Digit Triples in Lim Angle Space.pdf

Digit Triples in Lim Angle SpacePatrick C Hewphew@.auDepartment of MathematicsThe University of Western Australia2 August 1997AbstractWe inspect triples from digit edges in Lim Angle space.1 IntroductionThe concept of a triple of quadratic descriptors was introduced in [7, Sec-tion ], along with an angle scheme to support the classication of triplesas being smooth or irregular. This scheme was applied in the UpWriting oforiented quadratic local descriptors, as presented in [6].It was later realized that the requirement of orientation was undesir-able. Accordingly, the Lim Angle scheme was revisited and redened [1] forquadratic local descriptors [5] with no asserted orientation. We now inspecttriples from digit edges in the resulting Lim Angle space.2 Extracting the TriplesWe use 20 randomly chosen examples of each printed digit [2] to generateour triples, using the inspection procedure described in [4]. A window of 4perimeter pixels was used to calculate each descriptor.Each sequence of perimeter pixels may be considered in two ways, namelyanti-clockwise traversal, and clockwise traversal. The triples obtained in [6]were of anti-clockwise traversal only, resulting in biased data, and further-more, the traversal is solely from the chain-encoding algorithm [3], namelythe ordering of directions of inspection. To remove this eect, we inspecteach perimeter twice, once in its original anti-clockwise traversal, followedby its clockwise traversal. 1 alpha1 alpha2 beta1 beta2 Figure 3.1: All triples.3 All TriplesFigure 3.1 presents a view of the smooth and irregular triples, the smoothin yellow and the irregular in red. The smooth triples look to be in a singlecluster near the origin, whilst there appear to be ve clusters of irregulartriples. The dot plots in Figure 3.2 indicate that the smooth triples areequally distributed about the origin, with a spread that is constrained whencompared against that of the irregular triples.4 Smooth TriplesTwo views of the smooth tripl