## 3 Proposed Method  
### Determining the Watermark Inserting Region  
Figure 3 shows the basic structure of a JPEG 2000 standard encoder. The input image with an RGB channel is preprocessed and converted to a YCbCr channel. The DWT is then applied to each Y, Cb, and Cr component. In the JPEG 2000 standard, loss compression is performed using a single scalar quantization technique with a dead zone in the center. The quantized DWT coefficient undergoes bit-plane encoding and entropy coding. The entropy coding is lossless compression using the MQ-coder, a binary arithmetic coding method used in JBIG2. The bitstream is compressed in bit-plane units, and loss compression is done using bit-rate control to represent a compressed JPEG 2000 image [31; 32]. Since this paper uses a watermark-based technique to detect image modulation, the watermark should be extracted without loss if the watermarked image remains unchanged during the detection process. Therefore, the watermark embedded into the JPEG 2000 image must be embedded into the quantized DWT coefficient that has undergone bit-rate control. To achieve optimal modulation detection results, a larger watermark size is preferable, but this may result in lower-quality watermarked images. Hence, a balance between watermark size and image quality is necessary, and selecting the appropriate insertion location is a crucial feature of the watermarking algorithm. JPEG 2000 image compression uses the 9/7 Daubechies filter, a one-dimensional wavelet conversion filter, to perform DWT. The two-dimensional wavelet transformation is divided into four sub-bands: HH (diagonal frequency component), HL (horizontal frequency component), LH (vertical frequency component), and LL (low-frequency component). The LL band can be subjected to repeated wavelet transformations. Figure 4 shows the structure of the discrete wavelet pyramid at decomposition level 4. The LL band can be subjected to numerous wavelet transformations [33]. Low-frequency components are more vulnerable to common image processing techniques such as zooming, shrinking, resizing, cutting, compression, sharpening, and blurring, as they have less energy than high-frequency components. The energy formula is shown below [34]. \[e_{k}=\frac{1}{N_{k}M_{k}}\sum_{i}\sum_{j}|I_{k}(i,j)| \tag{1}\]  
The coefficient of the corresponding sub-bands is denoted by \(e\) while and represents the sub-band sizes at decomposition level \(k\). Figure 3: Basic encoding structure of JPEG 2000 image coding. Figure 2: A JUMBF box generated by the encapsulating procedure. The LL band contains the majority of the image's energy, which has a significant impact on image quality, making it unsuitable for watermark insertion. On the other hand, the HH band, which has a diagonal frequency component with less energy, has little effect on image quality and is easily removed or changed by general image processing and compression, making it suitable for image integrity-requiring watermarking algorithms. As a result, fragile watermarking algorithms such as the one proposed in this paper use the lowest level HH band to insert a watermark. Figure 5 shows the division result obtained by watermarking at the lowest level of the HH band. The paper proposes an algorithm for localizing and representing modulated areas by dividing the DWT band into groups of blocks (GOBs). When only the HH band is used, as shown in Figure 5, the number of watermark embeddable embedded bits is insufficient to divide, resulting in GOB localization of the detection area, so additional bands are required to provide more detail. As an additional band, it is possible to use the next level of the HH band with less energy as method 1 or the lowest level of HL, the LH band, as method 2. In this paper, experiments were conducted to explore better conditions among the two methods. 1. An original raw image and a JPEG 2000 encoded image with a selected rate parameter are provided.