Calculating IOU for bounding box predictions - object-detection

Question

I have these two bounding boxes as given in the image. the box cordinates are given as below :
box 1 = [0.23072851 0.44545859 0.56389928 0.67707491]
box 2 = [0.22677664 0.38237819 0.85152483 0.75449795]
The coordinate are like this : ymin, xmin, ymax, xmax
I am calculating IOU as follows :
def get_iou(box1, box2):
"""
Implement the intersection over union (IoU) between box1 and box2
    
Arguments:
box1 -- first box, numpy array with coordinates (ymin, xmin, ymax, xmax)
    box2 -- second box, numpy array with coordinates (ymin, xmin, ymax, xmax)
"""
# ymin, xmin, ymax, xmax = box
y11, x11, y21, x21 = box1
y12, x12, y22, x22 = box2
yi1 = max(y11, y12)
xi1 = max(x11, x12)
yi2 = min(y21, y22)
xi2 = min(x21, x22)
inter_area = max(((xi2 - xi1) * (yi2 - yi1)), 0)
# Calculate the Union area by using Formula: Union(A,B) = A + B - Inter(A,B)
box1_area = (x21 - x11) * (y21 - y11)
box2_area = (x22 - x12) * (y22 - y12)
union_area = box1_area + box2_area - inter_area
# compute the IoU
iou = inter_area / union_area
return iou
Based on my understanding these 2 boxes completely overlap each other so IOU should be 1. However I get an IOU of 0.33193138665968164
. Is there something which I am doing wrong or I am interpreting it in an incorrect way. Any suggestions in this regard would be helpful.

Answer 1

You are interpreting the IoU in an incorrect way.
If pay attention to your example, you notice that the union of the areas of the two bounding boxes is much bigger than the intersection of the areas. So it makes sense that the IoU - which is indeed intersection / union - is much smaller than one.
When you say
Based on my understanding these 2 boxes completely overlap each other so IOU should be 1.
that is not true. In your situation the two bounding boxes overlap only in the sense that one is completely contained in the other. But if this situation weren't penalized, IoU could be always maximized predicting a bounding box as big as the image - which clearly doesn't make sense.