3-D Cartesian Geometric Moment Computation using Morphological Operations and Its Application to Object Classification

Abstract

THREE-DIMENSIONAL CARTESIAN GEOMETRIC MOMENTS ARE IMPORTANT FEATURES FOR 3-D DOBJECTRECOGNITION AND SHAPE DESCRIPTION. COMPUTING THESE FEATURE IN THE 3-D CASE BY ASTRAIGHT FOR WARD METHOD REQUIRES A LARGE NUMBER OF OPERATIONS. SEVERAL AUTHORS HAVE PROPOSED FAST METHODS TO COMPUTE THE 3-D MOMENTS. MOST OF THEM REQUIRE COMPUTATIONS OF ORDER N3, ASSUMING THAT THE OBJECT IS REP RESENTED BY A N*N*N VOXEL IMAGE. RECENTLY, YANGET AL (1996) PRESENTED A METHOD REAUIRING COMPUTATION OF O (N2) BUUSING A DISCRETE DIVERGENCE THE O REM THAT AL LOWS TO COMPUTE THE SUM OF A FUNCTION OVER AN-DIMENSIONALDISCRETE REGION BY A SUMMATION OVER THE DISCRET SURFACE EN CLOSING THE OBJECT. IN THIS PAPER, WE PRESENT A BALLS (CUBES) UNDERD. THIS DECOMPOSITION FORMS A PARTITION. TRIPLE SUMMATIONS USED IN THE COMPUTATION OF THE MOMENTS ARE REPLACED BY THE SUM OF THE MOMENTS OF EACH CUBE OF THE PARTITION. THE MOMENTS OF EACH CUBE CAN BE COMPUTED IN TERMS OF A SET OF VERY SIMPLE EXPRESSIONS USING THE CENTER OF THE CUBE AND ITS RADIO. WE SHOW THAT ONCE THE PARTI TION IS OBTAINED, MOMENT COMPUTATION USING THE PROPOSED APPROACH IS MUCH FASTER THAN EAR LIER METH ODS; ITS COMPLEXITY IS IN FACT OF O (N). WE ALSO SHOW SEVERAL EXPERIMENTS WHERE THE DERIVED MOMENTS CAN BE USED TO COMPUTE INVARIANTS USEFUL IN THE RECOGNITION OF THRRE-DIMENSIONAL OBJECTS.