Arbitrary Ratio Image Resizing in DCT Domain
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Solution Overview
Problem
Existing arbitrary ratio image resizing methods in the discrete cosine transform (DCT) domain are computationally expensive and difficult to implement, especially for practical applications where resizing ratios vary and require complex matrix calculations and fast DCT/IDCT operations.
Innovation Solution
A method for arbitrary ratio resizing of compressed images in the DCT domain involving non-uniform sampling and resampling based on scaling parameters, with IDCT operations performed at specific lengths and permutation schemes to maintain synchronization and consistency across components, reducing computational complexity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If arbitrary ratio image resizing is performed in the DCT domain using conventional methods, then image quality is maintained, but computational complexity increases significantly
Solution Approach 1:
The image is divided into 8×8 DCT blocks, and the resizing operation is segmented into separate scanning and resampling stages. Each block is processed independently through non-uniform sampling in the DCT domain, avoiding the need for complex full-image transformations and reducing overall computational burden.
Solution Approach 2:
The patent introduces an intermediary scanning process that converts DCT coefficients into a resampled format before final image reconstruction. This intermediary step uses simple scaling operations rather than complex mathematical transformations, significantly reducing computational complexity while preserving image quality.
2Adaptability or versatility
If arbitrary ratio resizing is implemented with varying resizing ratios, then adaptability improves, but implementation difficulty increases due to required matrix calculations
Solution Approach 1:
The patent changes the approach from using fixed transformation matrices to using variable scanning parameters that adapt to any resizing ratio. By modifying the scan line spacing and block selection based on the desired output dimensions, the system achieves arbitrary ratio resizing without requiring pre-computed matrices for each possible ratio.
Solution Approach 2:
Instead of transforming the image to fit the target size through complex matrix operations, the patent inverts the approach by scanning and selecting coefficients that directly correspond to the target dimensions. This reverse engineering of the transformation process simplifies implementation for any arbitrary ratio.
3Measurement precision
If full DCT/IDCT operations are performed for each resizing ratio, then accuracy is maintained, but processing speed decreases
Solution Approach 1:
The patent performs only the necessary portion of DCT/IDCT operations by working directly with existing DCT coefficients through selective scanning and resampling. Instead of performing complete transform cycles for each resizing operation, it applies partial processing that maintains accuracy for the specific resizing task while significantly reducing computation time.
Data Source
AI summary
To resize a compressed image, first and second scaling parameters P and Q are determined in accordance with the block numbers L and M and the scaling ratio L/M or M/L. A non-uniform, 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.