Pattern recognition problems in geology and paleontology by Ulf Bayer

By Ulf Bayer

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The local method provides an approximation method which is based on a Shepard 'counting circle' as discussed above. SCHUMAKER (1976) shows that the local Shepard method is an optimal approximation s t r a t e g y for the local surface reconstruction. e. the data 1 points, are preserved. The local surface fitting method can be used to e s t i m a t e a density function if the samples become r a t h e r large. For a large sample, with space coordinates measured on a discrete scale (with fixed precision), one can expect that the resulting histogram is a good e s t i m a t i o n of the s t a t i s t i c a l universe.

Function over a finite area. Actually, they Variation of the thus, resembles the d i s t u r b a n c e of a signal {Fig. 1). The counting circle defines the area in which the data point will be found with a c e r t a i n probability, and this probability is everywhere equal (within the area of influence). The rectangular weighting function over the counting circle, therefore, can be i n t e r p r e t e d as a r e c t a n g u l a r probability distribution. A consequence is t h a t one can not e i t h e r assume t h a t a n o t h e r (sparse) sample from the identical universe shows the same e x t r e m a .

N: relative height of whorl, Dm: d i a m e t e r of the shell. During the late ontogeny, measured by size, an image inversion occurs, which can be i n t e r p r e t e d as a local fold. In the model t h e fold causes local i n t e r s e c t i o n s of the t r a j e c t o ries and an e m p t y area. e. that the i n t e r s e c t i o n s are due to the projection onto the two-dimensional p a r a m e t e r space. ior of the morphological t r a j e c t o r i e s can well be c o m p a r e d with a local fold.

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