Collage creation involves grid-based layout algorithms and image compositing techniques that are closely related to broader problems in computational geometry and computer science, particularly the bin packing problem.

Grid-based layout algorithms define how a rectangular canvas is subdivided into cells for placing images. The simplest approach is a uniform grid where all cells are equal size, but more sophisticated layouts use weighted grids where certain cells span multiple rows or columns to create visual hierarchy. The layout algorithm must solve several constraints simultaneously: fill the entire canvas without gaps, maintain pleasing proportions for each cell, and accommodate images of varying aspect ratios. This is often implemented as a constraint satisfaction problem where the algorithm tries to minimize wasted space and aspect ratio distortion across all cells.

Image compositing is the process of combining multiple images into a single output, and it involves coordinate transformation, scaling, and blending. For each cell in the layout, the source image must be scaled to fit the cell dimensions. When the source aspect ratio differs from the cell aspect ratio, the algorithm must choose between fitting (showing the entire image with letterboxing), filling (covering the entire cell with some cropping), or stretching (distorting the image to match exactly). Most collage tools use the fill approach with center-weighted cropping, which ensures cells are completely filled while preserving the most important central content of each image.

The bin packing problem, one of the classic NP-hard problems in computer science, is directly relevant to advanced collage layouts. The problem asks: given a collection of items of various sizes, how can they be packed into a container of fixed dimensions with minimal wasted space? For collages, the items are images with different aspect ratios, and the container is the output canvas. Optimal bin packing would arrange images of varying proportions to fill the canvas perfectly, but finding the mathematically optimal solution is computationally intractable for large numbers of images. Practical collage makers use heuristic algorithms like first-fit decreasing (placing the largest items first) or guillotine cutting (recursively splitting the canvas with horizontal or vertical cuts) to produce good-enough layouts quickly. These same algorithms are used in industrial applications like cutting fabric from bolts, arranging printed pages on press sheets, and packing shipping containers.