Polygonal Image Research Articles

Reconstruction of polygonal images

Let T be a two-dimensional region, and let X be a surface dejined on T. The values of X on T, constitute an image, or pattern. The true value of X at any point on T cannot be directly observed, but data can be recorded which provide information about X. The aim is to reconstruct X using the prior knowledge that X will vary smoothly over most of T, but may exhibit jump discontinuities over line segments. This information can be incorporated via Bayes' theorem, using a polygonal Markov random field on T as prior distribution. Under this continuum model, X may in principle be estimated according to standard criteria. In practice, the techniques rely on simulation of the posterior distribution. A natural family of conjugate priors is identified, and a class of spatial-temporal Markov processes is constructed on the uncountable state space; simulation then proceeds by a method of analogous to the Gibbs sampler.

A subjective judgment study of polygon based curved surface imagery

In the past computer graphics efforts, several researchers have demonstrated that polygon models can be used to produce images of curved surfaces that appear to be smooth and accurate. However, the authors know of no attempt to appraise such imagery by using multiple human observation ratings. The effectiveness of curved surface imagery generated from polygon models was investigated in a judgment study. Research subjects evaluated sphere model imagery derived from several polygon densities and shading procedures including flat shading, shade interpolation (Gouraud) and normal interpolation (Phong). Results of the evaluations indicated that little was gained by reducing the average polygon areas below approximately 110 pixels per polygon for spheres of 95 pixel radii displayed on a 512 x 512 resolution monitor. Evaluations for both shade and normal interpolution placed polygon image quality reasonably close to an “ideal” image. Although the evaluations indicated that normal interpolation was slightly superior to the shade interpolation, shade interpolation required significantly less computation. Most significantly, results from this study provide strong support for the notion that polygons can be used effectively to produce smooth shaded imagery of curved surface models.

Conditions for some polygonal functions to be Bazilevič

Univalent functions in the disc whose image is a particular eight-sided polygonal region determined by two parameters are studied. Whether such a function is Bazilevič is determined in terms of the two parameters, and the set of real α \alpha ’s is specified such that the function is ( α , β ) (\alpha ,\beta ) Bazilevič for some β \beta . For any interval [ a , b ] \left [ {a,b} \right ] where 1 > a ⩽ 3 ⩽ b 1 > a \leqslant 3 \leqslant b , a function of this type which is ( α , 0 ) (\alpha ,0) Bazilevič precisely when α \alpha is in this interval is found. Examples are given of non-Bazilevič functions with polygonal images and Bazilevič functions which are ( α , 0 ) (\alpha ,0) Bazilevič for a single value α \alpha .