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209 lines
7.2 KiB
Markdown
209 lines
7.2 KiB
Markdown
Image Pyramids {#tutorial_pyramids}
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==============
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@tableofcontents
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@prev_tutorial{tutorial_morph_lines_detection}
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@next_tutorial{tutorial_threshold}
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| Original author | Ana Huamán |
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| Compatibility | OpenCV >= 3.0 |
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Goal
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----
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In this tutorial you will learn how to:
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- Use the OpenCV functions **pyrUp()** and **pyrDown()** to downsample or upsample a given
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image.
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Theory
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------
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@note The explanation below belongs to the book **Learning OpenCV** by Bradski and Kaehler.
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- Usually we need to convert an image to a size different than its original. For this, there are
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two possible options:
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-# *Upsize* the image (zoom in) or
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-# *Downsize* it (zoom out).
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- Although there is a *geometric transformation* function in OpenCV that -literally- resize an
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image (**resize** , which we will show in a future tutorial), in this section we analyze
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first the use of **Image Pyramids**, which are widely applied in a huge range of vision
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applications.
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### Image Pyramid
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- An image pyramid is a collection of images - all arising from a single original image - that are
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successively downsampled until some desired stopping point is reached.
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- There are two common kinds of image pyramids:
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- **Gaussian pyramid:** Used to downsample images
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- **Laplacian pyramid:** Used to reconstruct an upsampled image from an image lower in the
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pyramid (with less resolution)
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- In this tutorial we'll use the *Gaussian pyramid*.
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#### Gaussian Pyramid
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- Imagine the pyramid as a set of layers in which the higher the layer, the smaller the size.
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- Every layer is numbered from bottom to top, so layer \f$(i+1)\f$ (denoted as \f$G_{i+1}\f$ is smaller
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than layer \f$i\f$ (\f$G_{i}\f$).
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- To produce layer \f$(i+1)\f$ in the Gaussian pyramid, we do the following:
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- Convolve \f$G_{i}\f$ with a Gaussian kernel:
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\f[\frac{1}{256} \begin{bmatrix} 1 & 4 & 6 & 4 & 1 \\ 4 & 16 & 24 & 16 & 4 \\ 6 & 24 & 36 & 24 & 6 \\ 4 & 16 & 24 & 16 & 4 \\ 1 & 4 & 6 & 4 & 1 \end{bmatrix}\f]
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- Remove every even-numbered row and column.
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- You can easily notice that the resulting image will be exactly one-quarter the area of its
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predecessor. Iterating this process on the input image \f$G_{0}\f$ (original image) produces the
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entire pyramid.
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- The procedure above was useful to downsample an image. What if we want to make it bigger?:
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columns filled with zeros (\f$0 \f$)
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- First, upsize the image to twice the original in each dimension, with the new even rows and
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- Perform a convolution with the same kernel shown above (multiplied by 4) to approximate the
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values of the "missing pixels"
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- These two procedures (downsampling and upsampling as explained above) are implemented by the
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OpenCV functions **pyrUp()** and **pyrDown()** , as we will see in an example with the
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code below:
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@note When we reduce the size of an image, we are actually *losing* information of the image.
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Code
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----
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This tutorial code's is shown lines below.
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@add_toggle_cpp
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You can also download it from
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[here](https://raw.githubusercontent.com/opencv/opencv/4.x/samples/cpp/tutorial_code/ImgProc/Pyramids/Pyramids.cpp)
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@include samples/cpp/tutorial_code/ImgProc/Pyramids/Pyramids.cpp
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@end_toggle
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@add_toggle_java
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You can also download it from
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[here](https://raw.githubusercontent.com/opencv/opencv/4.x/samples/java/tutorial_code/ImgProc/Pyramids/Pyramids.java)
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@include samples/java/tutorial_code/ImgProc/Pyramids/Pyramids.java
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@end_toggle
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@add_toggle_python
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You can also download it from
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[here](https://raw.githubusercontent.com/opencv/opencv/4.x/samples/python/tutorial_code/imgProc/Pyramids/pyramids.py)
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@include samples/python/tutorial_code/imgProc/Pyramids/pyramids.py
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@end_toggle
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Explanation
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-----------
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Let's check the general structure of the program:
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#### Load an image
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@add_toggle_cpp
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@snippet cpp/tutorial_code/ImgProc/Pyramids/Pyramids.cpp load
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@end_toggle
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@add_toggle_java
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@snippet java/tutorial_code/ImgProc/Pyramids/Pyramids.java load
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@end_toggle
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@add_toggle_python
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@snippet python/tutorial_code/imgProc/Pyramids/pyramids.py load
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@end_toggle
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#### Create window
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@add_toggle_cpp
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@snippet cpp/tutorial_code/ImgProc/Pyramids/Pyramids.cpp show_image
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@end_toggle
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@add_toggle_java
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@snippet java/tutorial_code/ImgProc/Pyramids/Pyramids.java show_image
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@end_toggle
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@add_toggle_python
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@snippet python/tutorial_code/imgProc/Pyramids/pyramids.py show_image
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@end_toggle
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#### Loop
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@add_toggle_cpp
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@snippet cpp/tutorial_code/ImgProc/Pyramids/Pyramids.cpp loop
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@end_toggle
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@add_toggle_java
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@snippet java/tutorial_code/ImgProc/Pyramids/Pyramids.java loop
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@end_toggle
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@add_toggle_python
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@snippet python/tutorial_code/imgProc/Pyramids/pyramids.py loop
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@end_toggle
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Perform an infinite loop waiting for user input.
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Our program exits if the user presses **ESC**. Besides, it has two options:
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- **Perform upsampling - Zoom 'i'n (after pressing 'i')**
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We use the function **pyrUp()** with three arguments:
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- *src*: The current and destination image (to be shown on screen, supposedly the double of the
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input image)
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- *Size( tmp.cols*2, tmp.rows\*2 )* : The destination size. Since we are upsampling,
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**pyrUp()** expects a size double than the input image (in this case *src*).
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@add_toggle_cpp
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@snippet cpp/tutorial_code/ImgProc/Pyramids/Pyramids.cpp pyrup
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@end_toggle
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@add_toggle_java
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@snippet java/tutorial_code/ImgProc/Pyramids/Pyramids.java pyrup
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@end_toggle
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@add_toggle_python
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@snippet python/tutorial_code/imgProc/Pyramids/pyramids.py pyrup
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@end_toggle
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- **Perform downsampling - Zoom 'o'ut (after pressing 'o')**
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We use the function **pyrDown()** with three arguments (similarly to **pyrUp()**):
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- *src*: The current and destination image (to be shown on screen, supposedly half the input
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image)
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- *Size( tmp.cols/2, tmp.rows/2 )* : The destination size. Since we are downsampling,
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**pyrDown()** expects half the size the input image (in this case *src*).
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@add_toggle_cpp
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@snippet cpp/tutorial_code/ImgProc/Pyramids/Pyramids.cpp pyrdown
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@end_toggle
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@add_toggle_java
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@snippet java/tutorial_code/ImgProc/Pyramids/Pyramids.java pyrdown
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@end_toggle
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@add_toggle_python
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@snippet python/tutorial_code/imgProc/Pyramids/pyramids.py pyrdown
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@end_toggle
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Notice that it is important that the input image can be divided by a factor of two (in both dimensions).
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Otherwise, an error will be shown.
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Results
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-------
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- The program calls by default an image [chicky_512.png](https://raw.githubusercontent.com/opencv/opencv/4.x/samples/data/chicky_512.png)
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that comes in the `samples/data` folder. Notice that this image is \f$512 \times 512\f$,
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hence a downsample won't generate any error (\f$512 = 2^{9}\f$). The original image is shown below:
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- First we apply two successive **pyrDown()** operations by pressing 'd'. Our output is:
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- Note that we should have lost some resolution due to the fact that we are diminishing the size
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of the image. This is evident after we apply **pyrUp()** twice (by pressing 'u'). Our output
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is now:
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