Comparison of sparse iou calculation against normal matrices iou calculation

The calculation for sparse is looking like the following:

1. determine the indices of the sparse which are located inside the bbox.
2. calculate area of the bbox.
3. Intersection is equal to the sum of mask pixels inside.
4. Union is equal the sum of all mask pixels plus area of bbox minus Intersection.

Formulas

\[area_{bbox} = (xmax -xmin) \cdot (ymax - ymin)\]

\[iou = {area_{inside}\over area_{bbox} + area_{total} - area_{inside}}\]

Scenario 1: Simple Square

The three example masks with given bbox are defined as the following:

• total image size: 5 x 5

	Pixels T-shape	Pixels Cross	Pixels Rects
\(count_{total}\)	\(9\)	\(5\)	\(7\)
\(count_{inside}\)	\(3\)	\(5\)	\(4\)
\(iou\)	\({3\over15}\)	\({5\over9}\)	\({4\over12}\)

	bbox
\(xmin\)	\(1\)
\(ymin\)	\(1\)
\(xmax\)	\(4\)
\(ymax\)	\(4\)
\(area\_{bbox}\)	\(9\)

Scenario 2: Rectangle unequal ratio

The three example masks with given bbox are defined as the following:

• total image size: 5 x 6

	Pixels T-shape	Pixels Cross	Pixels Rects
\(count_{total}\)	\(10\)	\(6\)	\(9\)
\(count_{inside}\)	\(4\)	\(6\)	\(6\)
\(iou\)	\({4\over18}\)	\({6\over12}\)	\({6\over15}\)

	bbox
\(xmin\)	\(1\)
\(ymin\)	\(1\)
\(xmax\)	\(4\)
\(ymax\)	\(5\)
\(area_{bbox}\)	\(12\)

Scenario 3: invalid single point, invalid size

A single Pixel.

Variable indices is valid, but the size of image is 2D.

Should raise a SizeValueError.

Scenario 4: valid single point, valid size

A single Pixel.

Variables indices is invalid (two axis), size of image is 3D.

Scenario 5: Mask Outside

The two example masks with given bbox are defined as the following:

• total image size: 5 x 5

	Pixels Cross	Pixels L-Shape
\(count_{total}\)	\(5\)	\(5\)
\(count_{inside}\)	\(5\)	\(0\)
\(iou\)	\({5\over9}\)	\({0\over14}\)

	bbox
\(xmin\)	\(1\)
\(ymin\)	\(1\)
\(xmax\)	\(4\)
\(ymax\)	\(4\)
\(area\_{bbox}\)	\(9\)

The test should show that, even so the calculation for the second example provides zero iou the value is also created.

Scenario 6: Empty Mask

Same Masks as in Scenario 5 but this time an empty mask is placed between them. This is done by moving the L-Shape on N layer with index = 2.

• total image size: 5 x 5

	Pixels Cross	Empty Mask	Pixels L-Shape
\(count_{total}\)	\(5\)	\(0\)	\(5\)
\(count_{inside}\)	\(5\)	\(0\)	\(0\)
\(iou\)	\({5\over9}\)	\(0\)	\({0\over14}\)

	bbox
\(xmin\)	\(1\)
\(ymin\)	\(1\)
\(xmax\)	\(4\)
\(ymax\)	\(4\)
\(area\_{bbox}\)	\(9\)