如何利用积分图像检测ROI内灰度变化？能否仅计算目标区域积分图像？

Great question—let’s break this down step by step since you’re focused on ROI-specific gray level change detection with integral images. I’ve worked with similar use cases in industrial inspection, so this is right up my alley.

First, a quick recap: integral images let you calculate the sum of any rectangular region in O(1) time once you’ve precomputed the integral map. That’s perfect for your work, since you only care about specific regions. Here’s how to put it to use for change detection:

• Precompute integral images for your baseline and comparison frames
  Generate integral images for both your reference image (say, the initial "no change" state) and the image you’re checking for shifts. Let’s call these I_baseline and I_current.

• Define your ROIs with rectangular bounds
  Even if your target region isn’t a perfect rectangle, start with a tight bounding box around it. For each ROI, note its top-left (x1, y1) and bottom-right (x2, y2) coordinates. If you need to exclude non-target pixels inside the box, you can use a mask later (more on that below).

• Calculate total gray sum for each ROI in both images
  Use the standard integral image region sum formula:

  region_sum = I[x2,y2] - I[x1-1,y2] - I[x2,y1-1] + I[x1-1,y1-1]
  

  Pro tip: If x1 or y1 is 0 (edge of the image), treat those out-of-bounds I values as 0 to avoid errors.

• Compute averages and compare for changes
  Divide each region sum by the ROI’s area (width * height) to get the average gray level. Then subtract the baseline average from the current average. If this difference crosses a threshold you set (based on your image’s noise level or detection sensitivity), you’ve found a gray level change in that ROI.

• For non-rectangular ROIs: Adjust with pixel counts
  If your ROI is irregular, calculate the region sum as above, but divide by the number of valid pixels in the ROI (instead of the bounding box area) to get an accurate average. You can precompute a mask for each ROI to count valid pixels quickly.

Short answer: Not exactly, but you don’t have to compute the entire image’s integral map to be efficient.

Integral images are inherently global—each pixel’s value depends on all pixels above and to the left of it. You can’t generate a "partial" integral image that only covers scattered ROIs because those local values rely on the global sum. But here are workarounds that get you the same efficiency:

• Compute local integral images for each ROI’s bounding box
  For each scattered ROI, extract its smallest enclosing rectangle, then compute the integral image only for that sub-image. This skips processing the rest of the original image, saving time and memory if your ROIs are small and sparse.

• Skip integral images entirely for very few ROIs
  If you only have 2-3 scattered ROIs, calculating their gray sums directly (by iterating over each pixel in the ROI) might be faster than building even a local integral image. But once you have more than a handful, integral images will pull ahead in speed.

• Use a masked integral image
  If you have a binary mask that marks only your ROIs (with 1s for target pixels, 0s elsewhere), compute an integral image of the masked original. This gives you a global integral map, but non-ROI pixels contribute nothing to the sum. It’s a good middle ground if you might need to adjust your ROIs later.

Wrap-up: Integral images are a fantastic tool for your use case—they make ROI average calculations lightning fast, which is key for efficient change detection. Stick to full integral images if you might tweak your ROI boundaries later, or local ones for maximum efficiency with scattered regions.

内容的提问来源于stack exchange，提问作者Adrián Arroyo Perez