Show how every Viola and Jones feature can be calculated from I (A) in a constant amount of time (that is, the runtime does not depend on the size of the rectangle defining the feature).

1. Let ≥ 1 be any integer. Prove that VCdim(L(Bd ,)) ≥ 0.5log(d).

Hint: Construct a set of instances by taking the rows of the matrix from the previous question, and the rows of the matrices 2A,3A,4A, . . ., A. Show that the resulting set is shattered by L(Bd ,).

2. Efficiently Calculating the Viola and Jones Features Using an Integral Image: Let be a 24×24 matrix representing an image. The integral image of A, denoted by (A), is the matrix such that Bi =_ _≤_≤j Ai . _ Show that (A) can be calculated from in time linear in the size of A. _ Show how every Viola and Jones feature can be calculated from (A) in a constant amount of time (that is, the runtime does not depend on the size of the rectangle defining the feature).

find the cost of your paper

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Draw a class diagram that shows the relationships among the classes in this new version of the system

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