docs/detector/fft.md

Fast Fourier Transform (FFT) Detector

def run_fft(image: Image.Image, threshold: float = 0.92) -> bool:

Overview

The run_fft function performs a frequency domain analysis on an image using the Fast Fourier Transform (FFT) to detect possible AI generation or digital manipulation. It leverages the fact that artificially generated or heavily edited images often exhibit a distinct high-frequency pattern.

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Parameters

Parameter	Type	Description
image	PIL.Image.Image	Input image to analyze. It will be converted to grayscale and resized.
threshold	float	Proportion threshold of high-frequency components to flag the image. Default is 0.92.

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Returns

Type	Description
bool	True if image is likely AI-generated/manipulated; otherwise False.

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Step-by-Step Explanation

1. Grayscale Conversion

All images are converted to grayscale:

gray_image = image.convert("L")

2. Resize

The image is resized to a fixed $512 \times 512$ for uniformity:

resized_image = gray_image.resize((512, 512))

3. FFT Calculation

Compute the 2D Discrete Fourier Transform:

$$F(u,v)=\sum _{x=0}^{M-1}\sum _{y=0}^{N-1}f(x,y)\cdot e^{-2\pi i(\frac{ux}{M}+\frac{vy}{N})}F(u,\; v)\; =\; \backslash sum\_\{x=0\}^\{M-1\}\; \backslash sum\_\{y=0\}^\{N-1\}\; f(x,\; y)\; \backslash cdot\; e^\{-2\backslash pi\; i\; \backslash left(\; \backslash frac\{ux\}\{M\}\; +\; \backslash frac\{vy\}\{N\}\; \backslash right)\}$$

fft_result = fft2(image_array)

4. Shift Zero Frequency to Center

Use fftshift to center the zero-frequency component:

fft_shifted = fftshift(fft_result)

5. Magnitude Spectrum

$$\mathrm{\mid }F(u,v)\mathrm{\mid }=\sqrt{{\mathrm{\Re }}^2+{\mathrm{\Im }}^2}|F(u,\; v)|\; =\; \backslash sqrt\{\backslash Re^2\; +\; \backslash Im^2\}$$

magnitude_spectrum = np.abs(fft_shifted)

6. Normalization

Normalize the spectrum to avoid scale issues:

$$\text{Normalized}(u,v)=\frac{\mathrm{\mid }F(u,v)\mathrm{\mid }}{\max (\mathrm{\mid }F(u,v)\mathrm{\mid })}\backslash text\{Normalized\}(u,v)\; =\; \backslash frac\{|F(u,v)|\}\{\backslash max(|F(u,v)|)\}$$

normalized_spectrum = magnitude_spectrum / max_magnitude

7. High-Frequency Detection

High-frequency components are defined as:

high_freq_mask = normalized_spectrum > 0.5

8. Proportion Calculation

$$\text{Ratio}=\frac{\sum \text{Mask}}{\text{Total pixels}}\backslash text\{Ratio\}\; =\; \backslash frac\{\backslash sum\; \backslash text\{Mask\}\}\{\backslash text\{Total\; pixels\}\}$$

high_freq_ratio = np.sum(high_freq_mask) / normalized_spectrum.size

9. Threshold Decision

If the ratio exceeds the threshold:

$$\text{is\_fake}=(\text{Ratio}>\text{Threshold})\backslash text\{is\backslash \_fake\}\; =\; (\backslash text\{Ratio\}\; >\; \backslash text\{Threshold\})$$

is_fake = high_freq_ratio > threshold

it is implemented in the api

Running Locally

Just put the function in a notebook or script file and run it with your image. It works well for basic images.

Worked By

Pujan Neupane