Shape preserving histogram approximation

Abstract

Abstract. We present a new method for reconstructing the density function underlying a given histogram. First we analyze the univariate case taking the approximating function in a class of quadratic-like splines with variable degrees. For the analogous bivariate problem we introduce a new scheme based on the Boolean sum of univariate B-splines and show that for a proper choice of the degrees, the splines are positive and satisfy local monotonicity constraints.

Constrained Interpolation via Cubic Hermite Splines

“…0.0078 0.0007 0.0112 [2,3] 0.0024 0.0005 0.0033 [3,4] 0.0005 0.0001 0.0008 [4,5] 0.0003 0.0005 0.0003 [5,6] 0.0014 0.0012 0.0014 [6,7] 0.0003 0.0007 0.0002 [7,8] 0.0030 0.0010 0.0027 [8,9]…”

On Smoothing Problems With One Additional Equality Condition

“…It is clear that Z 0 is a closed subspace of IR n , which implies that X 0 = A −1 (Z 0 ) is closed too. The closedness of L(X 0 ) for a closed subspace X 0 ⊂ X is proved in [5], p.13. Now an element s ∈ X r is an element with the minimal norm Ls− w V (i.e.…”

A survey on shape preserving interpolation

“…It has not only great significance in various areas of engineering such as ship design and manufacture, car body design and manufacture, aerospace industry, and precision mechanism industry, but also plans a crucial role in aerography, iatrology, and even in animation and games. Now, some emerging research fields, such as modern data analysis [5], mathematical finance [6], image processing [7], visualization [8], digital watermarking technique [9] are advancing higher standard for curve and surface shape preserving modeling system. Shape preserving modeling is always the study interest of many people.…”