Operations that can significantly change low-frequency DCT coefficients are essentially those that “alter overall brightness/contrast, reshape large-scale structures, or apply strong geometric/resampling transformations.” Among them, non-uniform scaling/perspective, strong low-pass blur, global tone mapping (exposure/contrast/gamma), large-area borders/occlusion/heavy cropping, and extreme compression quantization have the strongest impact; uniform scaling and small-angle rotation usually have a moderate to smaller impact, depending on interpolation and whether cropping/padding is involved.
Key points of the impact mechanism
DCT is similar in nature to the 2D Fourier transform: image energy tends to concentrate in the low frequencies in the upper-left corner, and low frequencies carry average brightness and large-scale light/dark 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 the frequency-domain spectrum to rotate by the same angle, while scaling causes the spectrum to scale accordingly. Therefore, geometric operations cause energy migration and mixing in the low-frequency neighborhood, with the impact depending on whether the scaling is uniform, the angle size, and the resampling kernel.
Strong impact (from strongest to weakest)
Global exposure/contrast/gamma/tone mapping: raises or lowers the DC component (average brightness) and reshapes the light/dark relationships of large regions. Nonlinear gamma also introduces harmonics in the frequency domain and redistributes energy, significantly changing the pattern of low-frequency coefficients.
Large-scale low-pass filtering/blur (Gaussian/mean, etc.): low-pass filtering suppresses high frequencies and relatively strengthens low frequencies, causing systematic changes in the amplitude and proportion of low-frequency blocks, even if visually it only appears “smoother.”
Large-area borders/occlusion/gradients (including vignetting and wide banner watermarks): superimposes slowly varying or step-like brightness patterns, changes overall average brightness, and introduces new low-frequency patterns, affecting low frequencies in groups (the same applies to cropping/layout changes).
Heavy cropping/content removal (including frame rearrangement): removes existing large-scale structures and changes global statistics. DCT/DFT statistics show detectable changes, and the low-frequency distribution is significantly restructured.
Non-uniform scaling/perspective/affine transformations (including shear): geometric axial stretching or perspective compression redistributes low-frequency energy directionally and changes spectral density, making it more likely to noticeably alter the structure of low-frequency blocks than uniform scaling.
Moderate impact
Rotation (without cropping or with padding): equal-angle rotation of the spectrum causes low-frequency energy to “leak/mix” among low-order terms in different directions. Small angles usually have a moderate impact; if cropping is also involved, the impact is amplified.
Uniform scaling followed by unified resampling: spectral scaling and interpolation work together. When resampled to the same size, the overall low-frequency pattern often remains, but coefficient values change in amplitude (depending on the kernel).
Choice of resampling/interpolation kernel (nearest neighbor/bilinear/bicubic/Lanczos/windowed sinc): differences in the frequency response of different kernels (passband/transition band/stopband) change low-frequency amplitude and leakage, causing low-frequency coefficients to vary by method.
Extreme compression quantization (low-quality JPEG): at low bitrates, not only are high frequencies strongly quantized, but the low-frequency neighborhood is also “stepped/coarsened,” producing visible shifts in low-frequency values (related to the quantization matrix and HVS).
Changes in the color-to-luminance pipeline (RGB→YCbCr matrix, white balance/color space differences): if DCT is performed on the luminance channel, changes in average/relative luminance mapping affect the DC component and low-frequency energy, thereby changing the distribution of low-frequency blocks.
Weaker impact (usually significant only when combined with other factors)
Small-angle rotation while avoiding cropping (with padding and intelligent edge handling): energy is mainly redistributed within the low-frequency neighborhood. If comparison uses energy aggregation rather than individual coefficients, the impact is relatively weak.
Small-scale uniform scaling (high-quality interpolation and normalization to a unified size): the overall low-frequency shape is largely stable, and differences in amplitude and details mainly come from the frequency-response characteristics of the interpolation.
Mild sharpening/mild denoising: mainly changes mid-to-high frequencies (edges and textures), with limited impact on the low-frequency skeleton unless extreme parameters or large-scale processing are used.
Special additions (“combo moves” related to low frequencies)
Layout-level changes (adding black bars for letterbox/side bars for pillarbox/picture-in-picture PiP): equivalent to superimposing large-scale shapes and brightness steps, making this one of the scene modifications to which low frequencies are most sensitive, often occurring together with cropping/scale changes.
Complex geometric pipelines (perspective→rotation→resampling): combining rotation/affine/perspective transformations with multiple interpolations transfers energy between low and mid frequencies multiple times, and the cumulative effect is often greater than any single-step transformation.
Overall ranking (from strongest to weakest, based on the “impact on low-frequency coefficients under typical parameters”)
Strong: global exposure/contrast/gamma ≈ large-scale low-pass filtering/blur ≈ large-area borders/occlusion/gradients ≈ heavy cropping/content removal ≈ non-uniform scaling/perspective/affine transformations.
Moderate: rotation (small angle without cropping) ≈ uniform scaling + resampling ≈ interpolation-kernel differences ≈ extreme compression quantization ≈ color→luminance pipeline changes.
Weak: small-angle rotation while avoiding cropping, slight uniform scaling, mild sharpening/denoising (with moderate parameters).
Note: the above ranking represents “relative trends.” The actual strength highly depends on parameters and implementation (such as whether rotation involves cropping, the choice of interpolation kernel, compression quality, blur-kernel size, etc.), but the overall pattern is consistent with the rotation/scaling properties of the 2D frequency domain and the frequency response of resampling.