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Joint photographic experts group (JPEG) compression is widely used in image processing and computer vision. Detecting double compressed JPEG images is a common problem in forensics and detecting compressed images with the same quantization matrix remains a challenging task. However, most existing methods were designed for detection in grayscale images and cannot fully use the unique characteristics of color images (such as the relationship between channels and color information). In addition, the performance of existing methods is unsatisfactory for low JPEG quality factors and in cross detection experiments. To solve these problems, we analyze the stability of a color image to obtain the convergence error and transposition error. According to the convergence characteristics of color JPEG images, the continuous compression by the same quantization matrix can make the JPEG image tend to be stable. The final stable state and the convergence process are determined by the number of compressions of the original image. Thus, continuously compressed JPEG images can be regarded as a continuous frame to obtain the convergence error. As the color image converges, its ability to resist interference decreases. To reflect the changes in anti-interference ability, the transposition operation is used to disturb the color JPEG image to obtain the transposition error. In addition, quaternion mapping is used to retain the relationship between continuously compressed JPEG images and enlarge the influence caused by transposition operation. In our experiments on several image databases, the proposed method outperforms existing methods in different settings. [ABSTRACT FROM AUTHOR]