We present a method for recovery of damaged parts of old paintings (frescoes), caused by degradation of the pigments contained in the paint layer. The original visible colour information in the damaged parts can be faithfully recovered from measurements of absorption spectra in the invisible region (IR and UV) and from the full spectral data of the well preserved parts of the image. We use the ...

Spend your few moment to read a book even only few pages. Reading book is not obligation and force for everybody. When you don't want to read, you can get punishment from the publisher. Read a book becomes a choice of your different characteristics. Many people with reading habit will always be enjoyable to read, or on the contrary. For some reasons, this mathematical and computational methods ...

In this special issue of Computer-Aided Design, mathematical and geometrical methods are presented for a set of problems in computer-aided design. In particular, the issue contains seven papers that deal with topics in the synthesis and analysis of surfaces and solids. The first three papers deal with topics in surface design. A basic problem in shape design is the fitting of smooth surfaces ov...

In the classical approach to elasticity problems, the components of the displacement field are the primary unknowns. In an “intrinsic” approach, new unknowns with more physical or geometrical meanings, such as a strain tensor field or a rotation field for instance, are instead taken as the primary unknowns. We survey here recent progress about the mathematical analysis of such methods applied t...

I. DIFFERENTIAL ENTROPY AND THE GAUSSIAN CHANNEL A. Differential Entropy Let X be a random variable with a continuous alphabet. • FX(x) = Pr(X ≤ x) Cumulative Distribution Function {CDF}. F (x) is a short notation for FX(x). • fX(x) = dFX(x) dx Probability Density Function {PDF} (in this course we will assume that the derivative exists). f(x) is a short notation for fX(x). Definition 1 ( Differ...

1 Department of Engineering Physics, Tsinghua University, Beijing 100084, China 2Medical Physics Program, GeorgeW.Woodruff School, Georgia Institute of Technology, 770 State Street, Atlanta GA 30332-0745, USA 3Department of Nuclear and Quantum Engineering, Korea Advanced Institute of Science & Technology, Yuseong-gu, Daejeon 305-701, Republic of Korea 4 Institute for Biomedical Engineering, Uni...