On the difference between solutions of discrete tomography problems II
نویسنده
چکیده
We consider the problem of reconstructing binary images from their horizontal and vertical projections. It is known that the projections do not necessarily determine the image uniquely. In a previous paper it was shown that the symmetric difference between two solutions (binary images that satisfy the projections) is at most 4α √ 2N . Here N is the sum of the projections in one direction (i.e. the size of the image) and α is a parameter depending on the projections. In this paper we give a lower bound: for each set of projections that has at least two solutions, we construct two solutions that have a symmetric difference of at least 2α+2. We also show that this is the best possible.
منابع مشابه
On the difference between solutions of discrete tomography problems
We consider the problem of reconstructing binary images from their horizontal and vertical projections. We present a condition that the projections must necessarily satisfy when there exist two disjoint reconstructions from those projections. More generally, we derive an upper bound on the symmetric difference of two reconstructions from the same projections. We also consider two reconstruction...
متن کاملPareto-optimal Solutions for Multi-objective Optimal Control Problems using Hybrid IWO/PSO Algorithm
Heuristic optimization provides a robust and efficient approach for extracting approximate solutions of multi-objective problems because of their capability to evolve a set of non-dominated solutions distributed along the Pareto frontier. The convergence rate and suitable diversity of solutions are of great importance for multi-objective evolutionary algorithms. The focu...
متن کاملA New Multi-objective Model for Multi-mode Project Planning with Risk
The purpose of this problem is to choose a set of project activities for crashing, in a way that the expected project time, cost and risk are minimized and the expected quality is maximized. In this problem, each project activity can be performed with a specific executive mode. Each executive mode is characterized with four measures, namely the expected time, cost, quality and risk. In this pap...
متن کاملOn Approximate Stationary Radial Solutions for a Class of Boundary Value Problems Arising in Epitaxial Growth Theory
In this paper, we consider a non-self-adjoint, singular, nonlinear fourth order boundary value problem which arises in the theory of epitaxial growth. It is possible to reduce the fourth order equation to a singular boundary value problem of second order given by w''-1/r w'=w^2/(2r^2 )+1/2 λ r^2. The problem depends on the parameter λ and admits multiple solutions. Therefore, it is difficult to...
متن کاملNew classes of Lyapunov type inequalities of fractional $Delta$-difference Sturm-Liouville problems with applications
In this paper, we consider a new study about fractional $Delta$-difference equations. We consider two special classes of Sturm-Liouville problems equipped with fractional $Delta$-difference operators. In couple of steps, the Lyapunov type inequalities for both classes will be obtained. As application, some qualitative behaviour of mentioned fractional problems such as stability, ...
متن کامل