ISTA 352 - Images: Past, Present, and Future - Fall 2012

Assignment Three (B)

Note change of format---this assignments has been broken into two smaller units

Due: Late (*) Sunday, October 21.

(*) "Late" means that the instructor might start grading by 8AM Monday. Once the instructor starts grading, no more assignments will be accepted.

5 points

This assignment should be done individually

 

You can do the programming parts of this assignment in any language you like, although if your results are anomalous, and the grader does not speak the language you use, they may be less able to quickly figure out what the problem is and give you reasonable part marks.

 

Regardless of what language you use, please follow the instructions linked here  carefully.

 

Deliverables

Deliverables within questions are flagged with ($).

 

This assignment has two questions. The first regular problem is worth 3 points, and the second one is worth 2, for a total of 5.

 

 

1. (+++) For this question you will need to click points on images and record the coordinates of where you clicked. You will need to do this for 8 pairs of corresponding points in two images. You can achieve this any way you like, but one way you could consider is to look at the Matlab routine impixel (with three output arguments).

The image pair

slide1.jpg         frame1.jpg

are an image of a PowerPoint slide and a frame from a video of the lecture using that slide.

 

i) (a) Select 4 pairs of corresponding points in the two images. For example, you may want to use the corners of the slide. Call this set (A,A’) where A is the (x,y) for 4 points on the slide image, and A’ is the (x’,y’) for 4 points on the frame image. Report your points and how you got them ($). Repeat this for 4 more pairs of points, (B,B’), and again report your points and you got them ($),

 

i) (b) Add squares of differing colors (for each pairs) to the images for both (A,A’) and (B,B’). (You can build on code that you should already have from a previous assignment). Put the two images into your report with an informative caption ($).

 

ii) (a) The Matlab function direct_linear_transform (linked) takes two matrices with 2 columns and the same number of rows (there must be at least four) computes the homography mapping, H, that maps the first one to the second. Use that function to compute the homography that maps the slide points in A to frame points in A’. Report the homography, H ($). Now use H to compute both where the slide points in A map to in the frame image, and similarly where B are mapped into the frame image. Visualize this by adding squares onto the modified frame image that shows your selected points (they are the “target”). Put this image into your report with an informative caption ($).

 

ii) (b) We can measure the effectiveness of the mapping by computing the average Euclidean distance between the mapped points (i.e., where H tells the points in A to go) and the selected points (i.e., the points in A’). Compute this distance for both sets of four points. Report the two error measures ($). Comment on whether the mapped points from A are closer to the target points than the mapped points from B or vice versa (you can also refer to your image to discuss this rather than just relying on what a single number tells you). If there is a difference (generally there will be one), offer an explanation ($).

 

iii) (a) By some process (perhaps by selecting 2 points) define a rectangle to put a box around the title of the slide, and a second one to put a box around the bullet points. Use the line drawing capability from a previous assignment to draw these to boxes in red on the slide image. Put the resulting image into your report with an informative caption.

 

iii) (b) Using the homography transformation already computed, “improve” the slide frame by putting a corresponding box (this time green) into the frame image. 

 

 

2. (++) The anti British colonialism society has hired you to make cylindrical projection maps that have the prime meridian on the left edge (and thus the right edge also). Referring to slide 18 of lecture 21, create two very sparse maps of the world using (a) the form of a “basic cylindrical projection” and (b) the analogous “Mercator” projection. For (a) you will need to do some simple trigonometry. For (b) you will need to pay close attention to the formula. Your map should extend from -85 to 85 degrees latitude (i.e., skip the last 5 degrees to the poles). If that does not work so well in one or both cases, use -80 to 80 degrees, but be sure to included which you used in your caption. Your maps should show some equally spaced meridians, and some equally spaced (in terms of degrees) lines of longitude. Finally, put differently colored squares for the following places (targeted for a campaign on the exaggerated importance of England): Hong Kong, Vancouver BC, Cape Town, and Sydney. Put the two  maps into your report with an informative caption, including which colors correspond to which cities.

 

 

What to Hand In

Consult the instructions linked here for conventions for preparing and handing in assignments. In 2012, hand in assignments via email to Kyle Simek (ksimek@email.arizona.edu).