the matching of part of objects. Matching problems can be further categorized based on the ava ailability of correspondence or initial transformation information between two obj ects a the application of scaling. The classification of matching problems is summarized in Table 21.1. In the table, acronyms are used for simplification as follows C: Correspondence information is provided I: Initial information on correspondence is provided .N: No correspondence information is available ·P: Partial matching ·G: Global matching ●WOS: Without scali ·Ws: With scaling Global matching Partial matching Criteria Without scaling With scaling Without scaling With scaling Correspondence CGWOS CGWS CPWOS CPWS nformation Initial information IGWOS IPWOS IPWS No information NGWOS NGWS NPWOS NPWS Table 21.1: Classification of matching problems I When correspondence information is provided, which is one of the types CGWOS or CP- OS, then a matching problem is simply reduced to calculation of the rigid body trans- formation 3, 4. If no correspondence is known, but a good initial approximation for the transformation is available(IGWOS or IPWOS), then popular iterative schemes such as the Iterative Closest Point(ICP)algorithm [1]can be employed. However, when no prior clue for correspondence or transformation is given(NGWOS or NPWOS), the matching problem be comes more complicated. In this case, the solution process must provide a means to establish such correspondence information such as in 2 Scaling is another factor that needs to be considered separately. If a matching problem involves scaling effects, then direct comparison of quantitative measures cannot be used any longer. For the global matching case, a scaling factor can be estimated by the ratio of surface areas and applied to resolve the scaling transformation. However, when it comes to partial matching, such area information becomes useless for the scaling factor estimation. When the correspondence information between two objects is known(CGWS or CPWS), the scaling factor between the objects can be easily obtained by using the ratio of Euclidean distances between two sets of corresponding points or areas, or the ratio of the principal curvatures. If an initial scaling value as well as a good initial approximation is provided (IGWS or IPWS) the ICP algorithm by Besl [1] or other optimization schemes such as the quasi-Newton methodthe matching of part of objects. Matching problems can be further categorized based on the availability of correspondence or initial transformation information between two objects and the application of scaling. The classification of matching problems is summarized in Table 21.1. In the table, acronyms are used for simplification as follows: • C : Correspondence information is provided. • I : Initial information on correspondence is provided. • N : No correspondence information is available. • P : Partial matching. • G : Global matching. • WOS : Without scaling. • WS : With scaling. Global matching Partial matching Criteria Without scaling With scaling Without scaling With scaling Correspondence information CGWOS CGWS CPWOS CPWS Initial information IGWOS IGWS IPWOS IPWS No information NGWOS NGWS NPWOS NPWS Table 21.1: Classification of matching problems When correspondence information is provided, which is one of the types CGWOS or CP￾WOS, then a matching problem is simply reduced to calculation of the rigid body trans￾formation [3, 4]. If no correspondence is known, but a good initial approximation for the transformation is available (IGWOS or IPWOS), then popular iterative schemes such as the Iterative Closest Point (ICP) algorithm [1] can be employed. However, when no prior clue for correspondence or transformation is given (NGWOS or NPWOS), the matching problem be￾comes more complicated. In this case, the solution process must provide a means to establish such correspondence information such as in [2]. Scaling is another factor that needs to be considered separately. If a matching problem involves scaling effects, then direct comparison of quantitative measures cannot be used any longer. For the global matching case, a scaling factor can be estimated by the ratio of surface areas and applied to resolve the scaling transformation. However, when it comes to partial matching, such area information becomes useless for the scaling factor estimation. When the correspondence information between two objects is known (CGWS or CPWS), the scaling factor between the objects can be easily obtained by using the ratio of Euclidean distances between two sets of corresponding points or areas, or the ratio of the principal curvatures. If an initial scaling value as well as a good initial approximation is provided (IGWS or IPWS), the ICP algorithm by Besl [1] or other optimization schemes such as the quasi-Newton method 3