İki boyutlu tonlamadan üç boyutlu görüntünün oluşturulması

Abstract

Bu çalışmada, iki boyutlu bir görüntüden biçime ait bilginin elde edilmesi hedeflenmiştir. Bu amaçla, `Shape from Shading` (tonlamadan biçim eldesi) problemi incelenmiş ve plakalar yöntemi bir çözüm önerisi olarak sunulmuştur. Plakalar yöntemi kullanılarak elde edilen hata fonksiyonuna `Gradient Algoritması` uygulanarak, tonlamadan biçim eldesi probleminde ortaya çıkan kısmi diferansiyel denklemin bir çözümü bulunmuştur. Plakalar yöntemi, sonsuz çözümü bulunan kısmi diferansiyel denklemin bir çözümünü mutlaka bulmaktadır. Ancak, bulunan çözümün çözüm ailesi içinde istenen bir noktaya yakınsaması, başlangıç koşullarına bağımlı olmaktadır. Yöntemin sınanması amacıyla, farklı yüzey fonksiyonlarının iki boyuttaki izdüşümü sentetik olarak elde edilmiş ve bilgisayar ortamında oluşturulan algoritmalara uygulanmıştır. Anahtar Kelimeler: Aydınlanmadan biçim, Görüntü işleme, Gradient algoritması, Plakalar yöntemi

In this project, extracting shape information from the 2-dimensional image was aimed. For this reason, `Shape from Shading` problem was analysed and the `Plates Method` was proposed as a solution technique. The gradient algorithm was applied to the error function which was generated from the plates method and found a solution for the partial differential equation which can be found from the shape from shading problem. Plates method usually founds a solution from this partial differential equation. But this pdf has infinitely many solutions. Finding a special solution from the huge solution family is dependent on initial conditions. For testing the plates method, images were generated from the surface functions synthetically and applied to the computer algorithms. Keywords: Shape from shading, Image processing, Gradient algorithm, Plates method.IV SUMMARY In this project, extracting shape information from the 2-dimensional image was aimed. For this reason, `Shape from Shading` problem was analysed and the `Plates Method` was proposed as a solution technique. The gradient algorithm was applied to the error function which was generated from the plates method and found a solution for the partial differential equation which can be found from the shape from shading problem. Plates method usually founds a solution from this partial differential equation. But this pdf has infinitely many solutions. Finding a special solution from the huge solution family is dependent on initial conditions. For testing the plates method, images were generated from the surface functions synthetically and applied to the computer algorithms. Keywords: Shape from shading, Image processing, Gradient algorithm, Plates method.