Ex Parte TAKEO et al - Page 10




          Appeal No. 1999-2069                                                        
          Application 08/397,639                                                      

          line 29).  Although Smilansky discusses rigid transformations               
          (e.g., col. 11, lines 42-43), which involve rotation and                    
          translation, but not scaling, equation 1b shows the use of                  
          scaling in the general case, where S x and Sy are scaling factors           
          (and where " would normally be B/2 for no angular deviation of              
          the sensor).  Thus, Smilansky discloses affine transformations              
          involving rotation, translation, and scaling (an enlargement or             
          reduction factor).  Smilansky discloses that a full affine                  
          transformation can be computed based on the theory of least-                
          squares data fitting (col. 11, lines 15-34).                                
               Frankot discloses that "[f]or any transformation more                  
          general than pure translation, scale factor (magnification) or              
          rotation for example, registration effectiveness depends on the             
          relative positions of each measurement in addition to the                   
          accuracy of the measurements themselves" (col. 1, lines 59-63),             
          where we note that translation, rotation, and scale factor are              
          affine transformations.  Frankot discloses selection criteria for           
          automatic subarea selection to improve image registration.                  
          Frankot discloses that "[i]mage registration requires estimation            
          of the coordinate transformation f that aligns two images"                  
          (col. 6, lines 4-6).  Frankot discloses that the transformation f           
          may be an affine transformation (col. 8, lines 65-67) and that              
          the coordinate transformation may be fitted with a weighted-                
          least-squares method (col. 6, lines 23-30).                                 

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