Görüntü İşleme Uygulamaları İçin Finsler Eğri Evrim Modeli İncelemesi

Abstract

Bu çalışmada Finsler geometrisi ile kurulan ve varyasyonlar hesabı ile eğri evrim modeline dönüşen Finsler eğri evrim modeli incelenecektir. Bu model, Riemann eğri evrim modelinde olduğu gibi sadece görüntü uzayındaki konumlar değil yönlerde dikkate alınarak anizotropik bir uzayda kurulmuştur. Model, görüntüye izotropik bir yapı olarak bakan Riemann modelinin aksine anizotropik yapı olarak bakarak daha esnek bir çalışma alanı sunar. Bu nedenle görüntü işleme üzerine çalışan araştırmacıların sıklıkla üzerinde çalıştıkları bir model haline gelmiştir. Bu çalışmada ele alınan Finsler eğri evrim modelinin matematiksel analizi kullanılarak gelecekteki görüntü işleme alanında yapılacak çalışmalara katkı sağlanması amaçlanmaktadır.

Keywords

• Finsler metrik
• görüntü işleme
• varyasyonlar hesabı
• eğri evrimi

Finsler Curve Evolution Analysis for Image Processing

Abstract

In this study, the Finsler curve evolution model, which was established with Finsler geometry and turned into a curved evolution model with the calculation of variations, will be examined. This model is not constructed by considering only locations in the image space as in the Riemann curve evolution model. It was established in an anisotropic space by considering both locations and directions. The model offers a flexible operation in the image by eliminating the necessity of isotropic spaces. Therefore, it has become a model that researchers working on image processing mostly work on. It is aimed to contribute to future studies in the field of image processing by using the mathematical analysis of the Finsler curve evolution model discussed in this study.

Keywords

• Finsler metric
• image processing
• variational calculus
• curve evolution.
• Finsler metrik
• görüntü işleme
• varyasyonlar hesabı
• eğri evrimi

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