Methods for Estimating Motion Blur Direction and Motion Blur Length Parameters

Motion blur is a common degradation phenomenon in image acquisition, primarily caused by relative motion between the camera and the subject. Accurate estimation of motion blur direction and length parameters is a critical step in image restoration. The following introduces several commonly used estimation methods:

### 1. Spectral Analysis-Based Estimation Method Motion blur creates distinct stripe patterns in the image frequency spectrum. By analyzing the Fourier transform (or log power spectrum) of the blurred image, one can observe parallel stripes perpendicular to the blur direction. The stripe spacing correlates with the blur length, while the stripe orientation has a 90-degree relationship with the motion blur direction. Implementation typically involves using FFT functions (e.g., numpy.fft.fft2 in Python) and analyzing the spectral magnitude for directional patterns.

### 2. Radon Transform Method The Radon transform detects linear features in images. By applying Radon transform to the edge map or spectrum of the blurred image, one can identify the direction of energy concentration, which corresponds to the motion blur direction. The blur length can be calculated from the peak intervals in the transform results. Code implementation often uses radon transform functions (e.g., scikit-image's radon transform) followed by peak detection algorithms to identify dominant directions.

### 3. Cepstrum Analysis Method Cepstrum is another effective tool for blur parameter estimation. In the cepstral domain, the periodic characteristics of the blur kernel manifest as distinct peaks. By analyzing the position of these peaks, one can infer the blur length, while the peak direction aligns with the blur direction. Implementation involves computing the inverse Fourier transform of the logarithm of the power spectrum and applying peak detection techniques to identify blur parameters.

### 4. Gradient-Based Local Estimation Method Using gradient information from blurred images enables extraction of local motion blur characteristics. For example, by calculating the gradient direction histogram, one can identify the dominant motion direction, while the blur length can be inferred from statistical properties of gradient magnitudes. This approach typically utilizes Sobel or Prewitt operators for gradient computation and histogram analysis functions for direction estimation.

### 5. Machine Learning and Deep Learning Methods In recent years, deep learning-based approaches (such as CNN or GAN) have been applied to blur parameter estimation. These methods train networks to directly regress blur direction and length from blurred images, demonstrating superior performance in complex scenarios compared to traditional methods. Implementation involves designing convolutional neural networks with regression outputs and training on synthetic or real blurred image datasets.

### Summary Estimating motion blur parameters is a crucial prerequisite for image restoration. Traditional methods (like spectral analysis and Radon transform) are computationally efficient and suitable for simple scenarios, while deep learning methods show advantages under complex blur conditions. In practical applications, combining multiple methods can improve estimation accuracy through ensemble techniques or hybrid approaches.