Image Blurring Using Cumulative Sum Segmentation
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Solution Overview
Problem
Conventional digital image processing techniques, such as convolution, are computationally intensive when handling large images with big kernels, particularly for generating heavily blurred images like bokeh, motion, spin, and zoom blur.
Innovation Solution
A method involving a kernel with contiguous elements of the same value, where cumulative sums are calculated for each pixel and differences between kernel regions are summed to reduce computational complexity, allowing for efficient processing of large images with simple geometric shapes like circles or diamonds.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If conventional convolution is used to process large images with big kernels, then image blurring can be achieved, but computational complexity increases to O(W×H×K×K)
Solution Approach 1:
The kernel is segmented into multiple equal-valued regions (first region, second region, third region, etc.), each with uniform non-zero values. This segmentation allows the convolution operation to be decomposed into separate processing steps for each region, reducing redundant calculations. The cumulative sum technique further segments the computation by pre-calculating row sums, enabling efficient region-wise processing that lowers overall computational complexity from O(W×H×K×K) to O(W×H×K).
Solution Approach 2:
The method performs preliminary calculation of cumulative sums for each row of the image data before executing the convolution operation. By pre-computing the cumulative sums (where cumsum[i][j] = image[i][j] + cumsum[i][j-1]), the patent eliminates redundant addition operations during the actual convolution, as each kernel region's contribution can be directly obtained from pre-computed cumulative sum differences rather than summing individual pixel values repeatedly.
2Reliability
If standard convolution is applied to generate heavily blurred images, then blur effects (bokeh, motion, spin, zoom) can be produced, but processing time increases significantly
Solution Approach 1:
The kernel is divided into multiple equal-valued regions that can be processed independently and efficiently. Each region's convolution contribution is calculated using the same optimized approach (multiplying the region's uniform value by the cumulative sum difference), allowing parallel or sequential processing that reduces total computation time while maintaining the composite blur effect quality needed for bokeh, motion, spin, and zoom blur variations.
Solution Approach 2:
The patent changes the parameter representation by using cumulative sum differences instead of direct pixel summation. This parameter transformation allows the convolution operation to be expressed in terms of pre-computed cumulative sums, where the sum of pixels under any kernel region equals the difference of cumulative sums at the region's boundaries. This parameter change reduces the computational operations from quadratic to linear in kernel size, significantly decreasing processing time for heavily blurred images.
3Shape
If big kernels are used for image processing, then heavier blur effects are achieved, but computational operations increase to O(W×H×K×K)
Solution Approach 1:
Large kernels are segmented into multiple equal-valued regions, each processed independently using the cumulative sum technique. This segmentation allows the computational complexity to scale linearly with kernel area (O(W×H×K)) rather than quadratically (O(W×H×K×K)), as each region's contribution is calculated in constant time relative to the image size by utilizing pre-computed cumulative sums and simple multiplication by the region's uniform value.
Solution Approach 2:
The patent transforms the computational parameters by introducing cumulative sum as an intermediate representation. Instead of directly summing pixel values under each kernel element (which requires O(K×K) operations per pixel), the method uses cumulative sum differences to obtain region sums in O(1) time per region. This parameter change enables large kernel processing with reduced computational operations, making heavy blur effects feasible for large images without quadratic complexity penalties.
Data Source
AI summary
A method is disclosed for processing at least a portion of an input digital image comprising rows of pixels extending in two mutually perpendicular directions over a 2D field. The method comprises defining a kernel for processing an image, the kernel comprising at least one row of contiguous elements of the same non-zero value (such rows being referred to herein as equal-valued kernel regions), the equal-valued kernel regions, if more than one, extending parallel to one another. For each pixel in at least selected parallel rows of pixels within the image portion, the cumulative sum of the pixel is calculated by adding a value of the pixel to the sum of all preceding pixel values in the same row of the image portion. The kernel is convolved with the image portion at successive kernel positions relative to the image portion such that each pixel in each selected row is a target pixel for a respective kernel position. For each kernel position, the convolving is performed, for each equal-valued kernel region, by calculating the difference between the cumulative sum of the pixel corresponding to the last element in the equal-valued kernel region and the cumulative sum of the pixel corresponding to the element immediately preceding the first element in the region, and summing the differences for all equal-valued kernel regions. The differences sum is scaled to provide a processed target pixel value.