by way of overview , applicants have recognized that the lack of robustness in prior template matching techniques stems from the use of only standard operations (*, +, or -) in the relationships between pair values of f ( x + y ) and g ( y ) per kernel or image position x . to that end , the present invention provides a user definable function s ( a , b ) to define arbitrarily complex relationships between f and g values , where operand a equals the value of f ( x + y ) and operand b equals the value of g ( y ). function s is referred to as the scoring function of the present invention . in turn , the present invention defines a generalized form ( equation ) of template matching hereinafter called &# 34 ; shape matching &# 34 ;, sm ( x ), in terms of the arbitrarily complex function s as follows : this equation states that the operator o processes the set of values produced by the 2 - d function s as y explores ros ( g ). it is noted : however , replacing prior art standard operations ( i . e . *,+, or -) on a and b with the present invention scoring function s ( a , b ) allows for the definition of arbitrarily complex relationships between values of f ( x + y ) and g ( y ). the power of this approach is discussed next in a general application of the present invention illustrated in fig2 through 3b . following that discussion is a specific application of the present invention described with reference to fig4 through 5c . referring to fig2 a subject input image is generally shown at 15 . the image input is two - dimensional and lies in the x1 - x2 plane illustrated in fig2 . for each point or position in the image 15 , there is an associated value defined by f ( x ) and indicated along an axis orthogonal to the xl and x2 axes . illustrating the input image f 15 in this manner allows for various cases of image input signals from video signals to radar signals , where the values of f ( x ) are temperature measurements , linear dimension measurements , mass measurements and the like . that is , this approach allows for n - dimensional image input signals . a template g 19 is applied to the input image 15 one image point x at a time . in particular , the template g 19 defines a region in the x1 &# 39 ;- x2 &# 39 ; coordinate system which is designated ros ( g ), i . e . the region of support of g . the region is formed of a reference point referred to as the template origin 22 and a plurality of points y spaced from the template origin 22 . for each point in the region of support of the template g 19 , there is a value defined by g ( y ) and indicated along an axis orthogonal to the x1 &# 39 ; and x2 &# 39 ; axes . operation of the template g 19 on an input image 15 is then as follows and outlined in fig3 b . for a given point x in the input image 15 , the template g 19 is positioned such that the template origin 22 corresponds with the position of the subject point x in the x1 - x2 plane . this step is indicated at 47 in fig3 b . for each point y in the region of support of template g 19 , the values of f ( x + y ) and g ( y ) are obtained . a variable &# 34 ; a &# 34 ; is then set equal to the obtained value of f ( x + y ), and variable &# 34 ; b &# 34 ; is set equal to the obtained value of g ( y ) as shown at 49 in fig3 b . variables a and b are then used as operands in the scoring function s ( a , b ). that is , a call to the scoring function s 21 with the assigned values of a and b is made and produces a scoring function value . this is illustrated in fig2 where the input variables a and b are indicated along respective axes a and b of the scoring function s 21 and the resulting function value is indicated along an axis perpendicular to the a and b axes . this resulting s function value is stored in a buffer 31 ( fig3 a ) and the foregoing calculations of f ( x + y ), g ( y ) and s ( a , b ) where a = f ( x + x ) and b = g ( y ) are repeated for each point y in the region of support of the template g 19 . as a result , for each yε ros ( g ) there is a resulting scoring function value held in the buffer 31 . the multiplicity of values held in the buffer 31 are then operated on by an operation o such as a mathematical average , the maximum , or the minimum , or the like as shown at 51 in fig3 b . the outcome of the operation o provides the value of a output image point x o corresponding to the given input image point x . the template 19 is similarly applied to each point x in the input image 15 to produce , through scoring function s and ultimately operation o , values for corresponding points x o in the output image 17 . to that end template g , scoring function s and operation 0 define output image 17 from a subject input image 15 . from the output image 17 , various patterns and shapes are presented as recognized or matched in the input image 15 with respect to the template g . fig3 a and 3b provide a block diagram and flow chart of computer software and / or hardware implementation of the present invention . fig3 b is discussed above and fig3 a is discussed next . in particular , fig3 a schematically diagrams an embodiment of the present invention as held in memory of a digital processor 45 of a computer system . the invention embodiment includes a working memory area 39 for receiving and holding an image f from an image source . another memory area 41 holds a predetermined template g . template g is applied to the image f held in the working memory 39 . this in turn generates output values g ( y ) from the template memory 41 and values f ( x + y ) from the working memory 39 . the two output values are used as inputs to the scoring function held in a register 37 or similar computational memory area ( e . g . module , routine or procedure ) of the digital processor 45 . the output of the s function register 37 is held in a buffer 31 . under the control of counting circuit 33 , buffer 31 stores the outputs of the s function register 37 for each y in the region of support of template g , for a given x placement of template g . after a last point y in the region of support of template g , the counting circuit 33 applies the values stored in buffer 31 to the o operation module 35 . output of o operation module 35 is then used to define the point x o in the output image 17 held in memory area 43 and corresponding to the subject point x in the input image held in working memory 39 . as formed by the foregoing steps , the output image is held in the memory area 43 in a manner which is accessible by the digital processor 45 for display on a display unit or similar output means . in a preferred embodiment , fuzzy set theory is incorporated with the present invention shape matching described for general application in fig2 through 3b . by way of background , in classical set theory , membership of an object in a set is denoted either by a 0 or 1 . in practice , however set membership is not a binary , either / or condition . to extend the functionality of set theory l . a . zadeh in &# 34 ; fuzzy sets &# 34 ; information and control no . 3 , vol . 8 , june 1965 , pages 338 - 353 , introduced the idea of representing set membership as a real number in the range [ 0 , 1 ], permitting varying degrees of membership reflecting uncertainty or contradiction . fuzzy set membership is calculated by a membership function f a ( x ) returning a value in the range [ 0 , 1 ] for a given object x , and representing the &# 34 ; a - ness &# 34 ; of object x . the use of fuzzy set theory has exploded in the last few years , being used extensively , for example , in computer vision , control processes , and artificial intelligence . in the present invention , a fuzzy template kernel g ( described later ) is constructed to encode the shape of an object to be sought in image f . in this technique , the scoring function s is implemented as a discrete array of indexed scoring functions , each of which , given a value of f ( x + y ), returns a match score . as later discussed , individual slices of s for a particular index m ( m being a point along the b axis in fig2 ) are denoted by s m ( a ) as an alternative way of expressing s ( a , m ). the kernel g can then be thought of as a set of labels ( or values of m ) that specify particular indexed scoring functions appropriate for different locations on the object . in the preferred embodiment , the o operation is the average over points yεros ( g ) and the final output ( defining an output image ) is defined according to the following two equations . first ## equ2 ## where n is the number of pixels in the ros ( g ) and o ≡ ## equ3 ## denotes mathematical average over points y . typically , the values returned are at this point approximately in the range [ 0 , 1 ]. however , for several practical reasons , the values returned by each s m are not restricted to the range [ 0 , 1 ]. consequently , the value of m ( x ) cannot be guaranteed to be in the range [ 0 , 1 ] and needs to be clipped : ## equ4 ## the final output is an image whose values are each a fuzzy membership score representing the degree of belief that the shape encoded in the fuzzy template g is found at each input image location x . given the possibility that the shape represented by a template may be scaled or rotated in the image , the fuzzy membership score may need to be computed with copies of the template that have been appropriately scaled or rotated . equation 6 handles only the case of scale and rotation invariance . situations where the shape to be searched in an input image is unconstrained with regard to scaling requires the construction of multiple templates from which a most appropriate copy is selected for probing a particular location x , depending on the distance to that location . similarly , situations where the orientation is unconstrained requires the use of multiple templates , each representing a different orientation . in this case , the membership value assigned to a location in the output image is the maximum membership value across all orientations tested . the following example illustrates the construction and use of fuzzy template correlation in automatic recognition of targets in downlooking laser radar range and intensity images . the scoring functions for the range image use height above ground as the independent variable . a simple template 60 for an elongated object ( a crude model of a semi - truck ) with expected height of 3 . 0 m is constructed as follows and shown in fig4 . first , the template function g is constructed as an array of indices ( fig4 ), where 1 &# 39 ; s indicate the top of the object , 2 &# 39 ; s indicate locations where ground values are expected , and n indicates a location of uncertainty where no scoring function should be evaluated ( i . e ., not in the region of support ). then , consider fig5 a as the indexed scoring function s 1 ( a ), i . e ., s ( a , 1 ) of fig2 for the surface expected to be 3 . 0 m above ground . image height values in the neighborhood of 3 . 0 m return a maximum score of 1 . 0 . the width of the maximal scoring interval can be adjusted to adapt to such conditions as sensor accuracy or the variability of surface height found in various instances of the target class . for height values from 2 . 5 down to 1 . 5 m , the scoring function returns progressively lower values , reflecting the decreasing confidence that the image height matches the expected surface height . below 1 . 5 m , the function s 1 returns negative values ( the need for negative values is explained later ). a similar drop off is evident with heights above 3 . 5 m . note however that the minimum returned value for heights above the expected surface height is 0 . 5 , a completely ambiguous score reflecting the fact that surfaces with heights above 3 . 0 m may be occluding the object . consequently , a sufficiently large surface that is 5 . 0 m above ground will elicit a target membership score of 0 . 5 , reflecting the possibility that the target might be totally concealed underneath . fig5 b shows the indexed scoring function s 2 ( a ), i . e ., s ( a , 2 ) of fig2 which encodes the scores for ground values surrounding the target ( in practice , one treats the ground surface in the immediate vicinity of an object as a part of the object ). maximal scores are returned for values within 0 . 25 m of ground , intermediate scores out to 0 . 5 m and an ambiguous score of 0 . 5 for heights above 0 . 5 m ( again , accommodating possibly occluding surfaces ). the reason the present invention permits negative numbers to be returned from the height distribution ( scoring ) function as shown in fig5 a is related to the practice of including neighboring ground as part of the target in the fuzzy template . preferably , the situation that generates a fuzzy membership value of 0 . 0 is a patch of bare ground ( by definition , ground height = 0 ). however as is evident in fig5 b , locations in the template where ground is expected return a value of 1 . 0 . looking again at fig4 consider what would happen if that template were superimposed on a uniform area of bare ground . all template locations with index 0 would return a score of 1 . 0 . consequently , in order for bare ground to result in a score of 0 . 0 , s 1 ( a ) must return sufficiently negative scores for an input height = 0 to balance the positive scores contributed by s o ( a ). one further example of an indexed scoring function illustrates how object articulation or multiple object configurations can be handled . consider a tank with an elongated turret . assume that the hull height is 1 . 5 m and the turret height is 3 . 5 m . some locations on the hull near the turret may or may not be occluded depending on the turret azimuth . fig5 c contains a bimodal height distribution for such a location near the turret : one maximum scoring range corresponds to the height of the turret , the other maximum scoring range corresponds to the height of the hull . in particular , fig5 c shows a scoring function for a location of an articulated object & amp ; with two possible surfaces at 1 . 5 m and 3 . 0 m above ground . although range information is generally necessary for purposes of scaling , scoring functions can accommodate sensory modalities other than height as long as reasonably accurate range information is available . for example , thermal distribution functions may be used as scoring functions to process passive infrared images . according to the foregoing , in situations where the effects of scaling or rotation can be minimized and the number of objects to be searched for is small , the present invention ( functional shape matching in general and fuzzy template correlation in particular ) is already computationally practical . the fuzzy template correlation embodiment of the present invention works best in situations where the objects to be modeled are either rigid or are articulated with rigid parts having known pivot points . fuzzy template correlation excels in its ability to perform shape matching in images containing significant amounts of clutter and / or occlusion ( i . e . natural scenes ) and for objects that have an uncertain or variable image signature . the following is an incomplete list of possible commercial ( non - military ) applications for fuzzy templates of the present invention : 1 . low level vision tools : traditional shape matching techniques are currently used in image processing for such things as edge detection , image segmentation , and feature extraction . a likely possibility is that wherever these techniques are already in use , fuzzy templates have the potential of doing it better . while the invention has been particularly shown and described with reference to a preferred embodiment thereof , it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims . for example multiple templates g may be employed for processing multiple measurements ( i . e . height , temperature , weight , etc .) at the same time through data fusion . further two templates g may be employed for articulating subjects in that case , a first ( dominant ) template is employed to recognize a main portion of the input image . from the main portion a pivot point is determined . the second template is then employed to recognize / detect the articulating portion of the subject out of image portions within the pivoting range of the determined pivot point . functions g and s could be modified as a function of the location x being probed . the modification can be specified a priori by specifying g and s as the 2 - dimensional function g ( x , y ) and the 3 - dimensional function s ( x , a , b ), respectively ( this processing strategy is usually termed &# 34 ; space - variant &# 34 ;). the modification can also be determined dynamically by adjusting g and s as a function of the values of the image f in some neighborhood of x ( this processing strategy is usually termed &# 34 ; adaptive &# 34 ;). more generally , the functions g and s could be modified arbitrarily as each location x in f is probed .