Homework Set #4 Edge Detection by Zero-crossing

CSE 473/573 Homework Set #4

Notice: Python programming for the following problems is preferred. However, solutions
obtained via another programming language is also acceptable.
Problem (1) (Edge Detection by Zero-crossing, DoG and LoG – Python Programming) 50%
Zero-crossing of the second derivative has been considered as strong indications for edges in
a given image. For practical implementations, robust computation of second derivative is
usually preceded by the smoothing of an image. Two popular approaches to zero-crossingbased edge detection are Difference-of-Gaussian (DoG) and Laplacian-of-Gaussian (LoG).
For the “UB Campus” test image, perform the following with Python programming:
(a) Obtain and display the DoG image by applying the following DoG mask to the test image
[






0 0 −1
0 −2 −3
−1 −3 5
−1
−3
5
−1 0 0
−3 −2 0
5 −3 −1
−1 −3 5 16 5 −3 −1
−1 −3 5
0 −2 −3
0 0 −1
5
−3
−1
5 −3 −1
−3 −2 0
−1 0 0 ]






(b) Compute and display the zero-crossing of the DoG image obtained in (a)
(c) Compute and display the zero-crossing strong edges by removing weak edges that do not
have first derivative support in (b)
(d) Compute and display the LoG zero-crossing edges by applying the following LoG mask
to the test image
[




0 0 1 0 0
0 1 2 1 0
1
0
0
2
1
0
−16 2 1
2 1 0
1 0 0]




(e) Compare the results in (c) and (d) and explain why the edges obtained in (c) and (d) are
different. Is there any way that we may obtain the same results? Please explain in detail.
Problem (2) (Region Merging Segmentation – Python Programming) 50%
Region merging is an effective scheme for region growing based segmentation. Region
growing may begin with each pixel within an image in which a pixel represents a single
region initially. Regions will be merged to satisfy the region segmentation conditions as
defined by Equations (6.30) and (6.31). Perform the following algorithm to the “Mixed
Vegetables” test image through Python programming:
(a) Perform Algorithm 6.18 – Region merging via boundary melting and display the results
of the final region merging. Each student is required to set their own thresholds and also
explain why such thresholds are selected.
Reference: