johu's profile - activity

Thanks for your reply. My actual goal is to take advantage of symmetry. However I noticed, that croping an rotated rectangle from an image and flipping does not give the same result than flipping the whole image and cropping the transformed rotated rectangle. I boiled it down to that problem. I see your point that round off errors can be neglected in many applications in CV, however, I would not make a distinction between math and images. I think it is strange, that we see such a huge roundoff error in a linear interpolation (float has an precission of 1e-6 which is 4 orders af magnitudes below the error). Anyway, thanks a lot.

The rounding error is what I want here. I don't see my error in the code. If you see it, please tell me. I also added a sanity check which shows, that something strange is going on.

I think the following examples shows a bug in warpAffine:

   Mat x(1,20, CV_32FC1);
    for (int iCol(0); iCol<x.cols; iCol++) { x.col(iCol).setTo(iCol); }
    Mat crop;
    Point2d c(10., 0.);
    double scale(1.3);
    int cropSz(11);
    double vals[6] = { scale, 0.0, c.x-(cropSz/2)*scale, 0.0, scale, c.y };
    Mat map(2, 3, CV_64FC1, vals);
    warpAffine(x, crop, map, Size(cropSz, 1), WARP_INVERSE_MAP |  INTER_LINEAR);
    float dx = (crop.at<float>(0, crop.cols-1) - crop.at<float>(0, 0))/(crop.cols-1);
    Mat constGrad = crop.clone().setTo(0);
    for (int iCol(0); iCol<constGrad.cols; iCol++) {
      constGrad.col(iCol) = c.x + (iCol-cropSz/2)*scale;
    }
    Mat diff = crop - constGrad;
    double err = norm(diff, NORM_INF);
    if (err>1e-4) {
      cout << "Problem:" << endl;
      cout << "computed output: " << crop << endl;
      cout << "expected output: " << constGrad << endl;
      cout << "difference: " << diff << endl;
      Mat dxImg;
      Mat dxFilt(1, 2, CV_32FC1);
      dxFilt.at<float>(0) = -1.0f;
      dxFilt.at<float>(1) = 1.0f;
      filter2D(crop, dxImg, crop.depth(), dxFilt);
      cout << "x-derivative in computed output: " << dxImg(Rect(1,0,10,1)) << endl;
      cout << "Note: We expect a constant difference of 1.3" << endl;
    }

Here is the program output:

Problem:
computed output: [3.5, 4.8125, 6.09375, 7.40625, 8.6875, 10, 11.3125, 12.59375, 13.90625, 15.1875, 16.5]
expected output: [3.5, 4.8000002, 6.0999999, 7.4000001, 8.6999998, 10, 11.3, 12.6, 13.9, 15.2, 16.5]
difference: [0, 0.012499809, -0.0062499046, 0.0062499046, -0.012499809, 0, 0.012499809, -0.0062503815, 0.0062503815, -0.012499809, 0]
x-derivative in computed output: [1.3125, 1.28125, 1.3125, 1.28125, 1.3125, 1.3125, 1.28125, 1.3125, 1.28125, 1.3125]
Note: We expect a constant difference of 1.3

I create an image with entries 0, 1, 2, ...n-1, and cut a region around (10,0) with scale 1.3. I also create an expected image constGrad. However, they are not the same. Even more, since the input image has a constant derivative in x-direction and the mapping is affine, I expect also a constant gradient in the resulting image. The problem is not a boundary stuff problem, the same happens at the inner of an image. It's also not related to WARP_INVERSE_MAP.

Is this a known issue? any comments on this?

In a linear SVM you can reduce the support vectors to a single vector by their weights. Thus, you only need to save that one and that's all you need to predict, correct? However, in OpenCV, the original support vectors are still saved. Is there a way to get rid of them? I can imagine, that they may be useful for online learning, but that does not apply in my case. So I don't need them and they are just using memory.