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A summed-area table is a data structure and algorithm for quickly and efficiently generating the sum of values in ... for example, the images have dimension = ...
Finding the sum of the shaded rectangular area. One of the contributions of Viola and Jones was to use summed-area tables, [3] which they called integral images. Integral images can be defined as two-dimensional lookup tables in the form of a matrix with the same size of the original image. Each element of the integral image contains the sum of ...
Summed-area tables can conserve memory and provide more resolutions. However, they again hurt cache coherence, and need wider types to store the partial sums, which are larger than the base texture's word size. Thus, modern graphics hardware does not support them.
Integral image application example: Image title: Example of the use of an integral image (2) of an order-6 magic square (1) to find the sum of a subrectangle of values by CMG Lee. Each spot shows the sum of the values inside the rectangle bounded by dashed/dotted lines of the same colour. Width: 100%: Height: 100%
If summed area tables are used to build the 3 tables, sum over , sum over , and sum over , then the runtime complexity is the maximum of (O(N_pixels), O(N_bins*N_bins)). Note that if only coarse resolution is needed in terms of threshold, N_bins can be reduced.
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Prefix sums are trivial to compute in sequential models of computation, by using the formula y i = y i − 1 + x i to compute each output value in sequence order. However, despite their ease of computation, prefix sums are a useful primitive in certain algorithms such as counting sort, [1] [2] and they form the basis of the scan higher-order function in functional programming languages.
Shoelace scheme for determining the area of a polygon with point coordinates (,),..., (,). The shoelace formula, also known as Gauss's area formula and the surveyor's formula, [1] is a mathematical algorithm to determine the area of a simple polygon whose vertices are described by their Cartesian coordinates in the plane. [2]