Answers to Questions:
  1. How many control points does it take to get a ``good'' transformation between images?
    2. Answer: Refer to the experiments section of the report for the mosaicing results for minimum number of control points.
    The minimum number of control points needed to get a good mosaic for this dataset is 6 and the results look as shown below :-
    View 0 Mosaic with 6
    control points between each image pair    		 View 1 Mosaic with 6
    control points between each image pair
    View 2 Mosaic with 6
    control points between each image pair    		 View 3 Mosaic with 6
    control points between each image pair


  2. How does the algorithm behave at the theoretical minimum of the number of control points?
    Answer:
    The theoretical minimum number of points needed is 4 to get 8 equations which can be solved for 8 parameters of the projective transformation. In case of the mosaicing example , only 4 points give results which do not look great( Refer to images as shown in experiments section of the report.Increasing the number of correspondences significantly improves mosaicing results.

  3. From your experiments how does the accuracy of the control points affect the results?
    Answer:
    I tried changing the values of the control points under two conditions
    1. When the number of control points is small (say 4) (dataset used :- planar mosaic example)
    2. When the number of control points is maximum.

    In the first case even a small change in the accuracy of the control point significantly distorts the resulting mosaic as we do not have an overconstrained system.
    For example in case of my planar mosaic changing the correspondences by 0, 10 and 20 pixels gave me the following result.

    Mosaic with an error of 20 pixels Mosaic with an error of 10 pixels in one of the correspondences Mosaic with an error of 20 pixels in one of the correspondences
    No error in correspondences Error of 10 pixels
    in 1 correspondence    		 Error of 20 pixels
    in 1 correspondence
    However for the mosaic example ,i used the maximum number of correspondences and changed one of the correspondences by 0, 10,20 ,30 pixels, this did not result in as significant a distortion as in the previous case. From the experiments, the sensitivity of mosaic results to control point accuracy is dependent on the number of control points (correspondences) used.
    Lesser the number of control points , more sensitive is the mosaiced image to control point accuracy , while more the number of correspondences , lesser is the sensitivity of the mosaiced image to control point accuracy.

    Mosaic with No error Mosaic with an error of 10 pixels in one of the correspondences Mosaic with an error of 20 pixels in one of the correspondences Mosaic with an error of 30 pixels in one of the correspondences
    No error in correspondences Error of 10 pixels
    in 1 correspondence    		 Error of 20 pixels
    in 1 correspondence     		Error of 30 pixels
    in 1 correspondence