DCT Domain Image Resizing via Non-Uniform Sampling
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Solution Overview
Problem
Existing arbitrary ratio image resizing methods in the DCT domain are computationally expensive and difficult to implement for practical applications, especially when the resizing ratio varies and requires complex matrix calculations and fast DCT/IDCT operations for different image dimensions.
Innovation Solution
A method for arbitrary ratio resizing of compressed images in the DCT domain involving non-uniform sampling and resampling of DCT coefficients, using scaling parameters and inverse DCT lengths to achieve efficient resizing with reduced computational complexity, and maintaining synchronization between color components.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If spatial domain resizing is performed through low-pass filtering and downsampling, then image quality is maintained, but computational cost is high due to full decoding and recompression
Solution Approach 1:
The invention extracts and processes only the essential DCT coefficients needed for resizing, rather than fully decoding the entire image to pixel domain. By working directly with compressed DCT coefficients and selectively transforming only necessary blocks, the method maintains image quality while avoiding the computational burden of complete decompression and recompression.
Solution Approach 2:
The invention transitions from spatial domain operations to frequency domain operations. Instead of performing low-pass filtering and downsampling in the pixel domain, the method operates on DCT coefficients in the frequency domain, enabling direct resizing without full decoding while preserving image quality through controlled coefficient manipulation.
2Device complexity
If arbitrary ratio resizing is performed in DCT domain using existing methods, then computational complexity is reduced, but implementation difficulty increases due to complex matrix calculations and fast DCT/IDCT operations
Solution Approach 1:
The invention segments the resizing operation into discrete block-level DCT coefficient transformations. Instead of requiring complex global matrix calculations, the method processes individual 8x8 blocks independently using standardized DCT/IDCT operations, significantly simplifying implementation while maintaining arbitrary ratio resizing capability.
Solution Approach 2:
The invention changes the approach from requiring fast DCT/IDCT implementations at every possible length to using only standard fixed-length DCT/IDCT operations (e.g., 8-point). By adjusting which blocks undergo transformation and how coefficients are sampled, the method achieves arbitrary resizing ratios using conventional, easily implementable DCT algorithms.
3Adaptability or versatility
If different resizing ratios are required for different images, then adaptability is improved, but device complexity increases due to requiring multiple matrices and fast DCT/IDCT at every length
Solution Approach 1:
The invention creates a universal resizing method that handles arbitrary ratios using the same standardized DCT/IDCT operations. A single implementation framework processes all resizing ratios by selectively applying transformations to different blocks and sampling coefficients at different rates, eliminating the need for multiple pre-calculated matrices or specialized fast DCT implementations for each ratio.
Data Source
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AI summary
A method and system for arbitrary resizing of a compressed image in the discrete cosine transform (DCT) domain. First and second scaling parameters P and Q are determined in accordance with the block numbers L and M and the scaling ratio UM or M/L. A nonuniform, or uneven, sampling in the DCT domain is then applied to coefficients of successive blocks in the compressed image in accordance with the scaling parameters. In an embodiment, P blocks are sampled and transformed from a given block length to |P| according to a |P|-point IDCT, while Q blocks are sampled and transformed from a given block length to |Q| according to a |Q|-point IDCT. The non-uniformly sampled and transformed pixel domain samples are then regrouped into a predetermined block size and transformed back to generate the DCT coefficient of the compressed image. The proposed method significantly reduces the computational complexity compared with other DCT domain arbitrary ratio image resizing approach. It also facilitates the practical implementations since only the fast implementations of IDCT with length N (1 <N<9) and DCT with length 8 are required.