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The J-integral represents a way to calculate the strain energy release rate, or work per unit fracture surface area, in a material. [1] The theoretical concept of J-integral was developed in 1967 by G. P. Cherepanov [2] and independently in 1968 by James R. Rice, [3] who showed that an energetic contour path integral (called J) was independent of the path around a crack.
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A path independent integral and the approximate analysis of strain concentration by notches and cracks. Department of Defense Advanced Research Projects Agency. Contract SD-86, Material Research Program, May 1967. Rice, James R. "Mathematical analysis in the mechanics of fracture." Fracture: an advanced treatise 2 (1968): 191–311.
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In the image processing domain, it is also known as an integral image. It was introduced to computer graphics in 1984 by Frank Crow for use with mipmaps . In computer vision it was popularized by Lewis [ 1 ] and then given the name "integral image" and prominently used within the Viola–Jones object detection framework in 2001.