STN-Homography: Direct Estimation of Homography Parameters for Image Pairs

Round 1

Reviewer 1 Report

The author attempts an implementation of the hierarchical STN to estimate the 2D homography matrix. For a better understanding, additional explanations are recommended in the following point.

In the proposed method, eight parameters of the homography matrix are estimated instead of the four-point homography parameterization. It means the degree-of-freedom of the unknown parameters to be estimated increases from four to eight. The eight parameters seem to be redundant to determine the image transformation that has a limited degree-of-freedom. The parameter estimation may become unstable. Nevertheless, what is the advantage to employ the eight parameters estimation?

Author Response

Thank you for your review and comments

 

First, we need to explain that the homography matrix H has eight degrees-of-freedom instead of four degrees-of-freedom (as depicted in section 2 in our paper). Given that the H can be multiplied by an arbitrary nonzero scale factor without altering the projective transformation, only the ratio of the matrix elements is significant, thus leaving H eight independent ratios corresponding to eight degrees-of-freedom. In fact, we always set the last element of H to be equal to 1.0.

 

Secondly, for the four-point homography parameterization scheme, the actual estimation is also eight independent parameters, because each point has two independent parameters (i.e., the coordinate offset values in x direction and y direction respectively) ​​to be estimated.

Reviewer 2 Report

well written paper, with a high degree of novelty and convincing results (runtime, quality of estimation) when compared with the state of the art in that field.

So a clear accept.

Recommondation: It would be good if the Tensorflow implementation is madepublically availabe on a github repository.

Author Response

Thanks for your review and positive comments.

 

I am very willing to open source the code on github. However, I recently graduated from school and entered the company, and so opening source code needs to go through the company's approval process. I will apply for opening the source code as soon as possible.

Reviewer 3 Report

This is an interesting contribution in the field of homography estimation. It builds up on a previous contribution by employing the STN in order to perform direct homography parameter estimation, either in a hierarchical manner or in a cascade (sequentially). The results prove that the new architectures provides better accuracy in homography estimation between image patch pairs.

My only question is why are the homography matrix estimations multiplied together in Eq. (3) instead of being added, as in [24].

 

Author Response

Please see the attachment.

Author Response File: Author Response.pdf