New progressive image transmission based on quadtree and shading approach with resolution control
Introduction
The progressive image transmission (PIT) is a technique to progressively approximate an image on the receiving device over the remote transmission. Instead of waiting a long time for a high resolution image, the remote user can grasp a rough image quickly, and then, continuously, finer and finer image will be constructed. Therefore, it is important and practical in managing large amount of images for remote users especially over low speed network channels.
There are several PIT methods that have been developed. Previously, Tzou (1987) presented a thorough review and comparison of some PIT methods, namely, the spatial domain, the transform domain, and the pyramid-structure approaches. Among these approaches, there are trade-offs between system complexity and performance. Based on the principal component analysis (Chang et al., 1997), Chen and Wu (1998) presented an efficient PIT method. Based on the watershed approach (Vincent and Soille, 1991), Caron and Rivest (1996) presented a segmentation-based coding method for PIT. Lu et al. (1997) presented a polynomial approximation coding approach for PIT. Jordan et al. (1998) presented a polygonal approximation approach for PIT of binary images. Based on the DCT coding, the spectral selection approach is applied on the progressive JPEG (PJPEG) (Pennebaker and Mitchell, 1993). Goldberg and Wang (1991) gave an excellent review of various pyramid structures for PIT methods. They demonstrated that the reduced-difference pyramid (RDP) (Wang and Goldberg, 1989) achieves the best performance. The Laplacian pyramid proposed by Burt and Adelson (1983) is widely used for lossless compression of image. Based on the Laplacian pyramid, several improved PIT methods were proposed (Aiazzi et al., 1996, Qiu, 1999, Said and William, 1996).
Recently, Chung and Wu (2000) presented an efficient image compression method using S-tree and shading approach named STC method. The STC method has the significant advantage on its execution time, especially the decoding time. As compared to the JPEG (Pennebaker and Mitchell, 1993), the STC method has shorter execution time while preserving the same image quality, although the bit rates are higher by a factor of about 2. However, the execution time is critical in the applications of real-time image retrieval and communication. Another advantage of the STC method is the tree-based spatial data structure (Samet, 1990) having wide applications in computer graphics, image processing, geographic information systems, image database, pattern recognition, etc.
In this paper, based on the STC method, a quadtree- and shading-based approach coding method, called the QSC method, is presented first. In the PIT encoding phase, using the QSC method, the original gray image is compressed into a quadtree structure. Then, the quadtree is partitioned into several disjoint subsets for each transmission stage such that the resolution of nodes in each stage must be in the specified interval. In the decoding phase, initially, as the first stage of the compressed image is received, the corresponding quadtree is constructed and the coarsest image can be displayed. While the next stage of data is received continuously, the PIT decoding algorithm appends the newly received data to the current quadtree and then displays a finer image. Finally, the decoding phase will refine the current image stage by stage until the required quality is achieved. Experimental results reveal that as compared to the RDP (Wang and Goldberg, 1989) and the PJPEG (Pennebaker and Mitchell, 1993), the proposed PIT scheme has a good feature-preserving capability under the similar peak signal to noise ratio (PSNR) and bits per pixel (bpp).
The rest of this paper is organized as follows. In Section 2, the proposed QSC method is presented. In Section 3, the proposed PIT scheme is presented. Some experimental results are demonstrated in Section 4. Finally, some concluding remarks are addressed in Section 5.
Section snippets
The proposed QSC method
Based on the STC method (Chung and Wu, 2000), this section presents a modified compression method called the QSC method.
In the QSC method, the original image is first partitioned into some homogeneous blocks based on the quadtree decomposition principle. While partitioning, the Gouraud shading method (Foley et al., 1990) is used to control the image quality under a specified error tolerance. Then, we apply the breath-first search (BFS) on the quadtree to obtain the S-tree representation.
The
The proposed PIT scheme
In this section, based on the QSC method, we first presents the PIT encoding algorithm which partitions the quadtree represented image into several disjoint subsets for PIT. Then, the decoding algorithm progressively reconstructs the image is presented.
In our proposed PIT scheme, the different error tolerance ϵ is considered as the resolution level of the image. While decomposing the image into a quadtree, we compute and keep the error value of each internal node. The error value is defined as
Experimental results
To demonstrate the performance comparison among the proposed method, the reduced-difference pyramid (RDP) (Wang and Goldberg, 1989), and the progressive JPEG (PJPEG) (Pennebaker and Mitchell, 1993), we take the F16 image of size 512×512 where each pixel needs 8 bits as the testing sample to evaluate the performance. The original image is shown in Fig. 4. In order to improve the compression ratio when applying the QSC method, we store the linear-tree table by discarding the leading 0's and only
Conclusion
We have presented a novel PIT method for gray images based on the quadtree and Gouraud shading approach. In the proposed PIT scheme, the number of stages can be specified by users and the image resolution can be controlled at each stage. Experimental results reveal the proposed scheme has a good feature-preserving capability as compared to the reduced-difference pyramid PIT scheme and the progressive JPEG.
Acknowledgements
The authors would like to thank the anonymous referees for their valuable suggestions that lead to the improved presentation of this paper.
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