Operations that can significantly alter the low-frequency coefficients of DCT are essentially about "changing overall brightness/contrast, reshaping large-scale structures, or performing strong geometric/resampling transformations." Among them, non-uniform scaling/perspective, strong low-pass filtering, global tone mapping (exposure/contrast/gamma), large-area borders/occlusion/cropping, and extreme compression quantization have the strongest impact; uniform scaling and small-angle rotation typically have moderate to minor effects, depending on interpolation and whether cropping/filling is applied.
Key Mechanisms of Impact
DCT and 2D Fourier are similar in nature: image energy tends to concentrate in the low-frequency region at the top-left corner, where low frequencies carry the average brightness and large-scale brightness contours. Therefore, any processing that changes "overall illumination or large-scale structure" will redistribute low-frequency energy.
Characteristic properties of 2D transforms: rotation in the spatial domain causes an equal-angle rotation of the frequency spectrum, while scaling causes corresponding stretching/compression of the spectrum. Thus, geometric operations cause energy migration and mixing in the low-frequency neighborhood, with the impact depending on whether scaling is uniform, the rotation angle, and the resampling kernel.
Strong Impact (from strong to weak)
Global exposure/contrast/gamma/tone mapping: raises or lowers DC (average brightness) and reshapes the light-dark relationship of large areas. Nonlinear gamma also introduces harmonics in the frequency domain and redistributes energy, significantly altering the pattern of low-frequency coefficients.
Large-scale low-pass/blurring (Gaussian/mean, etc.): low-pass suppresses high frequencies and relatively enhances low frequencies, systematically changing the magnitude and proportion of low-frequency blocks, even if visually it only appears "smoother."
Large-area borders/occlusion/gradients (including vignetting, wide horizontal watermarks): superimposes slowly varying or step-shaped brightness patterns, changes the overall average brightness, and introduces new low-frequency patterns, affecting low-frequency components in groups (similarly for cropping/layout changes).
Heavy cropping/content removal (including recomposition): removes original large-scale structures and changes global statistics, causing detectable changes in DCT/DFT statistics and a significant restructuring of low-frequency distribution.
Non-uniform scaling/perspective/affine (including shearing): geometric axial stretching or perspective compression redistributes low-frequency energy directionally and changes spectral density. Compared to uniform scaling, it is more likely to significantly alter low-frequency block structure.
Moderate Impact
Rotation (without cropping or with padding): spectral rotation by the same angle causes low-frequency energy to "leak/mix" among lower-order terms in various directions. Small angles typically have a moderate impact; if accompanied by cropping, the impact is amplified.
Uniform scaling followed by resampling: spectrum stretching and interpolation act together. When resampling to the same size, the overall low-frequency pattern often remains, but coefficient values change in magnitude (depending on the kernel).
Resampling/interpolation kernel choice (nearest neighbor/bilinear/bicubic/Lanczos/windowed sinc): different kernels have different frequency responses (passband/transition band/stopband), which alter low-frequency magnitude and leakage, leading to varying low-frequency coefficients depending on the method.
Extreme compression quantization (low-quality JPEG): at low bitrates, not only high frequencies but also the low-frequency neighborhood becomes "stepped/coarsened," causing visible shifts in low-frequency values (related to the quantization matrix and HVS perception).
Color-to-luminance pipeline changes (RGB→YCbCr matrix, white balance/color space differences): if DCT is applied to the luminance channel, changes in average/relative luminance mapping affect DC and low-frequency energy, thereby altering the distribution of low-frequency blocks.
Weak Impact (usually only significant when combined with other factors)
Small-angle rotation with avoided cropping (padding, smart edge processing): energy is mainly redistributed within the low-frequency neighborhood. If comparison uses energy aggregation rather than single coefficients, the impact is relatively weak.
Small-factor uniform scaling (high-quality interpolation and normalization to a uniform size): the overall low-frequency shape remains largely stable; amplitude and detail differences are more due to the frequency response of the interpolation.
Mild sharpening/mild denoising: mainly changes mid/high frequencies (edges and textures), with limited impact on the low-frequency skeleton, unless extreme parameters or large-scale processing are used.
Special Supplement (Low-Frequency-Related "Combination Moves")
Layout-level changes (adding letterbox/pillarbox/PiP): equivalent to superimposing large-scale shapes and brightness steps—this is one of the most sensitive scene modifications for low frequencies, often appearing together with cropping/scale changes.
Complex geometric pipeline (perspective → rotation → resampling): superimposed rotation/affine/perspective and multiple interpolations repeatedly transfer energy between low and mid frequencies, with a cumulative effect often greater than any single step.
Ranking Overview (from strong to weak, in terms of "impact on low-frequency coefficients under typical parameters")
Strong: global exposure/contrast/gamma ≈ large-scale low-pass/blur ≈ large-area borders/occlusion/gradients ≈ heavy cropping/content removal ≈ non-uniform scaling/perspective/affine.
Moderate: rotation (without cropping, small angle) ≈ uniform scaling + resampling ≈ interpolation kernel differences ≈ extreme compression quantization ≈ color-to-luminance pipeline changes.
Weak: small-angle rotation with avoided cropping, slight uniform scaling, mild sharpening/denoising (gentle parameters).
Note: The above ranking reflects "relative trends"; actual strength heavily depends on parameters and implementation (e.g., whether rotation is cropped, interpolation kernel choice, compression quality, blur kernel size, etc.), but the overall rules are consistent with the rotation/scaling properties of the 2D frequency domain and the frequency response of resampling.