Study On PDE And It’s Applications In Image Segmentation

Image segmentation is not only the fundamental problem in middle-level vision of thecognition of human being but also one of the most difficult problems exists in the long termrecognized by international academic circle. One of the difficulties for image segmentation isthat the problem of image segmentation is not completely belong to the problem of imagefeature, it’s still involves the conscious organization of various image features. In general sense,only by thoroughly comprehension of the contents of the image can achieve perfect segmentation.But just as what Hammouda has said:“Perfect segmentation only exists in the brain ofobservers”.Nowadays, there exists two apparent features in the image segmentation realm: Oneis that the general algorithm for image segmentation is not exist, the other is that suitablealgorithms are more and more relaying on the applications of the prior knowledge. The article ison the basis of the comprehensive analysis of the domestic and foreign experience in imagesegmentation, carried on the research and exploration of the application models and numericalmethods of the PDE in image segmentation, concluded theoretically and experimented throughprogramming some of algorithms, obtained some refering results. The specific work andinnovation are included:1.Summerized the research situation and problems exists in domestic and foreign circles,and then clarified and planned the aiming of the article is on the new mathematical theories inthe construction of models and numerical methods research in image segmentation.2. Elaborated the mathematical theories involves in the energy functions and curvedeformation in the inner homogenous targets of the images, segmented the water area by Snakemodel in the parameter active contour models, run the fundamental theory through experiment.3. Put forward the anti-diffusion ways to solve one of the pretreatment of image processingimage enhancement under the profound comprehension of the image smoothing by PDE.4. Emphasized on the analysis of the energy function construction of the geometry activecontour models, against to the problems of side effects replaced the density function bydouble-well function as the regularity term removed the side effect as well as avoid thereinitialization.5. Introduced the regularity term into the numerical calculation of the PDE, combined thetheory of narrow band, substituted the up-wind pattern by center partition pattern, guaranteed thestabilization of numerical calculation and improved the efficiency of calculation.Realized the segmentation of water area through programming; achieved the anti-diffusionmethods in image enhancement; in the use of geometry active contour models by addingimproved regular term and combing the center partition algorithm and narrow band theory, realized the segmentation of interest area of image. All those experimented results testified theefficiency and effectiveness of the algorithms.