RingingOvershoot

Description

Create ringing or overshoot artifacts by convolving the image with a 2D sinc filter.

    This transform simulates the ringing artifacts that can occur in digital image processing,
    particularly after sharpening or edge enhancement operations. It creates oscillations
    or overshoots near sharp transitions in the image.

    Args:
        blur_limit (tuple[int, int] | int): Maximum kernel size for the sinc filter.
            Must be an odd number in the range [3, inf).
            If a single int is provided, the kernel size will be randomly chosen
            from the range (3, blur_limit). If a tuple (min, max) is provided,
            the kernel size will be randomly chosen from the range (min, max).
            Default: (7, 15).
        cutoff (tuple[float, float]): Range to choose the cutoff frequency in radians.
            Values should be in the range (0, π). A lower cutoff frequency will
            result in more pronounced ringing effects.
            Default: (π/4, π/2).
        p (float): Probability of applying the transform. Default: 0.5.

    Targets:
        image

    Image types:
        uint8, float32

    Number of channels:
        Any

    Note:
        - Ringing artifacts are oscillations of the image intensity function in the neighborhood
          of sharp transitions, such as edges or object boundaries.
        - This transform uses a 2D sinc filter (also known as a 2D cardinal sine function)
          to introduce these artifacts.
        - The severity of the ringing effect is controlled by both the kernel size (blur_limit)
          and the cutoff frequency.
        - Larger kernel sizes and lower cutoff frequencies will generally produce more
          noticeable ringing effects.
        - This transform can be useful for:
          * Simulating imperfections in image processing or transmission systems
          * Testing the robustness of computer vision models to ringing artifacts
          * Creating artistic effects that emphasize edges and transitions in images

    Mathematical Formulation:
        The 2D sinc filter kernel is defined as:

        K(x, y) = cutoff * J₁(cutoff * √(x² + y²)) / (2π * √(x² + y²))

        where:
        - J₁ is the Bessel function of the first kind of order 1
        - cutoff is the chosen cutoff frequency
        - x and y are the distances from the kernel center

        The filtered image I' is obtained by convolving the input image I with the kernel K:

        I'(x, y) = ∑∑ I(x-u, y-v) * K(u, v)

        The convolution operation introduces the ringing artifacts near sharp transitions.

    Examples:
        >>> import numpy as np
        >>> import albumentations as A
        >>> image = np.random.randint(0, 256, [100, 100, 3], dtype=np.uint8)

        # Apply ringing effect with default parameters
        >>> transform = A.RingingOvershoot(p=1.0)
        >>> ringing_image = transform(image=image)['image']

        # Apply ringing effect with custom parameters
        >>> transform = A.RingingOvershoot(
        ...     blur_limit=(9, 17),
        ...     cutoff=(np.pi/6, np.pi/3),
        ...     p=1.0
        ... )
        >>> ringing_image = transform(image=image)['image']

    References:
        - Ringing artifacts: https://en.wikipedia.org/wiki/Ringing_artifacts
        - Sinc filter: https://en.wikipedia.org/wiki/Sinc_filter
        - "The Importance of Ringing Artifacts in Image Processing" by Jae S. Lim, 1981
        - "Digital Image Processing" by Rafael C. Gonzalez and Richard E. Woods, 4th Edition
    

Parameters

• blur_limit: int | tuple[int, int] (default: (7, 15))
• cutoff: tuple[float, float] (default: (0.7853981633974483, 1.5707963267948966))
• p: float (default: 0.5)

Targets

• Image