Fractal image compression with adaptive quadtree partitioning and non-linear affine map
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Fractal image compression with adaptive quadtree partitioning and non-linear affine map Utpal Nandi1 Received: 28 June 2019 / Revised: 4 June 2020 / Accepted: 24 June 2020 / © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract Fractal image compression techniques are now very popular for its high compression rates and resolution independence property. However, the qualities of decoded images of the existing techniques are not satisfactory. An adaptive partitioning scheme can improve the image quality significantly. These existing adaptive techniques use linear affine maps during encoding that have limited pixel intensity approximation ability. In order to increase the image quality further, non-linear affine maps can be used that generalizes the pixel intensity approximation and generates much better approximation. Here, a fractal based technique for image compression using non-linear contractive affine maps has been proposed that applies adaptive quadtree partitioning to partition image in a context dependent way to enhance decoded image quality. The technique partitions twice an image to be compressed to obtain collection of ranges and domains and finds the highest matching non-linear affine transformed domain of each range. The corresponding affine parameters are kept in the compressed file. However, a range may be broken into sub-ranges using adaptive quadtree partitioning for unavailability of enough matching domains and repeat the same on those. The comparative results show that the proposed technique greatly improves the decoded image quality than existing techniques and also maintains the high compression ratios. Two variants have also been proposed that improve compression ratio of the proposed technique without any degradation of image quality using loss-less coding. Keywords Fractal compression · Adaptive quadtree partition · Affine map · Non-linear affine map · Contractive transform · Compression ratio · Image quality
1 Introduction Multimedia uses a combination of image, audio, text, video and animation and its security [19, 20, 49] becomes one of the interesting areas of research today. Again, the sizes of multimedia data are much larger than classical media tools. As a result, it takes huge Utpal Nandi
[email protected] 1
Department of Computer Science, Vidyasagar University, Midnapore, West Bengal, Pin-721102, India
Multimedia Tools and Applications
storage space and high bandwidth to transfer over the network. Therefore, size reduction of multimedia data is also very important. Moreover, image size deduction that is the basis of multimedia data also depicts its significance. The compression techniques [32] provide a good solution to these problems. Several techniques and standards already developed to reduce the image size of multimedia data. The compression techniques are lossless or lossy [32]. Mainly the lossy techniques are applied for image coding like DCT based JPEG [39] and DWT based wavelet [2, 7, 8, 35, 36] image coding. The DCT based JPEG coding is res
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