Translate image by very small step by OpenCV in C++

Question

I'm doing image translation by very small step sizes (like translate in column by 1/1024)

Consider I have the following image (I create the image with "Mat" in opencv and with the type CV_64F):

255  0
 0   0

Now by doing translation in column by (1/1024) I would expect the following:

254.7509765625 0.2490234375
     0               0

But what I get is the same source image!:

255  0
 0   0 

How can I get the expected result?

Here is the code I'm doing the translation:

Mat sourceImg = (Mat_<double>(2, 2) << 255.0, 0, 0, 0);
double translateColumn, translateRow;
translateColumn = 1.0/1024.0;
translateRow = 0.0;   

Mat translationMatrix = (Mat_<double>(2, 3) << 1, 0, translateColumn, 0, 1, translateRow);

Mat translatedImage;
warpAffine(sourceImage, translatedImage, translationMatrix , sourceImage.size());

Any idea would be appreciated.

Answer 1

Found the reason of imprecision in file

imgproc.hpp

Interpolation uses precomputed lookup tables and number of used bits defines the size of these tables, and accuracy of approximation.

Seems it defined in fragment:

enum InterpolationMasks {
       INTER_BITS      = 5,
       INTER_BITS2     = INTER_BITS * 2,
       INTER_TAB_SIZE  = 1 << INTER_BITS,
       INTER_TAB_SIZE2 = INTER_TAB_SIZE * INTER_TAB_SIZE
     };

Alternatively you can use this method (found in web):

/* 
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 *  LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
 *  ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
 *  POSSIBILITY OF SUCH DAMAGE.
 *
 *  File:    shift.hpp
 *  Author:  Hilton Bristow
 *  Created: Aug 23, 2012
 */

#ifndef SHIFT_HPP_
#define SHIFT_HPP_

#include <limits>
#include <opencv2/core/core.hpp>
#include <opencv2/imgproc/imgproc.hpp>

/*! @brief shift the values in a matrix by an (x,y) offset
 *
 * Given a matrix and an integer (x,y) offset, the matrix will be shifted
 * such that:
 *
 *  src(a,b) ---> dst(a+y,b+x)
 *
 * In the case of a non-integer offset, (e.g. cv::Point2f(-2.1, 3.7)),
 * the shift will be calculated with subpixel precision using bilinear
 * interpolation.
 *
 * All valid OpenCV datatypes are supported. If the source datatype is
 * fixed-point, and a non-integer offset is supplied, the output will
 * be a floating point matrix to preserve subpixel accuracy.
 *
 * All border types are supported. If no border type is supplied, the
 * function defaults to BORDER_CONSTANT with 0-padding.
 *
 * The function supports in-place operation.
 *
 * Some common examples are provided following:
 * \code
 *  // read an image from file
 *  Mat mat = imread(filename);
 *  Mat dst;
 *
 *  // Perform Matlab-esque 'circshift' in-place
 *  shift(mat, mat, Point(5, 5), BORDER_WRAP);
 *
 *  // Perform shift with subpixel accuracy, padding the missing pixels with 1s
 *  // NOTE: if mat is of type CV_8U, then it will be converted to type CV_32F
 *  shift(mat, mat, Point2f(-13.7, 3.28), BORDER_CONSTANT, 1);
 *
 *  // Perform subpixel shift, preserving the boundary values
 *  shift(mat, dst, Point2f(0.093, 0.125), BORDER_REPLICATE);
 *
 *  // Perform a vanilla shift, integer offset, very fast
 *  shift(mat, dst, Point(2, 2));
 * \endcode
 *
 * @param src the source matrix
 * @param dst the destination matrix, can be the same as source
 * @param delta the amount to shift the matrix in (x,y) coordinates. Can be
 * integer of floating point precision
 * @param fill the method used to fill the null entries, defaults to BORDER_CONSTANT
 * @param value the value of the null entries if the fill type is BORDER_CONSTANT
 */
void shift(const cv::Mat& src, cv::Mat& dst, cv::Point2f delta, int fill=cv::BORDER_CONSTANT, cv::Scalar value=cv::Scalar(0,0,0,0)) {

    // error checking
    assert(fabs(delta.x) < src.cols && fabs(delta.y) < src.rows);

    // split the shift into integer and subpixel components
    cv::Point2i deltai(ceil(delta.x), ceil(delta.y));
    cv::Point2f deltasub(fabs(delta.x - deltai.x), fabs(delta.y - deltai.y));

    // INTEGER SHIFT
    // first create a border around the parts of the Mat that will be exposed
    int t = 0, b = 0, l = 0, r = 0;
    if (deltai.x > 0) l =  deltai.x;
    if (deltai.x < 0) r = -deltai.x;
    if (deltai.y > 0) t =  deltai.y;
    if (deltai.y < 0) b = -deltai.y;
    cv::Mat padded;
    cv::copyMakeBorder(src, padded, t, b, l, r, fill, value);

    // SUBPIXEL SHIFT
    float eps = std::numeric_limits<float>::epsilon();
    if (deltasub.x > eps || deltasub.y > eps) {
        switch (src.depth()) {
            case CV_32F:
            {
                cv::Matx<float, 1, 2> dx(1-deltasub.x, deltasub.x);
                cv::Matx<float, 2, 1> dy(1-deltasub.y, deltasub.y);
                sepFilter2D(padded, padded, -1, dx, dy, cv::Point(0,0), 0, cv::BORDER_CONSTANT);
                break;
            }
            case CV_64F:
            {
                cv::Matx<double, 1, 2> dx(1-deltasub.x, deltasub.x);
                cv::Matx<double, 2, 1> dy(1-deltasub.y, deltasub.y);
                sepFilter2D(padded, padded, -1, dx, dy, cv::Point(0,0), 0, cv::BORDER_CONSTANT);
                break;
            }
            default:
            {
                cv::Matx<float, 1, 2> dx(1-deltasub.x, deltasub.x);
                cv::Matx<float, 2, 1> dy(1-deltasub.y, deltasub.y);
                padded.convertTo(padded, CV_32F);
                sepFilter2D(padded, padded, CV_32F, dx, dy, cv::Point(0,0), 0, cv::BORDER_CONSTANT);
                break;
            }
        }
    }

    // construct the region of interest around the new matrix
    cv::Rect roi = cv::Rect(std::max(-deltai.x,0),std::max(-deltai.y,0),0,0) + src.size();
    dst = padded(roi);
}


#endif /* SHIFT_HPP_ */

It seems works fine.