Name and surname………………………………………………… Group…………
DIGITAL IMAGE PROCESSING EXAM – PART II
1. QUIZ
The subjects have equal weights. There are multiple correct answers possible (1, 2, 3 sau 4). Mark
(CAREFULLY!) the answers you consider correct.
Total quiz points: 3.5 pts
1. The following attributes are specific to the Fourier descriptors:
a)
b)
c)
d)
they are non-regenerative contour descriptors
they are used for shape recognition based on contour
they are invariant to certain transformations of the object (contour)
the number of descriptors needed to reconstruct a contour depends on the contour’s complexity
and on the desired reconstruction accuracy
2. The morphological opening implies the following:
a) apply a contrast enhancement, thus brightening (“opening”) the average grey of the image
b) apply an erosion and then a dilation
c) apply a dilation and then an erosion
d) apply a quad-tree image coding followed by an erosion
3. The maximum theoretically achievable compression rate for an M×N digital image, having the
brightness represented on L grey levels, is given by the expression:
1
a) C =
, where H is the entropy of the source of all possible images of size M×N, having the L
H
possible grey levels for each pixel;
b) is infinite;
B
c) C =
, where H is the entropy of the source of all possible images of size M×N, having
H +e
the L possible grey levels for each pixel, B – is the number of bits needed to store the image in
uncompressed format, and e – an arbitrarily small value;
4. The image in Fig. 2.b) is the result of applying a convolution on the image in Fig. 1.a) with a 3×3
convolution mask. Considering the processed image, one can say that:
1 1 1
1
a) most likely, the convolution mask was H 1 = 1 1 1;

9
1 1 1
− 1
1
b) most likely, the convolution mask was H 2 = − 1
9
 − 1
0
1
c) most likely, the convolution mask was H 3 = − 1
4
 0
− 1 − 1
− 1 − 1;

− 1 − 1
−1 0 
4 − 1 ;
− 1 0 
 0 0 0
1
d) most likely, the convolution mask was H 4 =
0 0 0.

9
 0 0 0
Fig. 2.a)
Fig. 2.b)
5. For the binary image in Fig. 3.a), the image in Fig. 3.b) represents (most likely):
a) the result of dilating the image in Fig. 3.a) by a black square structural element, of size 3×3 pixels;
b) the result of eroding the image in Fig. 3.a) by a black square structural element, of size 3×3 pixels;
c) the skeleton of the object region (composed by the black pixels) from the image in Fig. 3.a);
d) the result of the edge detection applied on the image in Fig. 3.a) through a compass edge detection
scheme.
Fig. 3.a)
Fig. 3.b)
Name and surname………………………………………………… Group…………
DIGITAL IMAGE PROCESSING EXAM – PART II
2. CLASSIC
Total points : 6.5 pts
All the subjects have the same weight.
1. The low-pass filtering of the digital images in the spatial domain; the modalities to obtain highpass spatial filters and band-pass spatial filters from low-pass spatial filters.
2. Describe: the chain codes for contour description; the polygonal approximation of the contours;
the quad-tree decomposition of binary images.
3. Consider the following 6×6 pixels block U, cropped from a grey level image.
16
16

16
U=
16
16

16
16
200
200
200
200
16
200
200
200
200
16
16
16 16 16
200 200 16

200 200 16
.
200 200 16
200 16 16

16 16 16
 0 −1 0 
1
Compute the result of convolving this block with the convolution mask H = − 1 4 − 1 . Do

4
 0 − 1 0 
not perform the computations for the first and last lines and columns of the block U; consider
setting to zero the values of the first line, last line, first column and last column of the processed
block. What are the absolute values of the convolution result? Prove, by examining these values, that the
result obtained corresponds to a contour detection for the inner object in the block.
4. Consider the binary image below, which represents an instance of the letter θ. We wish to apply a
morphological processing on this image, by morphological erosion with a binary structural
element, to obtain from it the digit 0. The black pixels are the object pixels, the white pixels are tha
background pixels.
a) Having available the following four structural elements (each having the origin in its
center), chose the most suitable structural element to give a black object as close as
possible to the digit 0 through the binary erosion. Draw the erosion result.
Comment the processing effect in achieving the desired goal.
b) Apply, on the eroded image, a dilation by the same structural element. Draw the resulting
binary image. What is the name of the morphological processing applied in these two
successive steps?
5. Encode the contour below by an 8 directional chain code, considering as start pixel – the pixel
marked in the figure, and the counter-clockwise direction for the contour following.
start
pixel