## CSC 249/449 Computer Vision: Midterm Study Questions

The following are examples of questions that have appeared on previous midterms. Similar or identical questions may appear on the current midterm. Some of these questions may be on areas we have not covered. They will not be asked. We may have covered areas not represented by any question here. You are responsible for those areas anyway.

### General

• Give three examples of problems to which computer vision / image processing techniques have been successfully applied.
• Give two examples of areas in computer vision which are the subject of current research.
• Who funds computer vision research and for what? (give at least two examples).

### Image Formation

• Assume the full moon is a Lambertian disk illuminated by the sun with 1000 watts per square meter, and reflecting 10% of the incident light. What is its brightness in watts per square meter per steradian? (Recall that for a totally reflecting (white) Lambertian surface, L = E / pi)
• Assume the disk of the moon subtends half a degree (or .01 radian), and that the sun irradiates the moon and the earth equally and the moon is a Lambertian disk reflecting 10% of the incident light. What is the ratio of the irradiance of the earth by the noonday sun to the irradiance of the earth by the midnight moon?
• What is the irradiance (in @Watts/ meter sup 2@) of a surface illuminated by a 100 watt lightbulb 1 meter distant. Assume the surface is oriented at 90 degrees to the line connecting it to the light source.
• What is the irradiance (in @Watts/ meter sup 2@ of a surface illuminated by a 200 watt lightbulb 1 meter distant. Assume the surface is oriented at 30 degrees to the line connecting it to the light source.
• You are interested in low-light video surveillance of home environments.
Suppose you have an indoor scene illuminated by a 5W incandescent nightlight bulb on the far wall, 10 meters away (this is a large living room). You have a video camera with an F2.0 lens, and a 500 x 500 pixel chip .5cm (5mm) across that you want to use to observe the scene. The maximum integration time for the camera is about 1/60 of a second. Start by computing the scene irradiance at the observation point. Then calculate the effective irradiance of the chip produced by imaging a perpendicularly oriented, perfectly reflecting matte (Lambertian) surface at the observation point (10 meters away from the light source) and use this value to approximate the number of photons transduced per pixel per integration time. Use this quantity to argue whether or not there is sufficient light to perform meaningful surveillance with this camera.
You will need to use the following information:
• The efficiency of an incandescent bulb in converting electrical energy to visible light photons is 10 percent.
• The efficiency of the chip in tranducing photons that fall on a pixel is 10 percent (that is, only 10 percent of the incident photons result in any electric charge accumulating in the CCD ``bucket''.
• The energy in a photon of visible light is given by h * frequency where h is Planck's constant = 6.63E-34 Joule-seconds. For visible light at 500nm, this gives a photon energy of about 3E-19 Joules.
The following may also be useful points to remember:
• The F-stop value of a lens is the ratio of the diameter to the focal length.
• From the point of view of the chip, an in-focus lens appears as a lens-sized disk whose brightness is equal to the radiance of the imaged scene point.
• The radiance of a Lamberian surface illuminated by irradiance E is E/pi.
• A Watt is one Joule per second.
• You only need values with less than one decimal precision to answer this question, so you do not need a calculator.
• Consider a camera with a focal length of 20 cm. For a pinhole approximation to the camera consider a coordinate system centered at the center of projection (the lens center) with the z axis aligned with the optical axis. Now consider a 10 cm square parallel to the image plane with its center at (1,1,1) (x,y,z coordinates in meters). What is the location, size and shape of the image of the square? Or consider a sphere with 10 cm radius centered at (1,1,1) (x,y,z coordinates in meters). What is the location, size and shape of the image of the sphere?
• Consider a camera with a lens aperture of 1 cm and a focal length of 10 cm. Assume the surface in part b (viewed from a large distance) is focussed on the image plane at the point (0,0) where it is pierced by the optical axis. If the surface is lambertian, what is the irradiance of the image plane at point (0,0)? Assume that 1 cm is small enough with respect to 10 cm so that the solid angle subtended by the lens can be reasonably approximated using the area of a disk. (Hint: Recall that from the focal plane, the lens looks like a uniform region of radiance equal to the object focussed on the plane at that point, and that for a Lambertian surface, L = E/pi)

### Image Processing

• Convolve the given 2x2 mask with the given 4x4 image (result should be 3x3)
• How do Gaussian and median filters compare as smoothing operators?
• How do block average and median filters compare as smoothing operators?
• Does it make sense to apply histogram equalization to a binary image? Why or why not?
• Does it make sense to apply histogram equalization to a color image? Why or why not?
• What are the advantages and limitations of using a template with an SSD or SAD metric to find patterns in an image? What are some approaches for dealing with the limitations?
• How would you use correlation matching to detect lines (as opposed to edges) in an image? Does it matter if the lines are dark on light or light on dark?
• What is a Hamming distance? How can it be employed for finding patterns in images, and how can its limitations be dealt with?
• What is a Hausdorf (distance transform) metric? How can it be employed for matching patterns in images, and what advantages and disadvantages does it have compared to simple template matching based on a Hamming or SSD metric?
• What is deblurring? How is it performed in the Fourier domain? What are some of the practical problems associated with the technique?
• What are two ways in which real images differ from those predicted by a simple "pinhole" camera model. What are some consequences of these effects for computer vision applications?

### Biology

• Briefly describe the following structures in the eye and their functional significance.
• Lens
• Cornea
• Iris
• Retina
• Fovea
• Rod
• Cone
• Ganglion cell
• Optic nerve
• Blind spot
• Draw a schematic diagram of the human eye showing all the above
• What is meant by the receptive field of a neuron? What is the significance of the concept?

### Edges, Countours

• Sketch the response of the Sobell operator as it moves across a step edge from left to right as shown. How would you use this as an edgel detector? what edges would it be sensitive to?
• Sketch the response of a digital Laplacian operator as it moves across a step edge. How would you use this as an edgel detector?
• Describe a method of obtaining (thinned) edgel points in an image. Describe any correlation masks and thinning and thresholding operations used. How well does your algorithm correspond to an "ideal" edgel-finding algorithm (e.g. can you think of any practical problems with it?).
• Describe, in general terms, how edgel linking techniques are used to extract contours from images. What are the problems and limitations of this approach?
• Describe, in general terms, how feature growing methods can be applied to the problem of segmenting extended boundary segments from images.
• Describe, in general terms, how graph search techniques can be applied to the problem of linking edgels into longer boundary segments.
• Describe, in general terms, how adaptive contour techniques (snakes) can be used to adjust approximate contours to fit underlying data.

### Regions

• What is a homogeneity condition? Give an example. How are they used in region segmentation?
• For ordinary compact regions, which region-growing algorithm is likely to be more space efficient, breadth-first or depth-first search? Explain.
• Name three different attributes that would be useful for characterizing regions.
• How can gray-level histograms be used to segment a region? What are the limitations of this method?
• How can color histograms be used to help segment a color image? What are the primary difficulties in implementing such a technique?
• What advantages might be obtained from attempting to segment "same stuff" regions in an image on the basis of characteristic texture rather than gray level? What difficulties and drawbacks might be associated with such an approach?
• With respect to region segmentation, what is a split and merge technique? What is needed to implement such an algorithm?

### Hough Transform

• Describe how you might use a Hough transform technique to detect squares in an image. Assume that some sort of preprocessing has already grouped the edgels into line segments. Make sure you describe the parameter space and the voting technique.
• Describe how you might use a Hough transform technique to detect rectangles. Make sure you describe the parameter space and the voting technique.
• Describe how you might use a Hough transform technique to detect pairs of parallel lines in an image. Make sure you describe the parameter space and the voting technique.
• Describe how you might use a Hough transform technique to detect circles in an image. Make sure you describe the parameter space and the voting technique.
• Describe how you might use a Hough transform technique to detect straight lines in a 3-dimensional image. This issue could arise in attempting to find translating objects in video sequences, or in processing tomographic data. Make sure you describe the parameter space and the voting technique in detail.
• Describe how you might use a Hough transform technique to detect planar features in a 3-dimensional image. This issue could arise in attempting to find translating objects in video sequences, or in processing tomographic data. Make sure you describe the parameter space and the voting technique in detail.

### Bayesian Probability

• Suppose you have the following information:
• One out of 10 million people who have ever lived is a great poet.
• 90% of all great poets are dead, and 50% of all people who have ever lived are dead.
Use Bayes formula to compute the a-posteriori probability that a person is a great poet give that the person is alive.
• Suppose you have the following information:
• 10% of all cars are sports cars.
• 50% of sports cars are red, and 5% of non-sports cars are red.
Use Bayes formula to compute the a-posteriori probability that a car is a sports car given that it is red.