maximumfilter

Maximum filter is a nonlinear image processing operation that replaces each pixel with the maximum value found in a local neighborhood around that pixel. The neighborhood is defined by a window, often a square of odd size such as 3x3 or 5x5, or by an arbitrary footprint. The result emphasizes bright regions within the window and smooths out small dark speckle.

In grayscale mathematics, the maximum filter is equivalent to dilation with a flat structuring element. Given an image I and a neighborhood N, the output at position x is J(x) = max_{y in N(x)} I(y). This makes it a special case of morphological dilation, with the window shape determining the footprint. The minimum filter is the dual operation, using the minimum value in the neighborhood.

Boundary handling varies between implementations. Common approaches pad the image, using modes such as reflect, constant, nearest, or wrap, and then apply the local maximum. The window size and shape determine the degree of smoothing and detail preservation.

Properties and effects include robustness to pepper (dark) noise, since dark outliers are raised to the neighborhood maximum, while salt (bright) noise can be spread or amplified. The filter is often used for noise reduction of dark speckle, for pre-processing in feature detection, and as a step in certain morphological pipelines.

Implementations exist in many libraries, such as SciPy’s ndimage.maximum_filter, OpenCV’s dilation with a rectangular kernel, and PIL’s maximum filter. It is a fundamental tool in image processing and computer vision, typically chosen when bright feature preservation is desired.