Topic Cascade Object Detection with deformable part models a suspicion

The author of this article is Pedro F. felzenszwalb wait a minute, famous DPM in the target detection model. The work of this article is a cascade of DPM (deformed component models) to speed up detection.

The accelerated way, now followed by the calculation of certain parts of the score, assumes that the values are less than a certain threshold value, discarding the position of the object to continue to detect, thought.

In the abstract, the author speaks of a core contribution of the article:

In analogy to probably approximately correct (PAC) learning, we introduce the notion of probably approximately admissible (PAA) thresholds. Such thresholds provide theoretical guarantees on the performance of the Cascade method and can is computed from a small s Ample of positive examples.

The concept of "probability approximate allowable (PAA) threshold" is proposed. This threshold is theoretically guaranteed in performance and requires only a small amount (training) of positive samples.

In Cascade classifiers, it is important to set thresholds at all levels. It is very good to have a method to determine the thresholds that are guaranteed by the theory.

Take a look at the threshold setting method and the proof of the theory guarantee in this paper.

First some concept notes:

Then the threshold setting method:

And then the theoretical proof:

My question is: the authors claim that their thresholds are theoretically guaranteed. However, the proof of theorem 1 is that if the threshold can guarantee a very small error.

This is not the main conclusion-the threshold value is theoretically guaranteed-it has not been proven?

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Topic Cascade Object Detection with deformable part models a suspicion