Assignment 1 – Part A (revised)
ELE 488 F06
Due Oct 10
1. The wavelength of visible light covers a range from about 380 nm to about 750 nm. Human
perception of color is based on the three rod types of receptors in the eye. These receptors
respond to different “bands” of wavelength, according to 3 response curves (Gonzalez-Woods,
Fig 6.3, 9/19 lecture slide 11) Denote these three curves by SR(λ), SG(λ) and SB(λ). Given a
light with energy distribution E(λ). The responses of the three channels are given by:
aR = ∫ E(λ) SR(λ) dλ,
aG = ∫ E(λ) SG(λ) dλ,
aB = ∫ E(λ) SB(λ) dλ.
A monochromatic light has a single wavelength λ0. Its energy distribution can be described
by a delta function E(λ) = δ(λ – λ0). The three primary colors of CIE can be taken as having
wavelengths of 440 nm, 550 nm, and 700 nm.
Suppose the three response curves SR(λ), SG(λ) and SB(λ) are approximated by
triangular shaped curves, as follows. SR(λ) has base from 480 nm to 720 nm and a peak
value of 0.6. SG(λ) has a base from 440 nm to 630 nm and a peak value of 0.75. SB(λ)
has base from 380 nm to 520 nm and a peak value of 1.
(a) If we take the white light as the sum in equal parts of the three primary colors, what
are the responses aR, aG, aB from the 3 channels?
(b) If we take the white light as a light with a constant E(λ), what are the 3 channel
responses in this case? (Normalize the total input energy to 1.)
(c) What are the proportion of the three primary lights if their sum will give the sodium
yellow light (wavelength 590 nm)?
(d) Suppose a light produces the 3 channel response: aR, aG, aB. How can you mix the
three primary colored lights to give you the same response?
2. (a) As discussed in class, an image I0 can be sharpened by using a ‘high boost’ filter
(Gonzalez-Woods, section 4.4.5, 9/26 lecture slide 28). The image I0 is first lowpass
filtered by HLP to obtain the image ILP. The difference
filtered image.
IHP = I0 – ILP is the highpass
The sharpened image IS is the weighted sum of ILP and IHP . IS can be
obtained from I0 by a sharpening filter Hs.
 1  1  1
Suppose Hs is given by  1 17  1 . Determine the lowpass filter HLP .


 1  1  1
Note: In Part B, you will apply this Hs to the image of Figure 4.20(a)
(b) Show that his is a special case of an mxm high boost filter:
 1 ...  1  1
:

 1
1 1
1 
1
1 w
m2 
 1
1 1

:
 1 ...  1  1

 1 ...  1
: 
1
 1

1
 1 , where w  A  m 2  1, A  1.
1
 1

: 
 1 ...  1
What is the lowpass filter HLP in this case?
ELE 488 F06
Assignment 1 – Part B
Due Oct 9
(You will need the images placed in the Blackboard Assignment 1 folder.)
1, Separate a color image into three components using Paint Shop Pro.
Start Paintshop Pro. Open Fig6.51(a) using Paint Shop Pro. Clicking on the icon
will display the histogram window. You can see the histograms of the luminance and of
the three components, displayed in different colors. You can get the gray scale image by
Image  Gray Scale.
By clicking on: Image  Split Channel  Split to RGB, you can split the image
into its red, green and blue components. Their histograms should match those of the
image before splitting. These three components are displayed as gray scale images.
The component images can be combined into a new image by:
Image  Combine Channel  Combine from RGB. Note that you can specify the
three components to be combined. To reconstruct the original image, use the three
components from ‘splitting’. If you want not to use one of the components, you need to
replace that component with a black image (all pixels have value 0).
A black image can be generated from any of the three components by clicking:
Adjust  Brightness and Contrast  Brightness/Contrast to pull out a panel
which will allow you to make adjustments of that image. Setting the Brightness to
– 255 will result in a black image. Setting the (Brightness to 255 gives a white image.)
To display the red component of Fig6.51(a) in red, you would combine the red
component and the black image as the green and as the blue components. Similarly, you
can display the green component in green and the blue component is blue.
Try to use two of the three components for combination by setting only one of the
components to black (zero). Is the color of these images what you expected?
2. Spatial Filtering
Open the gray scale image lena, in Paintshop Pro. Click on Effects  Effect
Browser, you will see a number of built-in filters. Some of these should be familiar,
some not. Apply these to your image and observe the effects of these filters. What
difference do you observe between Blur and Soften? Does Sharpen reverses the
effect of Soften?
You can also construct your own filter and apply it to the image. Clicking on:
Effects  User Defined Filters will display a dialog box, as illustrated below.
You can then specify the filter coefficients and name your filter. Build a few commonly
used ones, including the 3x3 average, 7x7 average, row and column Sobel filters, and
Sobel Laplacian.
Applying an average filter blurs the image. Try your 3x3 and 7x7 and observe the
result.
Repeat the above using different images, including Figure 4.50(a), peppers, mandrill.