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Merge pull request #8253 from adl1995:master
* Update linux_install.markdown Grammar improvements, fixed typos. * Update tutorials.markdown Improvements in grammar. * Update table_of_content_calib3d.markdown * Update camera_calibration_square_chess.markdown Improvements in grammar. Added answer. * Update tutorials.markdown * Update erosion_dilatation.markdown * Update table_of_content_imgproc.markdown * Update warp_affine.markdown * Update camera_calibration_square_chess.markdown Removed extra space. * Update gpu_basics_similarity.markdown Grammatical improvements, fixed typos. * Update trackbar.markdown Improvement for better understanding.
This commit is contained in:
Adeel Ahmad
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Alexander Alekhin
Alexander Alekhin
parent
da0b1d8821
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@@ -6,12 +6,12 @@ Goal
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In this tutorial you will learn how to:
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- Apply two very common morphology operators: Dilation and Erosion. For this purpose, you will use
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- Apply two very common morphological operators: Erosion and Dilation. For this purpose, you will use
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the following OpenCV functions:
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- @ref cv::erode
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- @ref cv::dilate
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Cool Theory
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Interesting fact
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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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@@ -21,7 +21,7 @@ Morphological Operations
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- In short: A set of operations that process images based on shapes. Morphological operations
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apply a *structuring element* to an input image and generate an output image.
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- The most basic morphological operations are two: Erosion and Dilation. They have a wide array of
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- The most basic morphological operations are: Erosion and Dilation. They have a wide array of
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uses, i.e. :
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- Removing noise
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- Isolation of individual elements and joining disparate elements in an image.
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@@ -32,19 +32,19 @@ Morphological Operations
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### Dilation
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- This operations consists of convoluting an image \f$A\f$ with some kernel (\f$B\f$), which can have any
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- This operations consists of convolving an image \f$A\f$ with some kernel (\f$B\f$), which can have any
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shape or size, usually a square or circle.
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- The kernel \f$B\f$ has a defined *anchor point*, usually being the center of the kernel.
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- As the kernel \f$B\f$ is scanned over the image, we compute the maximal pixel value overlapped by
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\f$B\f$ and replace the image pixel in the anchor point position with that maximal value. As you can
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deduce, this maximizing operation causes bright regions within an image to "grow" (therefore the
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name *dilation*). Take as an example the image above. Applying dilation we can get:
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name *dilation*). Take the above image as an example. Applying dilation we can get:
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The background (bright) dilates around the black regions of the letter.
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To better grasp the idea and avoid possible confusion, in this another example we have inverted the original
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To better grasp the idea and avoid possible confusion, in this other example we have inverted the original
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image such as the object in white is now the letter. We have performed two dilatations with a rectangular
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structuring element of size `3x3`.
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@@ -54,8 +54,8 @@ The dilatation makes the object in white bigger.
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### Erosion
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- This operation is the sister of dilation. What this does is to compute a local minimum over the
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area of the kernel.
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- This operation is the sister of dilation. It computes a local minimum over the
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area of given kernel.
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- As the kernel \f$B\f$ is scanned over the image, we compute the minimal pixel value overlapped by
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\f$B\f$ and replace the image pixel under the anchor point with that minimal value.
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- Analagously to the example for dilation, we can apply the erosion operator to the original image
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@@ -64,7 +64,7 @@ The dilatation makes the object in white bigger.
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In the same manner, the corresponding image resulting of the erosion operation on the inverted original image (two erosions
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In similar manner, the corresponding image results by applying erosion operation on the inverted original image (two erosions
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with a rectangular structuring element of size `3x3`):
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@@ -74,14 +74,14 @@ The erosion makes the object in white smaller.
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Code
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----
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This tutorial code's is shown lines below. You can also download it from
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This tutorial's code is shown below. You can also download it
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[here](https://github.com/opencv/opencv/tree/master/samples/cpp/tutorial_code/ImgProc/Morphology_1.cpp)
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@include samples/cpp/tutorial_code/ImgProc/Morphology_1.cpp
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Explanation
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-----------
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-# Most of the stuff shown is known by you (if you have any doubt, please refer to the tutorials in
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-# Most of the material shown here is trivial (if you have any doubt, please refer to the tutorials in
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previous sections). Let's check the general structure of the program:
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- Load an image (can be BGR or grayscale)
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@@ -118,8 +118,8 @@ Explanation
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- That is all. We are ready to perform the erosion of our image.
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@note Additionally, there is another parameter that allows you to perform multiple erosions
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(iterations) at once. We are not using it in this simple tutorial, though. You can check out the
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Reference for more details.
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(iterations) at once. However, We haven't used it in this simple tutorial. You can check out the
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reference for more details.
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-# **dilation:**
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@@ -14,9 +14,9 @@ Theory
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### What is an Affine Transformation?
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-# It is any transformation that can be expressed in the form of a *matrix multiplication* (linear
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-# A transformation that can be expressed in the form of a *matrix multiplication* (linear
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transformation) followed by a *vector addition* (translation).
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-# From the above, We can use an Affine Transformation to express:
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-# From the above, we can use an Affine Transformation to express:
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-# Rotations (linear transformation)
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-# Translations (vector addition)
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@@ -25,7 +25,7 @@ Theory
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you can see that, in essence, an Affine Transformation represents a **relation** between two
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images.
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-# The usual way to represent an Affine Transform is by using a \f$2 \times 3\f$ matrix.
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-# The usual way to represent an Affine Transformation is by using a \f$2 \times 3\f$ matrix.
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\f[
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A = \begin{bmatrix}
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@@ -49,7 +49,7 @@ Theory
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\f]
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Considering that we want to transform a 2D vector \f$X = \begin{bmatrix}x \\ y\end{bmatrix}\f$ by
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using \f$A\f$ and \f$B\f$, we can do it equivalently with:
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using \f$A\f$ and \f$B\f$, we can do the same with:
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\f$T = A \cdot \begin{bmatrix}x \\ y\end{bmatrix} + B\f$ or \f$T = M \cdot [x, y, 1]^{T}\f$
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@@ -60,35 +60,35 @@ Theory
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### How do we get an Affine Transformation?
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-# Excellent question. We mentioned that an Affine Transformation is basically a **relation**
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-# We mentioned that an Affine Transformation is basically a **relation**
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between two images. The information about this relation can come, roughly, in two ways:
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-# We know both \f$X\f$ and T and we also know that they are related. Then our job is to find \f$M\f$
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-# We know both \f$X\f$ and T and we also know that they are related. Then our task is to find \f$M\f$
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-# 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
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for \f$M\f$ may be explicit (i.e. have the 2-by-3 matrix) or it can come as a geometric relation
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between points.
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-# Let's explain a little bit better (b). Since \f$M\f$ relates 02 images, we can analyze the simplest
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-# Let's explain this in a better way (b). Since \f$M\f$ relates 2 images, we can analyze the simplest
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case in which it relates three points in both images. Look at the figure below:
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the points 1, 2 and 3 (forming a triangle in image 1) are mapped into image 2, still forming a
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triangle, but now they have changed notoriously. If we find the Affine Transformation with these
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3 points (you can choose them as you like), then we can apply this found relation to the whole
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pixels in the image.
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3 points (you can choose them as you like), then we can apply this found relation to all the
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pixels in an image.
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Code
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----
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-# **What does this program do?**
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- Loads an image
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- Applies an Affine Transform to the image. This Transform is obtained from the relation
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- Applies an Affine Transform to the image. This transform is obtained from the relation
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between three points. We use the function @ref cv::warpAffine for that purpose.
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- Applies a Rotation to the image after being transformed. This rotation is with respect to
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the image center
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- Waits until the user exits the program
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-# The tutorial code's is shown lines below. You can also download it from
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-# The tutorial's code is shown below. You can also download it here
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[here](https://github.com/opencv/opencv/tree/master/samples/cpp/tutorial_code/ImgTrans/Geometric_Transforms_Demo.cpp)
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@include samples/cpp/tutorial_code/ImgTrans/Geometric_Transforms_Demo.cpp
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@@ -113,10 +113,10 @@ Explanation
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@code{.cpp}
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warp_dst = Mat::zeros( src.rows, src.cols, src.type() );
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@endcode
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-# **Affine Transform:** As we explained lines above, we need two sets of 3 points to derive the
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affine transform relation. Take a look:
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-# **Affine Transform:** As we explained in lines above, we need two sets of 3 points to derive the
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affine transform relation. Have a look:
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@code{.cpp}
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srcTri[0] = Point2f( 0,0 );
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srcTri[0] = Point2f( 0, 0 );
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srcTri[1] = Point2f( src.cols - 1, 0 );
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srcTri[2] = Point2f( 0, src.rows - 1 );
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@@ -124,7 +124,7 @@ Explanation
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dstTri[1] = Point2f( src.cols*0.85, src.rows*0.25 );
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dstTri[2] = Point2f( src.cols*0.15, src.rows*0.7 );
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@endcode
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You may want to draw the points to make a better idea of how they change. Their locations are
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You may want to draw these points to get a better idea on how they change. Their locations are
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approximately the same as the ones depicted in the example figure (in the Theory section). You
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may note that the size and orientation of the triangle defined by the 3 points change.
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@@ -133,9 +133,9 @@ Explanation
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@code{.cpp}
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warp_mat = getAffineTransform( srcTri, dstTri );
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@endcode
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We get as an output a \f$2 \times 3\f$ matrix (in this case **warp_mat**)
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We get a \f$2 \times 3\f$ matrix as an output (in this case **warp_mat**)
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-# We apply the Affine Transform just found to the src image
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-# We then apply the Affine Transform just found to the src image
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@code{.cpp}
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warpAffine( src, warp_dst, warp_mat, warp_dst.size() );
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@endcode
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@@ -41,7 +41,7 @@ In this section you will learn about the image processing (manipulation) functio
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*Author:* Theodore Tsesmelis
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Here we will show how we can use different morphology operators to extract horizontal and vertical lines
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Here we will show how we can use different morphological operators to extract horizontal and vertical lines
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- @subpage tutorial_pyramids
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@@ -57,7 +57,7 @@ In this section you will learn about the image processing (manipulation) functio
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*Author:* Ana Huamán
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After so much processing, it is time to decide which pixels stay!
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After so much processing, it is time to decide which pixels stay
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- @subpage tutorial_threshold_inRange
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@@ -81,7 +81,7 @@ In this section you will learn about the image processing (manipulation) functio
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*Author:* Ana Huamán
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Where we learn how to pad our images!
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Where we learn how to pad our images
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- @subpage tutorial_sobel_derivatives
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@@ -89,7 +89,7 @@ In this section you will learn about the image processing (manipulation) functio
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*Author:* Ana Huamán
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Where we learn how to calculate gradients and use them to detect edges!
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Where we learn how to calculate gradients and use them to detect edges
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- @subpage tutorial_laplace_operator
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@@ -97,7 +97,7 @@ In this section you will learn about the image processing (manipulation) functio
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*Author:* Ana Huamán
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Where we learn about the *Laplace* operator and how to detect edges with it.
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Where we learn about the *Laplace* operator and how to detect edges with it
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- @subpage tutorial_canny_detector
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@@ -105,7 +105,7 @@ In this section you will learn about the image processing (manipulation) functio
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*Author:* Ana Huamán
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Where we learn a sophisticated alternative to detect edges.
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Where we learn a sophisticated alternative to detect edges
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- @subpage tutorial_hough_lines
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@@ -193,7 +193,7 @@ In this section you will learn about the image processing (manipulation) functio
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*Author:* Ana Huamán
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Where we learn how to get hull contours and draw them!
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Where we learn how to get hull contours and draw them
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- @subpage tutorial_bounding_rects_circles
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@@ -201,7 +201,7 @@ In this section you will learn about the image processing (manipulation) functio
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*Author:* Ana Huamán
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Where we learn how to obtain bounding boxes and circles for our contours.
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Where we learn how to obtain bounding boxes and circles for our contours
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- @subpage tutorial_bounding_rotated_ellipses
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@@ -209,7 +209,7 @@ In this section you will learn about the image processing (manipulation) functio
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*Author:* Ana Huamán
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Where we learn how to obtain rotated bounding boxes and ellipses for our contours.
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Where we learn how to obtain rotated bounding boxes and ellipses for our contours
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- @subpage tutorial_moments
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@@ -233,4 +233,4 @@ In this section you will learn about the image processing (manipulation) functio
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*Author:* Theodore Tsesmelis
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Where we learn to segment objects using Laplacian filtering, the Distance Transformation and the Watershed algorithm.
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Where we learn to segment objects using Laplacian filtering, the Distance Transformation and the Watershed algorithm.
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