COMPSCI373 Computer Graphics and Image Processing FIRST SEMESTER, 2018
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COMPSCI373
FIRST SEMESTER, 2018
Computer Graphics and Image Processing
Question 1
[1 mark] Consider the 2D Cartesian coordinates of the point P = 2(3) . Which statement
about P ' , the transformed point P , after performing first a rotation by +180 degrees, then a
translation by t = -(-)3(1) , and finally a scaling by 3 in both the x and y direction is true?
(a) P ' =
(b) P ' = 9(8)
(c) P ' = -(-)9(4)
(d) P ' = 4(9)
(e) None of the others
Question 2
( 1 2 5
[1 mark] Consider the matrix M = )||| . Which of the following statements about the
matrix M is true?
(a) M represents a translation of vector (5, 2), followed by a shearing of parameters (2, 0).
(b) M represents a rotation of -90, followed by a translation of vector (2, 0).
(c) M represents a translation of vector (1, 2), followed by a shearing of parameters (2, 0).
(d) M represents a rotation of 90, followed by translation of vector (2, 0).
(e) None of the others
Question 3
[1 mark] Consider a plane P defined by the equation: 3x + 4y + 2z = 1 . Which statement about the normalized vector v being orthogonal to the plane P is true?
( 3
(a) v = 2(4))|||
( 2
(b) v = 1(4))|||
( 3
(c) v = 2(4))||| ( 2
(d) v = 3(4))||| (e) None of the others
Question 4
[1 mark] Which of the following is the equation of the plane that passes through the point
( 1 ( 1
P = 3(2))||| and is orthogonal to the vector v = 1(2))||| ?
(a) x + 2y 一 3z = 1
(b) x 一 y 一 z = 4
(c) x + 2y + z = 8
(d) x 一 y 一 z = 1
(e) None of the others
Question 5
[1 mark] Which of the following statement is true for a surface where most of the incident energy of selected wavelengths travels through and exits the body, and some energy bounces off at the boundary?
(a) The surface has low absorbed energy and high reflected energy.
(b) The surface has high transmission and low reflection of energy.
(c) The surface has low transmitted energy and high reflected energy.
(d) The surface has high absorbed energy and high transmitted energy.
(e) None of the others
Question 6
[1 mark] Given a light source delivering blue light with a transmitted component of 30% and an object with a spectral response of 50% for blue light. What percentage of the full component of blue light is emitted from the object?
(a) 60%
(b) 80%
(c) 20%
15%
(e) None of the others
Question 7
[1 mark] The CIE XYZ colour space may be represented as a projection on the 2D plane: x + y + Z = 1 . Given the colour (10, 20, 20), what is the corresponding 2D colour?
(a) (0.2, 0.4)
(b) (10, 20)
(c) (0. 1, 0.2)
(d) (20, 20)
(e) None of the others
Question 8
[1 mark] Which of the following statements about shape representations, if any, isfalse?
(a) Parametric surfaces defined using splines, such as Bezier surfaces, have a high level of control and can be used to model a wide variety of shapes.
(b) CSG is an efficient way to create 3D objects, e.g. in engineering, by combining primitive objects using set operations.
(c) Manual modelling of polygon meshes, by defining vertices and connectivity, is an efficient way to define large and complex 3D models.
(d) Subdivision surfaces are an efficient way to model natural objects, by defining rough polygon models and rounding them using multiple subdivision steps.
(e) One of the other statements is false.
Question 9
[1 mark] Given is a triangle with the vertices A=(- 1,0,0), B=(1,0,0), C=(0,1,0). The triangle is rendered in OpenGL using fully saturated red for vertex A (C_A=(1,0,0)), fully saturated green for vertex B (C_B=(0,1,0)), and white for vertex C (C_C=(1,1,1)). What is the colour C_P at the point P=(0, 0.5, 0)?
(a) C_P=(1/3, 1/3, 1/3)
(b) C_P=(1/6, 1/6, 2/3)
(c) C_P=(1/2, 1/2, 1/2)
(d) C_P=(3/4, 3/4, 1/2)
(e) None of the others
Question 10
[1 mark] Which of the following OpenGL commands creates a rotation matrix, which performs a rotation by 60º in anti-clockwise direction around the x-axis?
(a) glRotatef(60, 0, 1, 0)
(b) glRotatef(60, 0, 0, 1)
(c) glRotatef(60, 1, 0, 0)
(d) glRotatef(-60, 1, 0, 0)
(e) None of the others
Question 11
[1 mark] Which of the following statements about mathematical morphology is true?
(a) An erosion operation is a closing followed by an opening
(b) A closing operation is an erosion followed by a dilation
(c) An opening operation is a dilation followed by an erosion
(d) Even if repeated enough times, the closing operation cannot close the holes inside objects of any given image regardless of their size
(e) None of the others are true
Question 12
[1 mark] Which of the following statements about mathematical morphology is false?
(a) The morphological gradient operation is obtained by subtracting both the morphological internal gradient operation and the morphological external gradient operation from the original image
(b) The morphological external gradient operation is obtained by subtracting an original image from the dilated image
(c) The morphological gradient operation is a morphological internal gradient operation plus a morphological external gradient operation
(d) The morphological internal gradient operation is obtained by subtracting the eroded image from the original image
(e) None of the other statements are true
Question 13
[1 mark] Which of the following statements is false?
(a) A given image has a unique histogram
(b) Up to 256 unique images can share the same histogram
(c) The histogram of an 8-bit image is the distribution of empirical probabilities, or counts of its pixel intensities
(d) A given image has a unique cumulative histogram (e) One of the other statements is false
Question 14
[1 mark] Which of the statements below about image filtering is true?
(a) All image filtering operations are linear filters
(b) Histogram equalisation is a linear filter
(c) Image thresholding is a linear filter
(d) Median filtering generally works better than the mean filter to remove “salt and pepper” noise from an image
(e) None of the other statements are true
Question 15
[1 mark] Which of the following statements about histogram equalisation is true?
(a) Histogram equalisation decreases the image contrast
(b) Histogram equalisation brightens all images
(c) Histogram equalisation darkens all images
(d) Histogram equalisation is a linear mapping process
(e) All of the other statements are false.
Question 16
[1 mark] What is the minimum number of bits needed to encode an image with 300 different grey shades (pixel intensities)?
(a) 9
(b) 10
(c) 16
(d) 7
(e) 8
Question 17
[1 mark] Which coefficients of the linear mapping operation, g(x,y) = af(x,y) + b, will map the pixel value f(x,y) = 50 to g(x,y) = 100 and pixel value f(x,y) = 250 to g(x,y) = 100?
(a) a=2, b=0
(b) a=-2, b=200
(c) a=- 1, b=150
(d) a=0, b=100
(e) None of the others
Question 18
[1 mark] Consider the greyscale image J defined at the beginning of this exam script. What is the image value at the pixel location (x=2,y=4) after applying a 10-90 percentile based mapping on J?
(a) 150
(b) 150
(c) 52
50
(e) None of the others
Question 19
[1 mark] Consider the greyscale image J defined at the beginning of this exam script. What is the histogram count for the pixel value 87 in this image?
(a) 195
(b) 87
(c) 21
4
(e) None of the others
Question 20
[1 mark] Consider the greyscale image J defined at the beginning of this exam script, and the cumulative histogram C = [C(0),C(1),…,C(255)] of the image J. What is the cumulative histogram count C(181)?
(a) 17
(b) 23
(c) 0
25
(e) None of the others
Question 21
[1 mark] Consider the greyscale image J defined at the beginning of this exam script, and the cumulative histogram C = [C(0),C(1),…,C(255)] of the image J. What is the cumulative histogram count C(86)?
(a) 21
(b) 25
(c) 23
17
(e) None of the others
Question 22
[1 mark] Consider the binary image I, which was introduced at the beginning of this exam script, with white objects on black background (“1”/”0”) and the 3 by 3 structuring element S. Assume that the border pixels are not processed (i.e. they are not modified by any morphological operator). What is the resulting image value at the pixel location (x=2,y=2) after eroding the binary image I with the structuring element S?
(a) 2
(b) 1
(c) 0
- 1
(e) None of the others
Question 23
[1 mark] Consider the binary image I, which was introduced at the beginning of this exam script, with white objects on black background (“1”/”0”) and the 3 by 3 structuring element S. Assume that the border pixels are not processed (i.e they are not modified by any morphological operator). What is the resulting image value at the pixel location (x=2,y=1) after opening the binary image I with the structuring element S?
(a) 0
(b) 1
(c) 2
- 1
(e) None of the others
Question 24
[1 mark] Consider the binary image I, which was introduced at the beginning of this exam script, with white objects on black background (“1”/”0”) and the 3 by 3 structuring element S. Assume that the border pixels are processed using padding with zero values. What is the resulting image value at the pixel location (x=2,y=1) after opening the binary image I with the structuring element S?
(a) 1
(b) 2
(c) 0
- 1
(e) None of the others
Question 25
[1 mark] Consider the binary image I, which was introduced at the beginning of this exam script, with white objects on black background (“1”/”0”) and the 3 by 3 structuring element S. Assume that the border pixels are processed using “Padding 1” which extends border values outside with the image boundary values. What is the resulting image value at the pixel location (x=2,y=1) after opening the binary image I with the structuring element S?
(a) 1
(b) 0
(c) 2
- 1
(e) None of the others
Question 26
[1 mark] Consider the binary image I, which was introduced at the beginning of this exam script, with white objects on black background (“1”/”0”) and a 3 by 3 structuring element S. Assume that the border pixels are not processed (i.e. they are not modified by any morphological operator). What is the resulting value at pixel location (x=3,y=3) of the morphological external gradient of I computed with the structuring element S?
(a) - 1
(b) 2
(c) 1
0
(e) None of the others
Question 27
[1 mark] Consider the greyscale image J defined at the beginning of this exam script. What is the image value at the pixel location (x=2,y=1) after applying the 3 rows by 3 columns median filter to J?
(a) 99
(b) 87
(c) 52
181
(e) None of the others
Question 28
[1 mark] Consider the greyscale image J defined at the beginning of this exam script. What is the image value at the pixel location (x=2,y=4) after applying the 1 row by 3 columns average filter to J?
(a) 52
(b) 20
(c) 58
19
(e) None of the others
Question 29
[1 mark] Consider the greyscale image J defined at the beginning of this exam script. What is the image value at the pixel location of the resultant image (x=3,y=0) after performing histogram equalisation?
(a) 180
(b) 60
(c) 12
4
(e) None of the others
Question 30
[1 mark] Consider the greyscale image J defined at the beginning of this exam script. What is the image value at the pixel location of the resultant image (x=2,y=3) after performing histogram equalisation?
(a) 160
(b) 221
(c) 195
21
(e) None of the others
Question 31
[1 mark] Consider the greyscale image J defined at the beginning of this exam script; and the equalised image J’, that is, the image J after histogram equalisation, and the cumulative histogram C = [C(0),C(1),…,C(255)] of the image J’ . What is the cumulative histogram count C(181) in image J’?
(a) 21
(b) 17
(c) 23
12
(e) None of the others
Question 32
[1 mark] Consider the greyscale image J defined at the beginning of this exam script; and the equalised image J’, that is, the image J after histogram equalisation. What is the image value at the pixel location of the resultant image (x=2,y=1) after applying the 3 rows by 3 columns median filter to the equalised image J’?
(a) 87
(b) 225
(c) 195
135
(e) None of the others
Question 33
[1 mark] Consider the greyscale image J defined at the beginning of this exam script. Assuming an initial threshold T0 = 100, what will be the threshold (rounded to the nearest integer) computed after running three iterations of the adaptive threshold technique as described in class?
(a) 20
(b) 87
(c) 100
125
(e) None of the others
Question 34
[1 mark] Which of the following statements about OpenGL isfalse?
(a) glVertexfv(const GLfloat *v )specifies a pointer to an array of float numbers representing a vertex. The length of the array determines the dimension of the vertex.
(b) glClear(GLbitfield mask) clears all pixels in the buffer specified by mask.
(c) glColor3f(GLfloat red, GLfloat green, GLfloat blue ) sets the colour for subsequent drawing commands.
(d) OpenGL is a computer graphics rendering API.
(e) OpenGL allows the graphics part of your application to be operating system independent & window system independent.
Question 35
[1 mark] Given are the vertices
const int numVertices=5;
const float vertices[numVertices][2] =
{{50,350},{50,200},{200,200},{400,200},{200,50}};
Which calling sequence of these vertices (using glVertex2fv) results in the shape below if we use
the OpenGL commands glBegin(GL_TRIANGLE_STRIP) and glEnd()?
(a) 4, 3, 2, 1, 0
(b) 2, 1, 0, 3, 4
(c) 1, 0, 2, 3, 4
(d) 2, 4, 3, 0, 1
(e) None of the others
Question 36
[1 marks] Given are the vertices
const int numVertices=6;
const float vertices[numVertices][2] =
{{50,50},{50,200},{200,200},{400,200},{50,350},{50,250}};
Which calling sequence of these vertices (using glVertex2fv) results in the shape below if we use
the OpenGL commands glBegin(GL_QUAD_STRIP) and glEnd()?
(a) 2, 1, 0, 3, 4, 5
(b) 4, 5, 3, 2, 1, 0
(c) 4, 3, 5, 2, 1, 0
(d) 1, 0, 2, 3, 5, 4
(e) None of the others
Question 37
[1 marks] Given is a scene with a light source at position L=(1, -2, 0)T, a viewpoint (virtual camera position) V=(4, 4, 0)T, and an illuminated object. In order to compute the Phong illumination at any point on the surface of that object, the halfway vector for that point needs to be computed. What is the halfway vector h at the point P=(1, 0, 0)T on the surface of the object? You can assume that the point P is visible from both the light source and view point.
NOTE 1: Please remember that the halfway vector must be normalised.
NOTE 2: The symbol V is the square root symbol, i.e. V5 is the square root of 5.
(a) h = (3/5, 4/5, 0)T
(b) h = (2/V5, - 1/V5, 0)T
(c) h = (3/V10, - 1/V10, 0)T
(d) h = (0, - 1, 0)T
(e) None of the others
Question 38
[1 mark] The image below shows a 3D scene consisting of a ground plane, five objects (teapot, cube, cylinder, sphere and cone), and projected shadows. What statement about the illumination of the rendered scene is true?
NOTE 1: The colour of projected shadows is usually hardcoded, i.e. not realistic, and hence should be ignored for the purpose of answering this question.
NOTE 2: Please note that the perceived colours of each object are constant, except for the highlight regions.
(a) The illumination has an ambient and specular component, but no diffuse component (b) The illumination has an ambient component, but no diffuse and no specular component (c) The illumination has an ambient and diffuse component, but no specular component (d) The illumination has specular component, but no ambient and no diffuse component (e) The illumination has a diffuse and specular component, but no ambient component
Question 39
[1 mark] An object with a yellow material colour is illuminated with a blue light source. What is the perceived colour of the object?
(a) Cyan
(b) Black
(c) Green
(d) Magenta
(e) White
Question 40
[1 mark] Consider ray casting and increasing the distance N between the eye and the view plane. Which of the following statements describes correctly the effect of this operation on the rendered scene?
(a) Zoom into the scene
(b) Zoom out of the scene
(c) Decrease the resolution of the image
(d) Increase the resolution of the image (e) None of the others
Question 41
[1 mark] In ray tracing, which illumination component(s) from Phong's model are used to compute the colour of objects in shadow?
(a) Ambient and specular
(b) Ambient and diffuse
(c) Ambient
(d) Ambient, diffuse and specular
(e) Objects in shadow are always rendered black
Question 42
[1 mark] Given is a plane 2x + 3y – z = 1 and a ray
p(t) = + t
For what value of c does the ray not intersect the plane?
(a) c = -2
(b) c = 0
(c) c = 1
(d) c = 5
(e) The ray always intersects the plane regardless of the value of c
Question 43
[1 mark] Given is a sphere with radius 1 centered at the origin. The sphere is transformed with the
matrix M = (0(3) 2(0) 0(0)). What is the first intersection point of the ray p(t) = ( )+t (1(0) 0(0) ) with the
transformed sphere?
(a) The intersection point is p(t0) where t0 = 1
(b) The intersection point is p(t0) where t0 = 2 - √5
(c) The intersection point is p(t0) where t0 = 2 - √3
(d) The intersection point is p(t0) where t0 = 2
(e) None of the others
Question 44
[1 mark] Given is a raytraced scene with a light source at position L=(2, 0, 4)T . The scene contains the xy-plane as ground plane and a sphere with radius 1 and centre point c=(c, 0, 2)T . For which values of c is the point P=(2, 0, 0)T in the shadow of the sphere?
HINT: Make yourself an illustration of the scene.
(a) 0 < c < 2
(b) 1 < c < 3
(c) 0 < c < 4
(d) 2 < c < 4
(e) The point P is never in the shadow of the sphere
Question 45
[1 mark] Given is a quadratic Bezier curve p(t) with the control points (1, 1)T, (0, 2)T, and (3, 1) T . What is the value for p(0.5)?
(a) p(0.5) = (0, 2)T
(b) p(0.5) = (4/3, 4/3)T
(c) p(0.5) = (1, 1.5)T
(d) p(0.5) = (0.75, 1.25)T
(e) None of the others
Question 46
[1 mark] Which of the following code segments defines the three basis functions of a quadratic Bezier curve?
(a) double B1(double t){ return 2*t*(1-t);}
double B2(double t){ return 2*t;}
double B3(double t){ return 1;}
(b) double B1(double t){ return (1-t)*(1-t);}
double B2(double t){ return 2*t*(1-t);}
double B3(double t){ return t*t;}
(c) double B1(double t){ return 1+2*t+t*t;} double B2(double t){ return 2*(1-t);} double B3(double t){ return -t*t;}
(d) double B1(double t){ return 1-t*t;} double B2(double t){ return 2*t;} double B3(double t){ return 1;}
(e) None of the others
Question 47
[1 mark] Which of the following statements about spline curves are true?
I A Bezier curve interpolates all of its control points.
II The geometric constraint vector of a Hermite curve defines the curves start and end point and start and end
tangent.
III A Bezier curve always lies in the convex hull of its control points.
IV A linear Bezier curve is a straight line segment.
V Hermite curves are quadratic curves.
(a) All statements are true
(b) Only statements I, II, III, and IV are true
2023-05-15