In this paper, by using the quaternion algebra, the conventional complex-type moments (CTMs) for gray-scale images are generalized to color images as quaternion-type moments (QTMs) in a holistic manner. We first provide a general formula of QTMs from which we derive a set of quaternion-valued QTM invariants (QTMIs) to image rotation, scale and translation transformations by eliminating the influence of transformation parameters. An efficient computation algorithm is also proposed so as to reduce computational complexity. The performance of the proposed QTMs and QTMIs are evaluated considering several application frameworks ranging from color image reconstruction, face recognition to image registration. We show they achieve better performance than CTMs and CTM invariants (CTMIs). We also discuss the choice of the unit pure quaternion influence with the help of experiments. $$(i-j-k)/\sqrt{3}$$ ( i - j - k ) / 3 appears to be an optimal choice.

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Color Image Analysis by Quaternion-Type Moments

Color medical image lossless watermarking using chaotic system and accurate quaternion polar harmonic transforms

Bu calismada 24 bit RGB formatinda 128 × 128 boyutlarinda gizli ve 24 bit RGB formatinda 512 × 512 boyutlarinda tasiyici goruntuler kullanilarak bir filigranlama uygulamasi gerceklestirilmistir. Calismada kullanilan gizli goruntulerin sifrelenmesinde, goruntu ozellik tabanli iki katmanli sifreleme kullanilmistir. Gizli goruntuler oncelikle kirmizi, yesil ve mavi renk uzaylarina ayrilmistir. Birinci katman sifrelemede; gizli goruntu renk uzaylari, kendi goruntu ozellikleri kullanilarak yer degistirme algoritmasi ile sifrelenmistir. Daha sonra gizli goruntu, renk uzaylarinin goruntu boyutlari yeniden duzenlenerek binary (ikili) formata donusturulmustur. Bu goruntuler ikinci katman sifrelemede; tasiyici goruntu ozellikleri kullanilarak sifrelenmis ve tasiyici goruntunun kirmizi, yesil ve mavi renk uzayina en onemsiz bit yontemi ile filigranlanmistir. Uc adet tasiyici goruntu ve iki adet gizli goruntu kullanilarak yapilan calismada goruntuler arasindaki degisimleri olcmek amaciyla tepe sinyal gurultu oranindan (TSGO) yararlanilmistir. Calisma sonucunda, 51.13 dB ile 51.91 dB arasinda degisen TSGO basarisi ile filigranlama gerceklestirilmistir.

/pdf/renkli-tasiyici-ve-renkli-gizli-goruntulerin-goruntu-ozellik-3odtapm3m7.pdf

Renkli̇ taşiyici ve renkli̇ gi̇zli̇ görüntüleri̇n görüntü özelli̇k tabanli i̇ki̇ katmanli şi̇freleme ve en önemsi̇z bi̇t yöntemi̇ kullanilarak fi̇li̇granlanmasi

A new color watermarking algorithm of colored images based on modified quaternion fast Fourier transform (QFFT) and discrete cosine transform (DCT) is presented By modifying the image vector, the real part and imaginary part of the carrier image after QFFT are symmetrical Then, the DCT is applied to the colored watermark, and after multiplying a factor, the RGB components of the watermark are embedded into the corresponding part of the carrier image lossless and spread into the whole image, hence enhancing the intangibility The experimental result shows that the presented algorithm improves peak signal-to-noise ratio (PSNR) by 10 dB compared with color watermarking algorithm based on traditional QFFT

Zuo Wei

Papers

Color Watermarking Algorithm Based on Modified QFFT and DCT