Add vs Intersect Selection in GIMP Explained

In GNU Image Manipulation Program (GIMP), selections function as mathematical sets of pixel coordinates and opacity values. The fundamental difference between adding to a selection and intersecting with a selection lies in the underlying set theory and Boolean algebra applied to these pixels: adding represents a set union where areas are combined, whereas intersecting represents a set intersection where only the common, overlapping areas are preserved.

Selections as Mathematical Sets

To understand the difference, consider a GIMP canvas as a universal set of pixels, \(U\). A selection can be defined as a subset of pixels, where each pixel has a selection intensity value ranging from 0 (completely unselected) to 1 (fully selected), or 0 to 255 in 8-bit channel terms. When you have an existing selection (\(A\)) and create a new selection area (\(B\)), GIMP uses distinct operations to determine the resulting selection (\(R\)).

Adding to a Selection (Set Union)

Adding to a selection corresponds to the mathematical Union (\(A \cup B\)) and uses Boolean OR logic.

• Binary Logic: A pixel is included in the new selection if it exists in set \(A\), set \(B\), or both. \[\text{Pixel} \in R \iff \text{Pixel} \in A \lor \text{Pixel} \in B\]
• Intensity Calculation: For feathered or anti-aliased selections with fractional values, GIMP adds the intensity of the selections, typically clamping the result at the maximum value: \[R(x, y) = \min(1.0, A(x, y) + B(x, y))\]
• Practical Result: The selected area expands or remains the same size. It never decreases.

Intersecting a Selection (Set Intersection)

Intersecting a selection corresponds to the mathematical Intersection (\(A \cap B\)) and uses Boolean AND logic.

• Binary Logic: A pixel is included in the final selection only if it exists concurrently in both set \(A\) and set \(B\). \[\text{Pixel} \in R \iff \text{Pixel} \in A \land \text{Pixel} \in B\]
• Intensity Calculation: For feathered selections, GIMP multiplies the normalized opacity values of both sets: \[R(x, y) = A(x, y) \times B(x, y)\] If a pixel has a value of 0 in either selection, the product is 0, completely deselecting that pixel.
• Practical Result: The selected area shrinks or remains the same size. It can never grow beyond the boundaries of the smaller selection.

Key Mathematical Differences