docs/detector/fft.md

#  Fast Fourier Transform (FFT) Detector

```python
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.

---

## **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`. |

---

## **Returns**

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

---

## **Step-by-Step Explanation**

### 1. **Grayscale Conversion**

All images are converted to grayscale:

```python
gray_image = image.convert("L")
```

### 2. **Resize**

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

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

### 3. **FFT Calculation**

Compute the 2D Discrete Fourier Transform:

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

```python
fft_result = fft2(image_array)
```

### 4. **Shift Zero Frequency to Center**

Use `fftshift` to center the zero-frequency component:

```python
fft_shifted = fftshift(fft_result)
```

### 5. **Magnitude Spectrum**

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

```python
magnitude_spectrum = np.abs(fft_shifted)
```

### 6. **Normalization**

Normalize the spectrum to avoid scale issues:

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

```python
normalized_spectrum = magnitude_spectrum / max_magnitude
```

### 7. **High-Frequency Detection**

High-frequency components are defined as:

$$
\text{Mask}(u,v) = 
\begin{cases}
1 & \text{if } \text{Normalized}(u,v) > 0.5 \\
0 & \text{otherwise}
\end{cases}
$$

```python
high_freq_mask = normalized_spectrum > 0.5
```

### 8. **Proportion Calculation**

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

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

### 9. **Threshold Decision**

If the ratio exceeds the threshold:

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

```python
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.


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