Reducing Aliasing Problem in Images using Neutrosophic Set-Based Diffusion Method

Öz

Image enhancement is a significant topic in computer vision and image processing applications. In this paper, a new neutrosophic set based diffusion method is proposed to reduce aliasing on edge regions. Based on the diffusion equation of Ziou ve Horé, the new calculation methodology for gradient and curvature in the diffusion equation is presented. In the proposed method, aliased image is converted into the neutrosophic set and defined by three membership sets: truth, indeterminacy, and falsity. Then the proposed method actively uses the truth and falsity memberships of the neutrosophic set, and reduces aliasing artifacts. In the gradient calculation, the proposed method uses the neutrosophic truth instead of the original input image. Also, the neutrosophic falsity has been used to calculate the curvature calculation. Since the neutrosophic membership sets are more immune to noise, the disadvantage of traditional diffusion equations has been resolved in terms of noise. The neutrosophic sets can suppress the noise components, and thus the smooth gradient and curvature models can be calculated. These gradient and curvature informations reflect both the edge changes and aliasing artifacts in aliased image. Thus inverse diffusivity process in the equation of Ziou ve Horé is performed efficiently. The proposed method reduces aliasing artifacts while preserving the details of edge regions through neutrosophic set. The experiment results show that the proposed method can detect the aliasing problems on edge regions. Also, Mean Square Error (MSE) metric is used to evaluate the proposed diffusion method's performance. The results are compared with results of other methods on the same images. This new method can be used as a pre-processing step for applications in image processing.

Anahtar Kelimeler

• Image enhancement
• Neutrosophic set
• Diffusion equation

Nötrozofik Küme Temelli Difüzyon Metodu Kullanılarak Görüntülerdeki Örtüşme Problemini Azaltma

Öz

Görüntü iyileştirme bilgisayar görmesi ve görüntü işleme uygulamalarında önemli bir konudur. Bu çalışmada kenar bölgelerindeki örtüşmeyi azaltmak için nötrozofik küme temelli yeni bir difüzyon metodu önerilmiştir. Ziou ve Horé’nin difüzyon denklemi temel alınarak, difüzyon denklemindeki gradyan ve eğrilik için yeni bir hesaplama metodolojisi önerilmiştir. Önerilen metotta örtüşme içeren görüntü nötrozofik kümeye dönüştürülür ve üç üyelik kümesi tarafından tanımlanır: doğruluk, belirsizlik ve yanlışlık. Daha sonra önerilen metot nötrozofik kümenin doğruluk ve yanlışlık üyeliklerini aktif olarak kullanır ve örtüşme etkilerini azaltır. Gradyan hesaplamasında önerilen metot orijinal giriş görüntüsü yerine nötrozofik doğruluk kümesini kullanır. Ayrıca eğrilik hesaplaması için nötrozofik yanlışlık kümesi kullanılmıştır. Nötrozofik üyelik kümeleri gürültüye karşı daha dayanıklı oldukları için, geleneksel difüzyon denklemlerinin dezavantajları gürültü açısından giderilmiştir. Nötrozofik kümeler gürültü bileşenlerini baskılayabilir ve böylece yumuşak gradyan ve eğrilik modelleri hesaplanabilir. Bu gradyan ve eğrilik bilgileri örtüşme içeren görüntüdeki hem kenar değişimlerini hem de örtüşme kalıntılarını yansıtır. Böylece Ziou ve Horé’nin denklemindeki ters yayınım işlemi etkili bir şekilde gerçekleştirilmiştir. Önerilen metot örtüşme kalıntılarını azaltırken nötrozofik küme vasıtasıyla kenar bölgelerinin detaylarını korumuştur. Deneysel sonuçlar önerilen metodun kenar bölgelerinde örtüşme problemlerini tespit edebildiğini göstermiştir. Yine önerilen difüzyon metodunun performansını değerlendirmek için Ortalama Karesel Hata (OKH) metriği kullanılmıştır. Sonuçlar aynı görüntüler üzerinde diğer metotların sonuçları ile karşılaştırılmıştır. Bu yeni metot görüntü işlemedeki uygulamalar için ön işlem adımı olarak kullanılabilecektir.

Anahtar Kelimeler

• Görüntü iyileştirme
• Nötrozofik küme
• Difüzyon denklemi

Kaynakça

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