init - 初始化项目

doc/tutorials/imgproc/imgtrans/warp_affine/warp_affine.markdown

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+Affine Transformations {#tutorial_warp_affine}
+======================
+
+@tableofcontents
+
+@prev_tutorial{tutorial_remap}
+@next_tutorial{tutorial_histogram_equalization}
+
+|    |    |
+| -: | :- |
+| Original author | Ana Huamán |
+| Compatibility | OpenCV >= 3.0 |
+
+Goal
+----
+
+In this tutorial you will learn how to:
+
+-  Use the OpenCV function @ref cv::warpAffine to implement simple remapping routines.
+-  Use the OpenCV function @ref cv::getRotationMatrix2D to obtain a \f$2 \times 3\f$ rotation matrix
+
+Theory
+------
+
+### What is an Affine Transformation?
+
+-#  A transformation that can be expressed in the form of a *matrix multiplication* (linear
+    transformation) followed by a *vector addition* (translation).
+-#  From the above, we can use an Affine Transformation to express:
+
+    -#  Rotations (linear transformation)
+    -#  Translations (vector addition)
+    -#  Scale operations (linear transformation)
+
+    you can see that, in essence, an Affine Transformation represents a **relation** between two
+    images.
+
+-#  The usual way to represent an Affine Transformation is by using a \f$2 \times 3\f$ matrix.
+
+    \f[
+    A = \begin{bmatrix}
+        a_{00} & a_{01} \\
+        a_{10} & a_{11}
+        \end{bmatrix}_{2 \times 2}
+    B = \begin{bmatrix}
+        b_{00} \\
+        b_{10}
+        \end{bmatrix}_{2 \times 1}
+    \f]
+    \f[
+    M = \begin{bmatrix}
+        A & B
+        \end{bmatrix}
+    =
+   \begin{bmatrix}
+        a_{00} & a_{01} & b_{00} \\
+        a_{10} & a_{11} & b_{10}
+   \end{bmatrix}_{2 \times 3}
+   \f]
+
+    Considering that we want to transform a 2D vector \f$X = \begin{bmatrix}x \\ y\end{bmatrix}\f$ by
+    using \f$A\f$ and \f$B\f$, we can do the same with:
+
+    \f$T = A \cdot \begin{bmatrix}x \\ y\end{bmatrix} + B\f$ or \f$T = M \cdot  [x, y, 1]^{T}\f$
+
+    \f[T =  \begin{bmatrix}
+        a_{00}x + a_{01}y + b_{00} \\
+        a_{10}x + a_{11}y + b_{10}
+        \end{bmatrix}\f]
+
+### How do we get an Affine Transformation?
+
+-#  We mentioned that an Affine Transformation is basically a **relation**
+    between two images. The information about this relation can come, roughly, in two ways:
+    -#  We know both \f$X\f$ and T and we also know that they are related. Then our task is to find \f$M\f$
+    -#  We know \f$M\f$ and \f$X\f$. To obtain \f$T\f$ we only need to apply \f$T = M \cdot X\f$. Our information
+        for \f$M\f$ may be explicit (i.e. have the 2-by-3 matrix) or it can come as a geometric relation
+        between points.
+
+-#  Let's explain this in a better way (b). Since \f$M\f$ relates 2 images, we can analyze the simplest
+    case in which it relates three points in both images. Look at the figure below:
+
+    ![](images/Warp_Affine_Tutorial_Theory_0.jpg)
+
+    the points 1, 2 and 3 (forming a triangle in image 1) are mapped into image 2, still forming a
+    triangle, but now they have changed notoriously. If we find the Affine Transformation with these
+    3 points (you can choose them as you like), then we can apply this found relation to all the
+    pixels in an image.
+
+Code
+----
+
+-   **What does this program do?**
+    -   Loads an image
+    -   Applies an Affine Transform to the image. This transform is obtained from the relation
+        between three points. We use the function @ref cv::warpAffine for that purpose.
+    -   Applies a Rotation to the image after being transformed. This rotation is with respect to
+        the image center
+    -   Waits until the user exits the program
+
+@add_toggle_cpp
+-   The tutorial's code is shown below. You can also download it
+    [here](https://raw.githubusercontent.com/opencv/opencv/master/samples/cpp/tutorial_code/ImgProc/Smoothing/Smoothing.cpp)
+    @include samples/cpp/tutorial_code/ImgTrans/Geometric_Transforms_Demo.cpp
+@end_toggle
+
+@add_toggle_java
+-   The tutorial's code is shown below. You can also download it
+    [here](https://raw.githubusercontent.com/opencv/opencv/master/samples/cpp/tutorial_code/ImgProc/Smoothing/Smoothing.cpp)
+    @include samples/java/tutorial_code/ImgTrans/warp_affine/GeometricTransformsDemo.java
+@end_toggle
+
+@add_toggle_python
+-   The tutorial's code is shown below. You can also download it
+    [here](https://raw.githubusercontent.com/opencv/opencv/master/samples/python/tutorial_code/ImgTrans/warp_affine/Geometric_Transforms_Demo.py)
+    @include samples/python/tutorial_code/ImgTrans/warp_affine/Geometric_Transforms_Demo.py
+@end_toggle
+
+Explanation
+-----------
+
+-   Load an image:
+
+    @add_toggle_cpp
+    @snippet samples/cpp/tutorial_code/ImgTrans/Geometric_Transforms_Demo.cpp Load the image
+    @end_toggle
+
+    @add_toggle_java
+    @snippet samples/java/tutorial_code/ImgTrans/warp_affine/GeometricTransformsDemo.java Load the image
+    @end_toggle
+
+    @add_toggle_python
+    @snippet samples/python/tutorial_code/ImgTrans/warp_affine/Geometric_Transforms_Demo.py Load the image
+    @end_toggle
+
+-   **Affine Transform:** As we explained in lines above, we need two sets of 3 points to derive the
+    affine transform relation. Have a look:
+
+    @add_toggle_cpp
+    @snippet samples/cpp/tutorial_code/ImgTrans/Geometric_Transforms_Demo.cpp Set your 3 points to calculate the  Affine Transform
+    @end_toggle
+
+    @add_toggle_java
+    @snippet samples/java/tutorial_code/ImgTrans/warp_affine/GeometricTransformsDemo.java Set your 3 points to calculate the  Affine Transform
+    @end_toggle
+
+    @add_toggle_python
+    @snippet samples/python/tutorial_code/ImgTrans/warp_affine/Geometric_Transforms_Demo.py Set your 3 points to calculate the  Affine Transform
+    @end_toggle
+    You may want to draw these points to get a better idea on how they change. Their locations are
+    approximately the same as the ones depicted in the example figure (in the Theory section). You
+    may note that the size and orientation of the triangle defined by the 3 points change.
+
+-   Armed with both sets of points, we calculate the Affine Transform by using OpenCV function @ref
+    cv::getAffineTransform :
+
+    @add_toggle_cpp
+    @snippet samples/cpp/tutorial_code/ImgTrans/Geometric_Transforms_Demo.cpp Get the Affine Transform
+    @end_toggle
+
+    @add_toggle_java
+    @snippet samples/java/tutorial_code/ImgTrans/warp_affine/GeometricTransformsDemo.java Get the Affine Transform
+    @end_toggle
+
+    @add_toggle_python
+    @snippet samples/python/tutorial_code/ImgTrans/warp_affine/Geometric_Transforms_Demo.py Get the Affine Transform
+    @end_toggle
+    We get a \f$2 \times 3\f$ matrix as an output (in this case **warp_mat**)
+
+-   We then apply the Affine Transform just found to the src image
+
+    @add_toggle_cpp
+    @snippet samples/cpp/tutorial_code/ImgTrans/Geometric_Transforms_Demo.cpp Apply the Affine Transform just found to the src image
+    @end_toggle
+
+    @add_toggle_java
+    @snippet samples/java/tutorial_code/ImgTrans/warp_affine/GeometricTransformsDemo.java Apply the Affine Transform just found to the src image
+    @end_toggle
+
+    @add_toggle_python
+    @snippet samples/python/tutorial_code/ImgTrans/warp_affine/Geometric_Transforms_Demo.py Apply the Affine Transform just found to the src image
+    @end_toggle
+    with the following arguments:
+
+    -   **src**: Input image
+    -   **warp_dst**: Output image
+    -   **warp_mat**: Affine transform
+    -   **warp_dst.size()**: The desired size of the output image
+
+    We just got our first transformed image! We will display it in one bit. Before that, we also
+    want to rotate it...
+
+-   **Rotate:** To rotate an image, we need to know two things:
+
+    -#  The center with respect to which the image will rotate
+    -#  The angle to be rotated. In OpenCV a positive angle is counter-clockwise
+    -#  *Optional:* A scale factor
+
+    We define these parameters with the following snippet:
+
+    @add_toggle_cpp
+    @snippet samples/cpp/tutorial_code/ImgTrans/Geometric_Transforms_Demo.cpp Compute a rotation matrix with respect to the center of the image
+    @end_toggle
+
+    @add_toggle_java
+    @snippet samples/java/tutorial_code/ImgTrans/warp_affine/GeometricTransformsDemo.java Compute a rotation matrix with respect to the center of the image
+    @end_toggle
+
+    @add_toggle_python
+    @snippet samples/python/tutorial_code/ImgTrans/warp_affine/Geometric_Transforms_Demo.py Compute a rotation matrix with respect to the center of the image
+    @end_toggle
+
+-   We generate the rotation matrix with the OpenCV function @ref cv::getRotationMatrix2D , which
+    returns a \f$2 \times 3\f$ matrix (in this case *rot_mat*)
+
+    @add_toggle_cpp
+    @snippet samples/cpp/tutorial_code/ImgTrans/Geometric_Transforms_Demo.cpp Get the rotation matrix with the specifications above
+    @end_toggle
+
+    @add_toggle_java
+    @snippet samples/java/tutorial_code/ImgTrans/warp_affine/GeometricTransformsDemo.java Get the rotation matrix with the specifications above
+    @end_toggle
+
+    @add_toggle_python
+    @snippet samples/python/tutorial_code/ImgTrans/warp_affine/Geometric_Transforms_Demo.py Get the rotation matrix with the specifications above
+    @end_toggle
+
+-   We now apply the found rotation to the output of our previous Transformation:
+
+    @add_toggle_cpp
+    @snippet samples/cpp/tutorial_code/ImgTrans/Geometric_Transforms_Demo.cpp Rotate the warped image
+    @end_toggle
+
+    @add_toggle_java
+    @snippet samples/java/tutorial_code/ImgTrans/warp_affine/GeometricTransformsDemo.java Rotate the warped image
+    @end_toggle
+
+    @add_toggle_python
+    @snippet samples/python/tutorial_code/ImgTrans/warp_affine/Geometric_Transforms_Demo.py Rotate the warped image
+    @end_toggle
+
+-   Finally, we display our results in two windows plus the original image for good measure:
+
+    @add_toggle_cpp
+    @snippet samples/cpp/tutorial_code/ImgTrans/Geometric_Transforms_Demo.cpp Show what you got
+    @end_toggle
+
+    @add_toggle_java
+    @snippet samples/java/tutorial_code/ImgTrans/warp_affine/GeometricTransformsDemo.java Show what you got
+    @end_toggle
+
+    @add_toggle_python
+    @snippet samples/python/tutorial_code/ImgTrans/warp_affine/Geometric_Transforms_Demo.py Show what you got
+    @end_toggle
+
+-   We just have to wait until the user exits the program
+
+    @add_toggle_cpp
+    @snippet samples/cpp/tutorial_code/ImgTrans/Geometric_Transforms_Demo.cpp Wait until user exits the program
+    @end_toggle
+
+    @add_toggle_java
+    @snippet samples/java/tutorial_code/ImgTrans/warp_affine/GeometricTransformsDemo.java Wait until user exits the program
+    @end_toggle
+
+    @add_toggle_python
+    @snippet samples/python/tutorial_code/ImgTrans/warp_affine/Geometric_Transforms_Demo.py Wait until user exits the program
+    @end_toggle
+
+Result
+------
+
+-   After compiling the code above, we can give it the path of an image as argument. For instance,
+    for a picture like:
+
+    ![](images/Warp_Affine_Tutorial_Original_Image.jpg)
+
+    after applying the first Affine Transform we obtain:
+
+    ![](images/Warp_Affine_Tutorial_Result_Warp.jpg)
+
+    and finally, after applying a negative rotation (remember negative means clockwise) and a scale
+    factor, we get:
+
+    ![](images/Warp_Affine_Tutorial_Result_Warp_Rotate.jpg)