--- /dev/null
+.. _remap:
+
+Remapping
+*********
+
+Goal
+====
+
+In this tutorial you will learn how to:
+
+a. Use the OpenCV function :remap:`remap <>` to implement simple remapping routines.
+
+Theory
+======
+
+What is remapping?
+------------------
+
+* It is the process of taking pixels from one place in the image and locating them in another position in a new image.
+
+* To accomplish the mapping process, it might be necessary to do some interpolation for non-integer pixel locations, since there will not always be a one-to-one-pixel correspondence between source and destination images.
+
+* We can express the remap for every pixel location :math:`(x,y)` as:
+
+ .. math::
+
+ g(x,y) = f ( h(x,y) )
+
+ where :math:`g()` is the remapped image, :math:`f()` the source image and :math:`h(x,y)` is the mapping function that operates on :math:`(x,y)`.
+
+* Let's think in a quick example. Imagine that we have an image :math:`I` and, say, we want to do a remap such that:
+
+ .. math::
+
+ h(x,y) = (I.cols - x, y )
+
+ What would happen? It is easily seen that the image would flip in the :math:`x` direction. For instance, consider the input image:
+
+ .. image:: images/Remap_Tutorial_Theory_0.jpg
+ :alt: Original test image
+ :width: 120pt
+ :align: center
+
+ observe how the red circle changes positions with respect to x (considering :math:`x` the horizontal direction):
+
+ .. image:: images/Remap_Tutorial_Theory_1.jpg
+ :alt: Original test image
+ :width: 120pt
+ :align: center
+
+* In OpenCV, the function :remap:`remap <>` offers a simple remapping implementation.
+
+Code
+====
+
+#. **What does this program do?**
+
+ * Loads an image
+ * Each second, apply 1 of 4 different remapping processes to the image and display them indefinitely in a window.
+ * Wait for the user to exit the program
+
+#. The tutorial code's is shown lines below. You can also download it from `here <https://code.ros.org/svn/opencv/trunk/opencv/samples/cpp/tutorial_code/ImgTrans/Remap_Demo.cpp>`_
+
+.. code-block:: cpp
+
+ #include "opencv2/highgui/highgui.hpp"
+ #include "opencv2/imgproc/imgproc.hpp"
+ #include <iostream>
+ #include <stdio.h>
+
+ using namespace cv;
+
+ /// Global variables
+ Mat src, dst;
+ Mat map_x, map_y;
+ char* remap_window = "Remap demo";
+ int ind = 0;
+
+ /// Function Headers
+ void update_map( void );
+
+ /**
+ * @function main
+ */
+ int main( int argc, char** argv )
+ {
+ /// Load the image
+ src = imread( argv[1], 1 );
+
+ /// Create dst, map_x and map_y with the same size as src:
+ dst.create( src.size(), src.type() );
+ map_x.create( src.size(), CV_32FC1 );
+ map_y.create( src.size(), CV_32FC1 );
+
+ /// Create window
+ namedWindow( remap_window, CV_WINDOW_AUTOSIZE );
+
+ /// Loop
+ while( true )
+ {
+ /// Each 1 sec. Press ESC to exit the program
+ int c = waitKey( 1000 );
+
+ if( (char)c == 27 )
+ { break; }
+
+ /// Update map_x & map_y. Then apply remap
+ update_map();
+ remap( src, dst, map_x, map_y, CV_INTER_LINEAR, BORDER_CONSTANT, Scalar(0,0, 0) );
+
+ /// Display results
+ imshow( remap_window, dst );
+ }
+ return 0;
+ }
+
+ /**
+ * @function update_map
+ * @brief Fill the map_x and map_y matrices with 4 types of mappings
+ */
+ void update_map( void )
+ {
+ ind = ind%4;
+
+ for( int j = 0; j < src.rows; j++ )
+ { for( int i = 0; i < src.cols; i++ )
+ {
+ switch( ind )
+ {
+ case 0:
+ if( i > src.cols*0.25 && i < src.cols*0.75 && j > src.rows*0.25 && j < src.rows*0.75 )
+ {
+ map_x.at<float>(j,i) = 2*( i - src.cols*0.25 ) + 0.5 ;
+ map_y.at<float>(j,i) = 2*( j - src.rows*0.25 ) + 0.5 ;
+ }
+ else
+ { map_x.at<float>(j,i) = 0 ;
+ map_y.at<float>(j,i) = 0 ;
+ }
+ break;
+ case 1:
+ map_x.at<float>(j,i) = i ;
+ map_y.at<float>(j,i) = src.rows - j ;
+ break;
+ case 2:
+ map_x.at<float>(j,i) = src.cols - i ;
+ map_y.at<float>(j,i) = j ;
+ break;
+ case 3:
+ map_x.at<float>(j,i) = src.cols - i ;
+ map_y.at<float>(j,i) = src.rows - j ;
+ break;
+ } // end of switch
+ }
+ }
+ ind++;
+ }
+
+Explanation
+===========
+
+#. Create some variables we will use:
+
+ .. code-block:: cpp
+
+ Mat src, dst;
+ Mat map_x, map_y;
+ char* remap_window = "Remap demo";
+ int ind = 0;
+
+#. Load an image:
+
+ .. code-block:: cpp
+
+ src = imread( argv[1], 1 );
+
+#. Create the destination image and the two mapping matrices (for x and y )
+
+ .. code-block:: cpp
+
+ dst.create( src.size(), src.type() );
+ map_x.create( src.size(), CV_32FC1 );
+ map_y.create( src.size(), CV_32FC1 );
+
+#. Create a window to display results
+
+ .. code-block:: cpp
+
+ namedWindow( remap_window, CV_WINDOW_AUTOSIZE );
+
+#. Establish a loop. Each 1000 ms we update our mapping matrices (*mat_x* and *mat_y*) and apply them to our source image:
+
+ .. code-block:: cpp
+
+ while( true )
+ {
+ /// Each 1 sec. Press ESC to exit the program
+ int c = waitKey( 1000 );
+
+ if( (char)c == 27 )
+ { break; }
+
+ /// Update map_x & map_y. Then apply remap
+ update_map();
+ remap( src, dst, map_x, map_y, CV_INTER_LINEAR, BORDER_CONSTANT, Scalar(0,0, 0) );
+
+ /// Display results
+ imshow( remap_window, dst );
+ }
+
+ The function that applies the remapping is :remap:`remap <>`. We give the following arguments:
+
+ * **src**: Source image
+ * **dst**: Destination image of same size as *src*
+ * **map_x**: The mapping function in the x direction. It is equivalent to the first component of :math:`h(i,j)`
+ * **map_y**: Same as above, but in y direction. Note that *map_y* and *map_x* are both of the same size as *src*
+ * **CV_INTER_LINEAR**: The type of interpolation to use for non-integer pixels. This is by default.
+ * **BORDER_CONSTANT**: Default
+
+ How do we update our mapping matrices *mat_x* and *mat_y*? Go on reading:
+
+#. **Updating the mapping matrices:** We are going to perform 4 different mappings:
+
+ a. Reduce the picture to half its size and will display it in the middle:
+
+ .. math::
+
+ h(i,j) = ( 2*i - src.cols/2 + 0.5, 2*j - src.rows/2 + 0.5)
+
+ for all pairs :math:`(i,j)` such that: :math:`\dfrac{src.cols}{4}<i<\dfrac{3 \cdot src.cols}{4}` and :math:`\dfrac{src.rows}{4}<j<\dfrac{3 \cdot src.rows}{4}`
+
+ b. Turn the image upside down: :math:`h( i, j ) = (i, src.rows - j)`
+
+ c. Reflect the image from left to right: :math:`h(i,j) = ( src.cols - i, j )`
+
+ d. Combination of b and c: :math:`h(i,j) = ( src.cols - i, src.rows - j )`
+
+ This is expressed in the following snippet. Here, *map_x* represents the first coordinate of *h(i,j)* and *map_y* the second coordinate.
+
+ .. code-block:: cpp
+
+ for( int j = 0; j < src.rows; j++ )
+ { for( int i = 0; i < src.cols; i++ )
+ {
+ switch( ind )
+ {
+ case 0:
+ if( i > src.cols*0.25 && i < src.cols*0.75 && j > src.rows*0.25 && j < src.rows*0.75 )
+ {
+ map_x.at<float>(j,i) = 2*( i - src.cols*0.25 ) + 0.5 ;
+ map_y.at<float>(j,i) = 2*( j - src.rows*0.25 ) + 0.5 ;
+ }
+ else
+ { map_x.at<float>(j,i) = 0 ;
+ map_y.at<float>(j,i) = 0 ;
+ }
+ break;
+ case 1:
+ map_x.at<float>(j,i) = i ;
+ map_y.at<float>(j,i) = src.rows - j ;
+ break;
+ case 2:
+ map_x.at<float>(j,i) = src.cols - i ;
+ map_y.at<float>(j,i) = j ;
+ break;
+ case 3:
+ map_x.at<float>(j,i) = src.cols - i ;
+ map_y.at<float>(j,i) = src.rows - j ;
+ break;
+ } // end of switch
+ }
+ }
+ ind++;
+ }
+
+
+Result
+======
+
+#. After compiling the code above, you can execute it giving as argument an image path. For instance, by using the following image:
+
+ .. image:: images/Remap_Tutorial_Original_Image.jpg
+ :alt: Original test image
+ :width: 250pt
+ :align: center
+
+#. This is the result of reducing it to half the size and centering it:
+
+ .. image:: images/Remap_Tutorial_Result_0.jpg
+ :alt: Result 0 for remapping
+ :width: 250pt
+ :align: center
+
+#. Turning it upside down:
+
+ .. image:: images/Remap_Tutorial_Result_1.jpg
+ :alt: Result 0 for remapping
+ :width: 250pt
+ :align: center
+
+#. Reflecting it in the x direction:
+
+ .. image:: images/Remap_Tutorial_Result_2.jpg
+ :alt: Result 0 for remapping
+ :width: 250pt
+ :align: center
+
+#. Reflecting it in both directions:
+
+.. image:: images/Remap_Tutorial_Result_3.jpg
+ :alt: Result 0 for remapping
+ :width: 250pt
+ :align: center
+
--- /dev/null
+.. _warp_affine:
+
+Affine Transformations
+**********************
+
+
+Goal
+====
+
+In this tutorial you will learn how to:
+
+a. Use the OpenCV function :warp_affine:`warpAffine <>` to implement simple remapping routines.
+b. Use the OpenCV function :get_rotation_matrix_2d:`getRotationMatrix2D <>` to obtain a :math:`2 \times 3` rotation matrix
+
+
+Theory
+======
+
+Code
+====
+
+.. code-block:: cpp
+
+ #include "opencv2/highgui/highgui.hpp"
+ #include "opencv2/imgproc/imgproc.hpp"
+ #include <iostream>
+ #include <stdio.h>
+
+ using namespace cv;
+ using namespace std;
+
+ /// Global variables
+ char* source_window = "Source image";
+ char* warp_window = "Warp";
+ char* warp_rotate_window = "Warp + Rotate";
+
+ /** @function main */
+ int main( int argc, char** argv )
+ {
+ Point2f srcTri[3];
+ Point2f dstTri[3];
+
+ Mat rot_mat( 2, 3, CV_32FC1 );
+ Mat warp_mat( 2, 3, CV_32FC1 );
+ Mat src, warp_dst, warp_rotate_dst;
+
+ /// Load the image
+ src = imread( argv[1], 1 );
+
+ /// Set the dst image the same type and size as src
+ warp_dst = Mat::zeros( src.rows, src.cols, src.type() );
+
+ /// Set your 3 points to calculate the Affine Transform
+ srcTri[0] = Point2f( 0,0 );
+ srcTri[1] = Point2f( src.cols - 1, 0 );
+ srcTri[2] = Point2f( 0, src.rows - 1 );
+
+ dstTri[0] = Point2f( src.cols*0.0, src.rows*0.33 );
+ dstTri[1] = Point2f( src.cols*0.85, src.rows*0.25 );
+ dstTri[2] = Point2f( src.cols*0.15, src.rows*0.7 );
+
+ /// Get the Affine Transform
+ warp_mat = getAffineTransform( srcTri, dstTri );
+
+ /// Apply the Affine Transform just found to the src image
+ warpAffine( src, warp_dst, warp_mat, warp_dst.size() );
+
+ /** Rotating the image after Warp */
+
+ /// Compute a rotation matrix with respect to the center of the image
+ Point center = Point( warp_dst.cols/2, warp_dst.rows/2 );
+ double angle = -50.0;
+ double scale = 0.6;
+
+ /// Get the rotation matrix with the specifications above
+ rot_mat = getRotationMatrix2D( center, angle, scale );
+
+ /// Rotate the warped image
+ warpAffine( warp_dst, warp_rotate_dst, rot_mat, warp_dst.size() );
+
+ /// Show what you got
+ namedWindow( source_window, CV_WINDOW_AUTOSIZE );
+ imshow( source_window, src );
+
+ namedWindow( warp_window, CV_WINDOW_AUTOSIZE );
+ imshow( warp_window, warp_dst );
+
+ namedWindow( warp_rotate_window, CV_WINDOW_AUTOSIZE );
+ imshow( warp_rotate_window, warp_rotate_dst );
+
+ /// Wait until user exits the program
+ waitKey(0);
+
+ return 0;
+ }
+
+Explanation
+===========
+
+Result
+======
+
+.. image:: images/Warp_Affine_Tutorial_Original_Image.jpg
+ :alt: Original image
+ :width: 250pt
+ :align: center
+
+.. image:: images/Warp_Affine_Tutorial_Result_Warp.jpg
+ :alt: Original image
+ :width: 250pt
+ :align: center
+
+.. image:: images/Warp_Affine_Tutorial_Result_Warp_Rotate.jpg
+ :alt: Original image
+ :width: 250pt
+ :align: center
+
projects / profile / ivi / opencv.git / commitdiff
