gives an image in which each pixel represents a sum of all pixels below and to the left of that pixel in image.

Details and Options

  • ImageAccumulate[image] pads the image with one row of zeros at the bottom and one column of zeros on the left of the image after accumulating the pixels and returns an image whose dimensions are 1+ImageDimensions[image].
  • ImageAccumulate operates separately on each channel in an image.
  • ImageAccumulate gives an image of a real type.
  • ImageAccumulate[image,Method->"CompensatedSummation"] uses compensated summation to reduce numerical error in the result.
  • ImageAccumulate also works with Image3D objects.


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Basic Examples  (2)

Compute the accumulated area of an image:

Accumulated area of a 3D image:

Options  (1)

Method  (1)

The default method is fast, but may have some computation artifacts:

Use Method->"CompensatedSummation" for a more accurate result:

Applications  (1)

Approximate the determinant of the Hessian using 9×9 box filters as in a SURF keypoints detector:

Visualize the function evaluated for every pixel:

Find the position of the peaks in the determinant of the Hessian matrix:

Properties & Relations  (1)

Accumulated pixel values inside an upright rectangle defined by its bottom-left and top-right corners:

Define the upright rectangular area by its bottom-left corner and its width and height:

Accumulating the pixel values of the corresponding subimage yields the same result:

Accumulate pixel values extracted from the original image:

Wolfram Research (2012), ImageAccumulate, Wolfram Language function, (updated 2014).


Wolfram Research (2012), ImageAccumulate, Wolfram Language function, (updated 2014).


Wolfram Language. 2012. "ImageAccumulate." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2014.


Wolfram Language. (2012). ImageAccumulate. Wolfram Language & System Documentation Center. Retrieved from


@misc{reference.wolfram_2024_imageaccumulate, author="Wolfram Research", title="{ImageAccumulate}", year="2014", howpublished="\url{}", note=[Accessed: 20-June-2024 ]}


@online{reference.wolfram_2024_imageaccumulate, organization={Wolfram Research}, title={ImageAccumulate}, year={2014}, url={}, note=[Accessed: 20-June-2024 ]}