Veysel Aslanta, MDoru, Genetik Algoritma (GA) kullanarak (Singular Value Decomposition - SVD) resim Ç (scaling factors - SFs) kullanarak alues - SVs) metotta, maksimum optimize maksimum saydam da S Anahtar Kelimeler Abstract In this paper, a novel fragile image watermarking scheme based on SVD using GA is presented. Watermark of every line is scaled by using multiple SFs. Host image is divided into blocks. Watermarked image is obtained by embedding a different line of watermark to SVs of the every block. In this proposed method, the SFs are optimized using GA to achieve maximum transparency. Experimental results indicate that reached the highest transparency. Fragility detected under various attacks. When an attack does not occur exactly the original embedded watermark is achieved or else the embedded watermark is intensely corrupted. Index Terms Genetic Algorithm, Fragile Image Watermarking, Singular Value Decomposition. I. AYISAL S unun -4]. ; resim ve frekans Bilgisayar T(e-mail:aslantas@erciyes.edu.tr)., Bilgi, Ankara, T (email:mevlut_dogru@milliemlak.gov.tr). 10 Cosine Transform - (Discrete Wavelet Transform - eklenerek [2,5-7]. ; verinin [2]. - n etkilenmemelidir -, olabilmelidir [6,8,9 SVD, damgalama dahil bir teknikleri [10-12], de maliyet fonksiyonu - damgalama [13] - teknikleri de mevcuttur. O damgalama metotlar ve bu makalede e Bu gri seviye resimler rak leri ler Damga ekleme leri en
TABLO I METOT VE BAZI METOTLARIN MASI Teknik ve Algoritma Aslantas vd. (2007) Aslantas vd. (2008) GA, PSO, KSA, Diferansiyel Aslantas vd. (2009) SVD - GA Modaghegh vd. (2009) SVD GA II. SVD TABANLI DAMGALAMA SVD ile NxN A matrisi A=USV T olacak NxN U ve V T ortogonal matris, NxN boyutndaki S S matrisi, A [5,6]. A. Orijinal resim (IW NxN ve Mx2M (N>2da Burada, W i i. I (m,n) ise b m. n. 1) Orijinal resim M/2xM/2. 2) (1) (2) 3) S (m,n) B. Damga SVD nde 1) resim, T (m,n) (m,n) (m,n) (6) 2) 3) W * ) elde edilir. III. NIN TEMEL YAPISI 16 uygunluk prazlama ve mutasyon) inden durdurma kriteri, maliyet fonksiyonu ve parametreler da bir dizi, o her bir dizinin uygunluk lendirmesi, maliyet fonksiyonuna Rastgele sretici (7) (8) 4) (3) Seleksiyon = U (m,n) S * (m,n)v T (m,n) (4) 5) I W ) elde edilir. (5) Mutasyon Durdurma kriteri Evet Bitir 1. 11
Uygunluk seleksiyon fonksiyonunu yerine getirir. Bireyleri temsil eden dizilerden an sonraki crossover rate - CR) utation rate - eyi temsil Orijinal resim D a m g a k IV. GA VE SVD TABANLI KIRILGAN DAMGALAMA GA, F lere uygulanarak II. damgalanmii. ikili (binary) olanlara 0, 0.5 ve daha olanlara ise 1 atanarak yeniden ikili ve ortalama filtreleme (O corr I ) sayesinde orijinal - BCR) sayesinde de ; W t W * t M W N W, simgesi ise lojik XOR BCR [17]. BCR = (9) Korelasyon ve BCR maliyet fonksiyonu denklem (10 s, Burada t f i ise i. jenerasyondaki maliyet f i = (10) I W I W* Son jenerasyon Evet. V. damga olarak, 3 64 boyutundaki orijinal ikili resmin 32k bloklar mesiyle o ve 3 256x8ik ikili Kaynak resim olarak da 3 resim ve ktedir. Her uygulamadan e de Test 128256), DN (bilineer: 3 0 ), GG ve OF 500, seleksi mutasyon, mutasyon W 12
3. Orijinal damga,. 4. Orijinal BaboonBaboon. 5. Orijinal GemiGemi. TABLO III T SF'LER corr I BCR Baboon 1 100 GA SF'ler Gemi 1 99,6582 Baboon Gemi Sabit SF'ler 1 1 42,1875 20 0,9983 93,7988 40 0,9938 88,1836 1 1 44,3359 20 0,9985 89,3066 40 0,9943 84,7309-15;15 500 jenerasyon sonucunda optimi korelasyon ve BCR resimde corr I BCR esminde de 99.6582 BCR 54-57. GA ile eld1, 20, 40 sabit II g corr I 1 BCR corr I BCR 6. Baboon Gemien. Baboon Gemi YO DN (c) GG (d) OF 7. TABLO II VE corr I BCR YO DN GG OF Baboon 1 100 56,1523 54,9316 56,1523 54,8340 Gemi 1 99,6582 56,3477 54,8828 54,9805 55,5664 VI., yeni bir resim damgalama leri ler ekle Deneysel testler, GA ile optimize edilen sabit orijinal resim ile., YO, DN, GG ve O. 13
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