This paper describes the calculation of P(F) and P(D) for the Hough transform technique when the primary threshold crossings are weighted by their power before transforming (i.e., noncoherent integration). After expressions for P(F) and P(D) are derived, we examine the question of optimal granularity of the Hough accumulator space. We also investigate the relationship between primary and secondary thresholds and its effect on detectability.