Multiresolution graph Fourier transform for compression of piecewise smooth images

Area of Science:

• Image processing
• Graph signal processing
• Computer vision

Background:

• Piecewise smooth (PWS) images, like depth maps, have distinct features such as sharp edges and smooth interiors.
• Traditional compression methods struggle to efficiently represent these unique signal characteristics.

Purpose of the Study:

• To develop an adaptive compression method for PWS images using Graph Fourier Transforms (GFTs).
• To minimize the total signal representation cost by optimizing transform selection and reducing computational complexity.

Main Methods:

• Utilizing graph optimization techniques like spectral clustering and minimum graph cuts to select optimal GFTs for pixel blocks.
• Implementing a multiresolution approach with low-pass filtering, downsampling, and adaptive upsampling with arithmetic edge coding.
• Employing pre-computed GFTs for reduced computational complexity during encoding and decoding.

Main Results:

• The proposed multiresolution-GFT scheme achieves superior compression performance compared to H.264 intra coding.
• Experimental results show an average improvement of 6.8 dB in peak signal-to-noise ratio (PSNR) at the same bit rate for depth maps and computer-graphics images.
• The method effectively preserves sharp object boundaries while compressing slowly varying regions.

Conclusions:

• Adaptive GFTs offer a powerful tool for compressing PWS images, outperforming conventional methods.
• The proposed multiresolution strategy and computational optimizations make the technique practical for real-world applications.
• This approach advances the field of image compression by leveraging graph signal processing for complex image structures.