Homework #6 Due 10/19/07

1. As discussed in class, an intensity-gradient operator can be approximated by application of the mask to the raw grayscale data in a manner slightly different from that used previously. In particular the gradient operator itself produces a vector. If a continuous field of intensity were denoted by V(x,y) then the gradient of this yields V_xi+V_yj, where V_x is the partial derivative of V with respect to x and V_y is the partial derivative of V with respect to y. The magnitude of this gradient at any point x,y is sqrt(V_x²+V_y²).

We wish to replace the center pixel (over which the central 0 is currently placed) with an approximation to this gradient magnitude. That would entail approximating V_x using the shaded, horizontal operator, applied to the indicated pixels, and applying the vertical to approximate V_y.

For example, if the grayscale elements were as shown to the left, the center value would become

sqrt[(-1*127+0*129+1*132)²+(1*126+0*129-1*131)²].

Subsequently, we normalize and otherwise condition the resulting matrix (with outermost rows and columns untouched by the transformation) in order to print the consequent image outlines with reasonable density. Toward this end, select one of your existing (raw) images from the lab and

(a) apply the algorithm above to change all interior pixel values.

(b)write a program that will sweep through the resulting array enough times to ascertain a threshold “th” of the conditioned array magnitudes such that between five percent and ten percent of all pixel magnitudes take on values above this threshold.

(c) apply your resulting threshold to all conditioned pixels such that in a new array each pixel above th is set to 0 and each pixel below the th is set to 255.

(d)Print the resulting image.

2. The second problem is a two-team effort.

Team 1: Write a code in C++ that will cause the arm of the Rover to undergo ten separate poses. Ensure that these poses can be repeated at will via reuse of the program, and that each corresponds with (reasonably accurate), specific (i.e. known to you) q₁ and q₂ values in radians or degrees. We will use these values in a subsequent exercise to initialize our Cs. Take q₁ and q₂ to be defined as per the class discussion, i.e. as indicated to the right. Keep the range of both angles comparatively small, within about 30 degrees.

Team 2: Go to the lab and note all cues on the Rover arm. Measure and record in mm, to the nearest half-mm, the x y and z coordinates of the nonunique cue centers relative to the unique-cue cue center (i.e. this unique cue would be the origin of your coordinate system). Indicate on a drawing the unique-cue-relative x y and z directions you are using on one or more pictures acquired of the end member.