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ROI Pooling

Computer Vision

Hard

Convert each rectangular region of a feature map into a fixed square grid with max pooling. Each region is $[x_1,y_1,x_2,y_2]$ with half-open bounds, so it contains rows $y_1$ through $y_2-1$ and columns $x_1$ through $x_2-1$ .

For output row $i$ , use:

h_{\mathrm{start}}=y_1+\left\lfloor\frac{iH_R}{S}\right\rfloor

h_{\mathrm{end}}=y_1+\left\lfloor\frac{(i+1)H_R}{S}\right\rfloor

For output column $j$ , use:

w_{\mathrm{start}}=x_1+\left\lfloor\frac{jW_R}{S}\right\rfloor

w_{\mathrm{end}}=x_1+\left\lfloor\frac{(j+1)W_R}{S}\right\rfloor

Here, $H_R=y_2-y_1$ , $W_R=x_2-x_1$ , and $S$ is output size. Expand an empty bin to one pixel, then take its maximum. Return one square two-dimensional list per region, preserving region order.

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Examples

Input: feature_map = [[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16]], rois = [[0, 0, 4, 4]], output_size = 2

Output: [[[6, 8], [14, 16]]]

Explanation: The full map splits into four two-by-two bins, and each output contains one bin maximum.

Input: feature_map = [[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16]], rois = [[0, 0, 2, 2], [2, 2, 4, 4]], output_size = 2

Output: [[[1, 2], [5, 6]], [[11, 12], [15, 16]]]

Hint 1

Use math.floor on each scaled bin boundary.

Hint 2

Collect values between each pair of half-open row and column boundaries, then take max.

Requirements

Divide every region into the requested number of rows and columns
Use the stated floor-based half-open bin boundaries
Expand empty bins to cover one pixel
Return one pooled grid per region in input order

Constraints

The feature map is a nonempty rectangular list
Region coordinates are integer, ordered, and within the feature map
Output size is a positive integer

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