Robustness is an essential characteristic of a watermarking algorithm. In order to achieve higher robustness, this paper proposes a novel Triangular Vertex Transform (TVT) and Walsh Hadamard Transform (WHT) based robust color image watermarking by elliptical phase modification. The existing TVT converts the RGB components of an image to U, V and W coefficients suitable for data embedding. However, embedding data directly on W coefficient of TVT using traditional embedding algorithms highly affects the quality of the image and reduces the robustness of the watermarking algorithm. Therefore an elliptical phase modification embedding algorithm is introduced to embed the data efficiently in the W coefficient. Initially, this embedding scheme transforms the RGB color image to TVT coefficients using the TVT. The WHT coefficients are then estimated by subdividing the W coefficients into 4 × 4 subblocks. Three WHT coefficients from the first row are chosen for elliptical coordinate formation. The elliptical coordinate is formed such that the minimum and maximum values from three selected WHT coefficients form the length of the semiminor and semimajor axis of an ellipse, respectively. The phase (θ) of intermediate coefficients is estimated from the ellipse, such that the intermediate coefficients act as the radius at point P. The data is embedded by modifying the phase (θ) and the new radius provides the data embedded new intermediate WHT coefficient. The embedded 4 × 4 subblocks are then merged after obtaining the inverse WHT. Finally, the watermarked image is estimated by obtaining the inverse TVT. In the extraction phase, the ellipse is again formed using the same three WHT coefficients. The embedded phase \( \hat{\theta } \) is estimated from the intermediate value, which is used for extracting the hidden data. The proposed watermarking algorithm shows higher performance than those of the traditional watermarking algorithms; particularly, it attains optimal Peak Signal to Noise Ratio of 44.76 dB and 43.46 dB for two different embedding capacities.

鲁棒性是水印算法的基本特征。为了获得更高的鲁棒性，本文提出了一种新颖的基于三角相位修改的三角形顶点变换（TVT）和Walsh Hadamard变换（WHT）的鲁棒彩色图像水印技术。现有的TVT将图像的RGB分量转换为适合数据嵌入的U，V和W系数。但是，使用传统的嵌入算法将数据直接嵌入TVT的W系数会极大地影响图像质量，并降低水印算法的鲁棒性。因此，引入了椭圆相位修正嵌入算法，可以将数据有效地嵌入到W中。系数。最初，此嵌入方案使用TVT将RGB彩色图像转换为TVT系数。然后通过将W系数细分为4×4子块来估算WHT系数。从第一行选择三个WHT系数以形成椭圆坐标。形成椭圆坐标，使得来自三个选择的WHT系数的最小值和最大值分别形成椭圆的半短轴和半长轴的长度。从椭圆估计中间系数的相位（θ），使得中间系数充当点P处的半径。通过修改相位（θ）和新的半径提供了嵌入数据的新中间WHT系数。然后，在获得逆WHT之后，将合并的4×4子块合并。最后，通过获得逆TVT来估计水印图像。在提取阶段，再次使用相同的三个WHT系数形成椭圆。从中间值估计嵌入相位\（\ hat {\ theta} \），该中间值用于提取隐藏数据。提出的水印算法具有比传统水印算法更高的性能。特别是，对于两种不同的嵌入能力，它可获得44.76 dB和43.46 dB的最佳峰值信噪比。