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Georges Matheron was a mathematician who developed geostatistics from problems of estimating mineral resources using spatially distributed measurements. His work put kriging and spatial variability into a systematic probabilistic framework. He also developed mathematical morphology with Jean Serra, connecting geometric operations on sets with image processing.^[ref] In kriging, nearby measurements are combined using weights determined by a model of spatial dependence. The point is to account for both proximity and redundancy: many closely clustered observations need not contain as much new information as equally many well-separated observations.

A mathematician.^[ref]

Jean Serra developed methods in mathematical morphology, using geometric operations on sets to analyze images. His 1986 introductory paper presents the subject as a mathematical approach to image structure.^[ref]

In a binary image, the foreground can be treated as a set. Morphological erosion keeps positions where a translated test shape fits completely inside it; morphological dilation takes the union of translated copies of that shape placed on foreground points. These operations connect local shape tests with global effects such as removing narrow features or joining nearby regions. Their geometric assumptions are explicit, so the operation can be chosen for the scale and shape being investigated.

Mathematical morphology studies shape-transforming operations defined through a chosen structuring element. For foreground pixels represented as a set $A$ and a finite footprint $B$, morphological dilation iswhile morphological erosion is $A\ominus B=\{x:x+B\subseteq A\}$. Dilation adds footprint translates around the foreground; erosion retains placements whose entire footprint fits.

For a one-dimensional example, $A=\{0,1,2\}$ and $B=\{0,1\}$ give dilation $\{0,1,2,3\}$ and erosion $\{0,1\}$. Morphological opening, erosion followed by dilation with the same footprint, removes an isolated set $\{0,2\}$ for that footprint because neither placement contains two consecutive points. grayscale variants use local minima and maxima rather than binary membership. The footprint and boundary conventions determine the exact operation.^[ref]

A structuring element specifies the neighborhood shape and reference position used by an operation in mathematical morphology. In binary image processing, represent it as a finite set $B$ of offsets. Morphological erosion tests where a translated $B$ fits inside the foreground; morphological dilation adds its offsets to foreground positions.

A three-by-three square uses all nine offsets around its center, while a cross uses the center and its four horizontal or vertical neighbors. They treat diagonal features differently despite having the same width. Scikit-image's morphology demonstration uses a disk-shaped footprint whose radius controls the affected scale.^[ref] The reference position matters for asymmetric shapes, and finite-image border rules must specify how neighborhoods outside the image are treated.