1. Suppose that a list contains the values 20 44 48 55 62 66 74 88 93 99 at index positions 0 through 9. Trace the values of the variables….

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

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

2. Efficiently Calculating the Viola and Jones Features Using an Integral Image: Let *A *be a 24×24 matrix representing an image. The integral image of *A*, denoted by *I *(*A*), is the matrix *B *such that *Bi **, **j *=_ *i *_≤*i **, **j *_≤*j Ai **, **j *. _ Show that *I *(*A*) can be calculated from *A *in time linear in the size of *A*. _ 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).