A quiz on the regions laboratory

Adrian F. Clark

1. Which of the following expressions works out the rectangularity of a region having a bounting box of width $W$, height $H$ and area $A$?

   • $HAW$

   • $WH/A$

   • $HA/W$
   • $WA/H$

   The rectangularity is the ratio of the area of the bounding box to the area of the actual shape.

2. What is the rectangularity of a region which is twice as long as it is wide?

   • about 2
   • about one-half
   • negative

   • about 1

   The rectangularity of a rectangular region should be about unity irrespective of its width and height.

3. What is the area of the image from sxcv.arrowhead?

   • 5

   • 7
   • 10
   • 6

   You mean you didn't work this out and keep a record of it? ;-)

4. Which of the following CANNOT be returned by calling an OpenCV routine with a contour?

   • the best-fit line
   • the best-fitting ellipse
   • the minimum enclosing circle

   • the concave hull

   OpenCV routine compute all of these but the contave hull. It can compute convex hull though.

5. Which of the following expressions is circularity?

   • $C/A^2$
   • $A^2/C$

   • $C^2/A$

   • $C*2A$

   Circularity is conventionally measured as $C^2/A$.

6. Why is circularity calculated using the forumla $C^2/A$?

   • it is always non-zero
   • it is easy to compute using OpenCV

   • it is independent of radius

   • it is independent fo shape

   The particular formula for circularity makes it independent of radius: $C = 2\pi r$ and $A = \pi r^2$ so the $r$s cancel.

7. The area of the contour from sxcv.arrowhead is not the same as the number pixels in it set to 255. Why is this?

   • the algorithm used in cv2.contourArea excludes the perimeter
   • the number of pixels set to 255 is not the area of a contour

   • the algorithm used in cv2.contourArea does not count pixels

   • the algorithm used in cv2.contourArea is wrong

   OpenCV uses Green's formula (a contour integral, for people who do maths) to compute areas in cv2.contourArea. To be honest, I think it would be better if they somply counted the number of pixels wholly within a region.

8. On what basis does sxcv.largest_contour work?

   • the contour with the largest area

   • the contour with the largest number of points
   • the contour with the largest perimeter
   • the contour with the largest bounding box

   This routine should have been written to reeturn the contour that encloses the largest area.

9. Which of the following tasks would region-based processing be useful for?

   • distinguishing between plants in a garden
   • distibguishing different types of cloth

   • distinguishing between buildings and trees

   • building panorama images from a set of individual photographs

   Region-based processing is based around finding shapes and using measures of them to characterize different classes of region. The only task listed above in which there is a definite shape is distinguishing man-made objects such as buildings from objects in the natural world, such as trees.

10. If you compute the ratio between the height and width of a bounding box, which of the following would it be most useful for?

    • identifying biscuits oriented at an angle to the edges of the image
    • identifying broken biscuits
    • distinguishing square biscuits from round ones

    • distinguishing square biscuits from rectangular ones

    Although this aspect raio measure could conceivably be used for identifying broken biscuits, it would be most useful for distinguishing betwee square ones (where the aspect ratio is about unity) from rectangular ones.