Colorizing Grey Scale Images

The purpose of this thesis is to develop a working methodology to color a grey scale image. This thesis is based on approach of using a colored reference image. Coloring grey scale images has no exact solution till date and all available methods are based on approximation. This technique of using a color reference image for approximating color information in grey scale image is among most modern techniques.Method developed here in this paper is better than existing methods of approximation of color information addition in grey scale images in brightness, sharpness, color shade gradients and distribution of colors over objects.Color and grey scale images are analyzed for statistical and textural features. This analysis is done only on basis of luminance value in images. These features are then segmented and segments of color and grey scale images are mapped on basis of distances of segments from origin. Then chromatic values are transferred between these matched segments from color image to grey scale image.Technique proposed in this paper uses better mechanism of mapping clusters and mapping colors between segments, resulting in notable improvement in existing techniques in this category.

Confidence in heuristic solutions?

Solutions to combinatorial optimization problems frequently rely on heuristics to minimize an objective function. The optimum is sought iteratively and pre-setting the number of iterations dominates in operations research applications, which implies that the quality of the solution cannot be ascertained. Deterministic bounds offer a mean of ascertaining the quality, but such bounds are available for only a limited number of heuristics and the length of the interval may be difficult to control in an application. A small, almost dormant, branch of the literature suggests using statistical principles to derive statistical bounds for the optimum. We discuss alternative approaches to derive statistical bounds. We also assess their performance by testing them on 40 test p-median problems on facility location, taken from Beasley’s OR-library, for which the optimum is known. We consider three popular heuristics for solving such location problems; simulated annealing, vertex substitution, and Lagrangian relaxation where only the last offers deterministic bounds. Moreover, we illustrate statistical bounds in the location of 71 regional delivery points of the Swedish Post. We find statistical bounds reliable and much more efficient than deterministic bounds provided that the heuristic solutions are sampled close to the optimum. Statistical bounds are also found computationally affordable.

Network density and the p-median solution

The p-medianmodel is commonly used to find optimal locations of facilities for geographically distributed demands. So far, there are few studies that have considered the importance of the road network in the model. However, Han, Håkansson, and Rebreyend (2013) examined the solutions of the p-median model with densities of the road network varying from 500 to 70,000 nodes. They found as the density went beyond some 10,000 nodes, solutions have no further improvements but gradually worsen. The aim of this study is to check their findings by using an alternative heuristic being vertex substitution, as a complement to their using simulated annealing. We reject the findings in Han et al (2013). The solutions do not further improve as the nodes exceed 10,000, but neither do the solutions deteriorate.