherical structure which initially had a diameter of 100 data points would have a diameter of 98 data points (i.e. the outer layer on both sides of the sphere is eliminated). In most embodiments several erosion steps are consecutively performed, thereby reducing the size of each structure within the array. 
     While most structures within the array are maintained throughout the erosion process, some structures are entirely eliminated. For example, small structures, such as a single data point having a one value, are eliminated during a first erosion process. During a second erosion process, a sphere initially having a four data point diameter would be eliminated, and so on. Such elimination is intended, as most such small structures are attributable to localized noise. 
     After the erosion process, the dilation process is performed on the eroded array. Dilation is the opposite of erosion and adds layers to each structure within an array instead of removing layers. For example, during dilation, where the spherical structure mentioned above includes a diameter of 96 data points after erosion, the sphere would have a diameter of 98 after a first dilation process, and the diameter would be 100 after a second dilation process, and so on. 
     After dilation the resulting binary array can be used to generate an image or, in the alternative, can be used as a mask to select sections of data from the initial TDDP array for generating an image. 
     In addition to eliminating background noise, the binary filter also eliminates free standing localized noise from the TDDP array and therefore is generally a better filtering option than simple thresholding. Unfortunately, like thresholding, binary filtering cannot eliminate noise components which are combined with true signals to form combined signals. 
     Gray level morphological filters reduce data point intensities to minimize noise. Thus, for each data point in a TDDP array, a gray level filter compares the intensity of the data point and all surrounding data points in the TDDP array (e.g. above, below, left, right, front and behind) and replaces the data point intensity with the minimum intensity level of adjacent points. The resulting data point array includes minimal background noise and minimal localized noise throughout the entire array. 
     While gray level filters are advantageous, they can cause reduction in anatomical edge annunciation as resulting images have “smeared” gray levels (i.e. the gray scale contrast is reduced). 
     The above described filtering techniques have been combined in advantageous ways to reap benefits of each of the separate techniques. While filtered images have proven good enough for most diagnostic purposes there is always a desire to have better imaging techniques wherein the effects of noise are further eliminated without reducing the effects of true signals. 
     SUMMARY OF THE INVENTION 
     An exemplary embodiment of the invention includes a method for reducing noise in a three dimensional rectilinear parallelepiped data point array, the three dimensions being first, second and third dimensions and each data point associated with a point value. The method constitutes an erosion process for each array data point, wherein the data point is a point of interest, and comprises determining first, second and third erosion gradients through the point of interest along the first, second and third dimensions, respectively, and modifying the point of interest value as a function of the erosion gradients, thereby generating an updated point of interest value. 
     The method also constitutes a dilation process comprising, for each updated point of interest value, determining first, second and third dilation gradients through the updated point of interest along the first, second and third dimensions, respectively, and modifying the updated point of interest value as a function of the dilation gradients, thereby generating a revised point of interest value. 
     By using gradients to erode and then dilate TDDP array data point values, both background and localized noise can essentially be eliminated from a data set without appreciably deteriorating edges. In any event, images resulting from use of the inventive filter have better and more accurate characteristics than images generated using other filters. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a block diagram of an NMR system employing the present invention; 
     FIG. 2 is a block diagram of the transceiver which forms part of the NMR system of FIG. 1; 
     FIG. 3 is a schematic illustrating a TDDP array point of interest and surrounding data points used to determine first, second and third gradients according to the invention; 
     FIG. 4 is a schematic diagram of an image processor of FIG. 1; and 
     FIG. 5 is a flow chart illustrating a method of operation according to the invention. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENT 
     A. Hardware 
     FIG. 1 illustrates the major components of an NMR system which incorporates the invention and is sold by General Electric Company under the trademark “SIGNA”. Operation of the system is controlled from an operator console  100  which includes a console processor  101  that scans a keyboard  102  and receives inputs from a human operator through a control panel  103  and a plasma display/touch screen  104 . Console processor  101  communicates through a communications link  116  with an applications interface module  117  in a separate computer system  107 . Through keyboard  102  and controls  103 , an operator controls production and display of images by an image processor  106  in computer system  107 , which is coupled to a video display  143  on console  100  through a video cable  105 . 
     Computer system  107  includes modules which communicate with each other through a backplane  123 . In addition to application interface  117  and image processor  106 , these include a CPU  108  that controls the backplane, and an SCSI interface  109  that couples computer system  107  through a bus  110  to a set of peripheral devices, including disk storage  111  and tape drive  112 . Computer system  107  also includes a memory  113 , known in the art as a frame buffer, for storing image data arrays, and a serial interface  114  that links computer system  107  through a high speed serial link  115  to a system interface module  120  located in a system control cabinet  122 . 
     System control  122  includes a series of modules coupled together by a common backplane  118 . Backplane  118  is comprised of bus structures, including a bus structure controlled by a CPU module  119 . Serial interface module  120  connects backplane  118  to high speed serial link  115 , and pulse generator module  121  connects backplane  118  to operator console  100  through a serial link  125 . It is through serial link  125  that system control  122  receives commands from the operator designating which scan sequence is to be performed. 
     Pulse generator module  121  operates the system components to carry out the desired scan sequence, producing data designating the timing, strength and shape of the RF pulses to be produced, and the timing of and length of a data acquisition window. Pulse generator module  121  also connects through a serial link  126  to a set of gradient amplifiers  127 , and conveys data thereto which indicate timing and shape of the gradient pulses to be produced during the scan. Pulse generator module  121  also receives patient data through a serial link  128  from a physiological acquisition controller  129 . A physiological acquisition controller  129  can receive a signal from various sensors attached to the patient. For example, controller  129  may receive ECG (electrocardiogram) signals from electrodes or respiratory signals from a bellows and produce pulses for pulse generator module  121  that synchronizes the scan with the patient&#39;s cardiac cycle or respiratory cycle. Pulse generator module  121  also connects through a serial link to a scan room interface circuit  133  which receives signals at inputs  135  from various sensors associated with the position and condition of the patient and the magnet system. Additionally, a patient positioning system  134  receives commands through scan room interface circuit  133  for moving the patient cradle and transporting the patient to the desired position for the scan. 
     The gradient waveforms produced by pulse generator module  121  are applied to a gradient amplifier system  127  comprised of G x , G y  and G z  amplifiers  136 ,  137  and  138 , respectively. Each amplifier  136 ,  137  and  138  is utilized to excite a corresponding gradient coil in an assembly generally designated  139 . Gradient coil assembly  139  forms part of a magnet assembly  141  which includes a polarizing magnet  140  that produces either a 0.5 or a 1.5 Tesla polarizing field extending horizontally through a bore  142 . Gradient coils  139  encircle bore  142  and, when energized, generate magnetic fields in the same direction as the main polarizing magnetic field, but with gradients G x , G y  and G z  directed in the orthogonal x-, y- and z-axis directions of a Cartesian coordinate system. That is, if the magnetic field generated by the main magnet  140  is directed in the z direction and is termed B 0 , and the total magnetic field in the z direction is referred to as B z , then G x =∂B z /∂x, G y =∂B z /∂y and G z =∂B z /∂z, and the magnetic field at any point (x,y,z) in the bore of magnet assembly  141  is given by B(x,y,z)=B 0 +G x x+G y y+G z z. The gradient magnetic fields encode spatial information into the NMR signals emanating from the patient being scanned. 
     Located within bore  142  is a circular cylindrical whole-body RF coil  152  that produces a circularly polarized RF field in response to RF pulses provided by a transceiver module  150  in system control cabinet  122 . These pulses are amplified by an RF power amplifier  151  and coupled to RF coil  152  by a transmit/receive switch  154 . Waveforms and control signals are provided by pulse generator module  121  and utilized by transceiver module  150  for RF carrier modulation and mode control. The resulting NMR signals radiated by the excited nuclei in the patient may be sensed by the same RF coil  152  and coupled through transmit/receive switch  154  to a preamplifier  153 . The amplified NMR signals are demodulated, filtered, and digitized in the receiver section of transceiver  150 . Transmit/receive switch  154  is controlled by a signal from pulse generator module  121  to couple RF amplifier  151  to coil  152  during the transmit mode and to couple coil  152  to preamplifier  153  during the receive mode. Transmit/receive switch  154  also enables a separate RF coil (for example, a head coil or surface coil) to be used in either the transmit or receive mode. 
     In addition to supporting polarizing magnet  140 , gradient coils  139  and RF coil  152 , main magnet assembly  141  also supports a set of shim coils  156  associated with main magnet  140  to correct inhomogeneities in the polarizing magnet field. A main power supply  157  is utilized to bring the polarizing field produced by main magnet  140  to the proper operating strength and is then removed. 
     The NMR signals picked up by RF coil  152  are digitized by transceiver module  150  and transferred to a memory module  160  of system control  122 . When the scan is completed and an entire array of data has been acquired in memory modules  160 , an array processor  161  operates to Fourier transform the data into an array of image data. The image data are conveyed through serial link  115  to computer system  107  for storage in disk memory  111 . In response to commands received from operator console  100 , the image data may be archived on tape drive  112 , or may be further processed by image processor  106  and conveyed to operator console  100  for presentation on video display  143 . 
     Referring to FIGS. 1 and 2, transceiver  150  includes components that produce RF excitation field B 1  through RF power amplifier  151  at a coil  152 A and components which receive the resulting NMR signal induced in a coil  152 B. Coils  152 A and  152 B may be separate, as shown in FIG. 2, or they may be a single, wholebody coil, as shown in FIG.  1 . The base, or carrier, frequency of the RF excitation field is produced under control of a frequency synthesizer  200  (FIG. 2) which receives a set of digital signals (CF) through backplane  118  from CPU module  119  and pulse generator module  121 . These digital signals indicate the frequency and phase of the RF carrier signal which is produced at an output  201  (FIG.  2 ). The commanded RF carrier is applied to a modulator and up converter  202  (FIG. 2) where it is amplitude modulated in response to a signal R(t) also received through backplane  118  from pulse generator module  121 . Signal R(t) defines the envelope, and therefore the bandwidth, of the RF excitation pulse to be produced in module  121  by sequentially reading out a series of stored digital values that represent the desired envelope. These stored digital values may be changed from operator console  100  to enable any desired RF pulse envelope to be produced. Modulator and up converter  202  produces an RF pulse at the desired Larmor frequency at an output  205 . 
     The magnitude of the RF excitation pulse from output  205  of modulator and up converter  202  is attenuated by an exciter attenuator circuit  206  (FIG. 2) which receives a digital command from backplane  118 . The attenuated RF excitation pulses are applied to power amplifier  151  that drives RF coil  152 A. For a more detailed description of this portion of the transceiver  122 , reference is made to commonly assigned Stormont et al. U.S. Pat. No. 4,952,877, RF Synthesizer or an NMR Instrument, issued Aug. 28, 1990, which is incorporated herein by reference. 
     The NMR signal produced by the patient is picked up by receiver coil  152 B (FIG. 2) and applied through preamplifier  153  to the input of a receiver attenuator  207  (FIG.  2 ). Receiver attenuator  207  further amplifies the NMR signal which is attenuated by an amount determined by a digital attenuation signal from backplane  118 . Receiver attenuator  207  is turned on and off by a signal from pulse generator module  121  so as not to be overloaded during RF excitation. 
     The received NMR signal is at or around the Larmor frequency, which, in a preferred embodiment, is about 63.86 MHz for 1.5 Tesla and 21.28 MHz for 0.5 Tesla. This high frequency signal is down converted in a two step process by a down converter  208  (FIG. 2) which first mixes the NMR signal from receiver attenuator  207  with the carrier signal from synthesizer  200  and then mixes the resulting difference signal with the 2.5 MHz reference signal on input  204 . The resulting down converted NMR signal has a maximum bandwidth of 125 kHz and is centered at a frequency of 187.5 kHz. The down converted NMR signal is applied to the input of an analog-to-digital (A/D) converter  209  which samples and digitizes the analog signal at a rate of 250 kHz. The output signal of A/D converter  209  is applied to a digital detector and signal processor  210  which produces 16-bit in-phase (I) values and 16-bit quadrature (Q) values corresponding to the received digital signal. The resulting stream of digitized I and Q values of the received NMR signal is supplied through backplane  118  to memory module  160  where these values are employed to reconstruct an image. 
     To preserve the phase information contained in the received NMR signal, both modulator and up converter  202  in the exciter section and down converter  208  in the receiver section are operated with common signals. More particularly, the carrier signal at the output of frequency synthesizer  200  and the 2.5 MHz reference signal at the output of reference frequency generator  203  are employed in both frequency conversion processes. Phase consistency is thus maintained and phase changes in the detected NMR signal accurately indicate phase changes produced by the excited spins. The 2.5 MHz reference signal as well as 5, 10 and 60 MHz reference signals are produced by reference frequency generator  203  from a common 20 MHz master clock signal. The latter three reference signals are employed by frequency synthesizer  200  to produce the carrier signal. For a more detailed description of the receiver, reference is made to commonly assigned Stormont et al. U.S. Pat. No. 4,992,736, “Radio Frequency Receiver for a NMR Instrument”, issued Feb. 12, 1991, which is incorporated herein by reference. 
     It will be assumed that a full set of NMR imaging data of a region of interest has been acquired and processed to generate a three dimensional data point (TDDP) array indicating at least one property of the region of interest. The data point array is stored in memory  113 . For example, the physical properties of the TDDP array may be spin-spin or lattice-spin relaxation times, as well known in the art. 
     A TDDP array includes adjacent cubic voxel elements, each element having eight vertices. Associated with each vertex is one data value which represents the physical property at the corresponding spatial position within the region of interest. The spatial positions are located in regular patterns defining regularly spaced grid locations within the region of interest. The grid locations in turn define a plurality of adjacent voxels within the region. For purposes of this explanation it will be assumed that the grid positions are aligned with the x, y and z axes of bore  142  where the z axis is along the bore length, the x axis is horizontal and the y axis is vertical. 
     Each array data point is surrounded by six other data points. For example, referring to FIG. 3, a data point P separates east and west points E and W, respectively, along an X axis (i.e. an east-west axis), separates north and south points N and S, respectively, along a Y axis (i.e. a north-south axis) and separates forward and rearward points, F and R, respectively, along a z axis (i.e. a fore-rear axis). For purposes of this explanation point P will be referred to as a point of interest, north and south points N, S will be referred to as a first point pair, east and west points E, W will be referred to as a second point pair, forward and rearward points F, R will be referred to as a third point pair, each of the north, east and forward points N, E and F, respectively, will be referred to as the first point value p 1  in an associated pair and each of the values of the south, west and rearward points S, W and R, respectively, will be referred to as the second point value p 2  in an associated pair. In addition, a first point set will include the first point pair (N, S) and the point of interest P, a second point set will include the second point pair (E, W) and the point of interest P, and a third point set will include the third point pair (F, R) and the point of interest P. 
     Memory  113  of FIG. 1 includes, as shown in FIG. 4, two buffers  10  and  20 . An initial TDDP array is stored in buffer  10  and a modified TDDP array according to the present invention is stored in buffer  20 . The modified arrays are described in more detail below. 
     In one embodiment of the invention, image processor  106  of FIG. 1 includes a data point comparator  256 , a gradient determiner  258  and a point value update/revise determiner  260 , as shown in FIG.  4 . 
     Comparator  256  is linked to memory  113  for accessing data stored in buffer  10 . Comparator  256  is equipped to compare three separate data point values to determine the relationship of one of the three values to the other two. Specifically, given a specific TDDP array, then for each data point set in the array wherein each data point is a point of interest, comparator  256  receives the first, second and third data point values in the set. 
     For each data point set, comparator  256  compares the value of point P to the values of the other points in the set to determine if the point P value is greater than, less than, or between both of the other values in the set and, if between the values in the set, to determine which of the other values is greater than the point P value. For example, with respect to the first point set (i.e. N-P-S), comparator  256  determines the relationship between point P and the first point value p 1  (i.e. point N value) and the second point value p 2  (i.e. point S value). 
     Comparator  256  provides a relationship signal to the gradient determiner for each point set indicating the relationship between the points in the set. Thus, for each point of interest P (i.e. point in TDDP array), comparator  256  provides three relationship signals to determiner  258 . For example, referring to FIG. 3, three relationship signals corresponding to point P may include a first signal indicating that the point P value is greater than the values of points N and S, a second signal indicating that the point P value is less than the point W value and greater than the point E value and a third signal indicating that the point P value is less than each of the values corresponding to points F and R. 
     Determiner  258  determines a gradient for each relationship signal received. The equations used to determine the gradients include two equation sets, one set used during an erosion process and the other set used during a dilation process. The erosion equation set includes the following rules for generating an erosion gradient Gn where n is NS, EW or FR corresponding to the axes in FIG.  3  and hence to the first, second and third sets (i.e. N-P-S; W-P-E and F-P-R), respectively, p 1  is the first point (i.e. N, E or F) in each point set and p 2  (i.e. S, W or R) is the last point in each point set: 
     P&gt;p 1  and p 2 , then: 
     
       
           G   n ={square root over (( p   1 − P ) 2 +( p   2 − P ) 2 )}  (2) 
       
     
     P&lt;p 1  and p 2 , then: 
       G   n =0  (3) 
     p 1 &lt;P&lt;p 2 , then: 
     
       
           G   n   =|P−p   1 |  (4) 
       
     
     p 2 &lt;P&lt;p 1 , then: 
     
       
           G   n   =|P−p   2 |  (5) 
       
     
     The dilation equation set includes the following rules for generating a dilation gradient G n  using the same nomenclature as indicated above: 
     P&gt;p 1  and p 2 , then: 
     
       
           G   n =0  (6) 
       
     
     P&lt;p 1  and p 2 , then: 
     
       
           G   n ={square root over (( p   2 = P ) 2 +( p   1 − P ) 2 )}  (7) 
       
     
     p 2 &lt;P&lt;p 1   
     
       
           G   n   =|P−p   1 |  (8) 
       
     
     p 1 &lt;P&lt;p 2   
     
       
           G   n   =|P−p   2 |  (9) 
       
     
     After generating the three gradients G NS , G EW  and G FR , one for each relationship signal, determiner  258  combines the gradients G NS , G EW  and G FR  by solving the following equation: 
       G={square root over (G NS   2   +G   EW   2   +G   FR   2 )}   (10) 
     Combined gradient G is provided to determiner  260 . 
     Determiner  260  receives third gradient G for a point of interest and modifies the point of interest value as a function of the gradient. Thus, determiner  260  generates a modified point of interest value P′ by subtracting or adding a selected fraction of gradient G from the initial point of interest value, depending on whether the present process is an erosion process or a dilation process. In an exemplary embodiment of the invention the selected fraction of gradient G is one third. Thus, to determine modified point of interest values P′, determiner  260  solves the following equation for erosion: 
     
       
           P′=P−G/ 3  (11) 
       
     
     and for dilation: 
     
       
           P′=P−G/ 3  (12) 
       
     
     The resulting point of interest value P′ is either an eroded value or a dilated value, depending on the rule set (i.e. Equations 2 through 5 or Equations 6 through 9) applied by determiner  258 . 
     According to an exemplary embodiment of the invention, beginning with an initial TDDP array stored in buffer  10 , the erosion equation set (i.e. Equations 2 through 5) is applied to the TDDP array once and the resulting eroded TDDP array is stored in buffer  20 . After a complete eroded array is stored in buffer  20 , the eroded array is moved to buffer  10  and is effectively written over the initial TDDP array. The erosion process is then repeated N times (where N is an integer), to further erode the TDDP array data point values. At the end of the final erosion process the final TDDP array in buffer  20  is moved buffer  10 . The final erosion array is referred to herein as an “updated” array and includes updated point values. 
     After the updated array has been generated and stored, the dilation equation set (i.e. Equations 6 through 9) is applied to the updated TDDP array once and the resulting dilated TDDP array is stored in buffer  20 . After a dilated array is completely formed in buffer  20 , the dilated array is moved into buffer  10  The dilation equation set is then applied N times, each time to the array in buffer  10 , providing a new dilated array in buffer  20  which is then moved to buffer  10  prior to the next application of the dilation set. After the dilation set has been applied N times, the final dilated array is a revised array and includes revised array point values. An example of how this inventive system operates is instructive. 
     B. Exemplary Operation 
     Referring to FIG. 3, an exemplary inventive process will be described in the context of point of interest P and surrounding point pairs N and S, E and W and F and R which are part of an initial TDDP array. Each point P, N, S, E, W, F and R has a characteristic intensity value. For the purposes of this explanation it will be assumed that the characteristic values are: P=10, N=8, S=8, E=12, W=13, F=12 and R=7. 
     An exemplary inventive method of operation is illustrated in FIG.  5 . Referring to FIGS. 3,  4  and  5 , at process step  270 , comparator  256  receives point values for each point P, N, S, E, W, F and R. At step  272 , comparator  256  groups the point values into three point value sets including a first set N, P, S, a second set E, P, W and a third set F, P, R. In each set, the values corresponding to points N, E and F are considered first point values p 1  and the values corresponding to points S, W and R values are considered second point values p 2 . 
     At step  274 , comparator  256  compares intra-set point values to determine the relationship between the point of interest P value and values p 1  and p 2 . In the present example, for the first point set (i.e. N, P, S) where p 1  is 8 (i.e. N is 8) and p 2  is 8 (i.e. S is 8), comparator  256  determines that the point P value (i.e. 10) is greater than values p 1  and p 2  and generates a first relationship signal indicating so. 
     For the second point set (i.e. E, P, W), where p 1  is 12 (i.e. E is 12) and p 2  is 13 (i.e. W is 13), comparator  256  generates a second relationship signal indicating that the point P value is less than values p 1  and p 2 . Similarly, for the third point set (i.e. F, P, R) where p 1  is 12 (i.e. F is 12) and p 2  is 7 (i.e. R is 7), comparator  256  generates a third relationship signal indicating that the point P value is less than value p 1  and greater than value p 2 . Thus, comparator  256  provides three relationship values to determiner  258 , one for each point set. 
     At step  276 , determiner  258  receives the first, second and third relationship rules and also receives the point values corresponding to points P, N, S, E, W, F and R and applies the erosion rule set (i.e. Equations 2 through 5) once for each relationship signal to generate first, second and third erosion gradients G NS , G EW  and G FR , respectively. 
     With respect to the first relationship signal, because the point P value is greater than p 1  and p 2 , Equation 2 is applied to yield a first erosion gradient G NS  of  {square root over (8)} (i.e. by inserting p1= 8, p 2 =8 and p=10 into Equation 2). Similarly, for the second relationship signal, because the P value is less than p 1  and p 2 , Equation 3 is applied and gradient G EW  is 0. For the third relationship signal, because the P value is less than p 1  and greater than p 2  Equation 5 is applied and the third erosion gradient G FR  is 3 (i.e. by inserting p 2 =7, P=10 into Equation 5). 
     At step  278 , determiner  258  solves Equation 10 to generate combined gradient G. In the present example gradient G is 4.1231 (i.e. {square root over (8+0 2 +3 2 )}=4.1231). Gradient G is provided to determiner  260 . 
     Next, at step  280 , determiner  260  solves Equation 11 to determine a modified value for point P 1 . In the present example, the value for point P 1  is 8.6256 (i.e. P-G/3=10−4.1231/3=8.6256). The P 1  point value is stored in buffer  20  in a location corresponding to the position of point P in the initial TDDP array. 
     The above process is repeated for each point in the initial TDDP array using point values from the initial TDDP array, thereby generating a modified value in buffer  20  for each point in the initial TDDP array of buffer  20  After a complete modified/eroded TDDP array is amassed in buffer  20 , the array is moved into buffer  10 . 
     While many more subsequent erosion processes may be performed on the array in buffer  10 , to simplify this explanation it is assumed that only one more erosion process is performed and that thereafter the values of points P, N, S, E, W, F and R are 7, 6, 5, 11, 10, 9 and 5. 
     Next, because two erosion processes were performed on the initial TDDP array, two dilation processes are performed on the updated TDDP array in buffer  10 . Thus, with reference to FIGS. 4 and 5, comparator  256  receives values of points P, N, S, E, W, F and R at step  270  and generates three relationship values (steps  272  and  274 ) corresponding to the three point sets (i.e. N-P-S; E-P-W and F-P-R). Determiner  258  applies the dilation equations (i.e. Equations 6-9) to generate first, second and third dilation gradients G NS , G EW  and G FR  (step  276 ) and then solves Equation 10 to generate a combined gradient G (step  278 ) which is provided to determiner  260 . At step  280 , determiner  260  solves Equation 12, generating a modified point of interest value P′ which is stored in buffer  20  at block  282 . 
     After a complete dilated array has been stored in buffer  20 , the dilated array is moved to buffer  10  and dilation is repeated. After completion of the second dilation process the array in buffer  20  is a filtered, final and revised array which can be used for image processing. 
     The invention contemplates modifications to the exemplary embodiments provided above. For example, the specific fraction (i.e. ⅓) of the combined gradient in Equations 11 and 12 may be altered (e.g. may be ¼ or ⅕). In addition, slight variations in the equation sets are also contemplated. 
     While only certain preferred features of the invention have been illustrated and described, many modifications and changes will occur to those skilled in the art. It is, therefore, to be understood that the appended claims are intended to cover all such modifications and changes as fall within the true spirit of the invention.