Contours Hierarchy {#tutorial_py_contours_hierarchy}
==================

@prev_tutorial{tutorial_py_contours_more_functions}

Goal
----

This time, we learn about the hierarchy of contours, i.e. the parent-child relationship in Contours.

Theory
------

In the last few articles on contours, we have worked with several functions related to contours
provided by OpenCV. But when we found the contours in image using **cv.findContours()** function,
we have passed an argument, **Contour Retrieval Mode**. We usually passed **cv.RETR_LIST** or
**cv.RETR_TREE** and it worked nice. But what does it actually mean ?

Also, in the output, we got three arrays, first is the image, second is our contours, and one more
output which we named as **hierarchy** (Please checkout the codes in previous articles). But we
never used this hierarchy anywhere. Then what is this hierarchy and what is it for ? What is its
relationship with the previous mentioned function argument ?

That is what we are going to deal in this article.

### What is Hierarchy?

Normally we use the **cv.findContours()** function to detect objects in an image, right ? Sometimes
objects are in different locations. But in some cases, some shapes are inside other shapes. Just
like nested figures. In this case, we call outer one as **parent** and inner one as **child**. This
way, contours in an image has some relationship to each other. And we can specify how one contour is
connected to each other, like, is it child of some other contour, or is it a parent etc.
Representation of this relationship is called the **Hierarchy**.

Consider an example image below :

![image](images/hierarchy.png)

In this image, there are a few shapes which I have numbered from **0-5**. *2 and 2a* denotes the
external and internal contours of the outermost box.

Here, contours 0,1,2 are **external or outermost**. We can say, they are in **hierarchy-0** or
simply they are in **same hierarchy level**.

Next comes **contour-2a**. It can be considered as a **child of contour-2** (or in opposite way,
contour-2 is parent of contour-2a). So let it be in **hierarchy-1**. Similarly contour-3 is child of
contour-2 and it comes in next hierarchy. Finally contours 4,5 are the children of contour-3a, and
they come in the last hierarchy level. From the way I numbered the boxes, I would say contour-4 is
the first child of contour-3a (It can be contour-5 also).

I mentioned these things to understand terms like **same hierarchy level**, **external contour**,
**child contour**, **parent contour**, **first child** etc. Now let's get into OpenCV.

### Hierarchy Representation in OpenCV

So each contour has its own information regarding what hierarchy it is, who is its child, who is its
parent etc. OpenCV represents it as an array of four values : **[Next, Previous, First_Child,
Parent]**

<center>*"Next denotes next contour at the same hierarchical level."*</center>

For eg, take contour-0 in our picture. Who is next contour in its same level ? It is contour-1. So
simply put Next = 1. Similarly for Contour-1, next is contour-2. So Next = 2.

What about contour-2? There is no next contour in the same level. So simply, put Next = -1. What
about contour-4? It is in same level with contour-5. So its next contour is contour-5, so Next = 5.

<center>*"Previous denotes previous contour at the same hierarchical level."*</center>

It is same as above. Previous contour of contour-1 is contour-0 in the same level. Similarly for
contour-2, it is contour-1. And for contour-0, there is no previous, so put it as -1.

<center>*"First_Child denotes its first child contour."*</center>

There is no need of any explanation. For contour-2, child is contour-2a. So it gets the
corresponding index value of contour-2a. What about contour-3a? It has two children. But we take
only first child. And it is contour-4. So First_Child = 4 for contour-3a.

<center>*"Parent denotes index of its parent contour."*</center>

It is just opposite of **First_Child**. Both for contour-4 and contour-5, parent contour is
contour-3a. For contour-3a, it is contour-3 and so on.

@note If there is no child or parent, that field is taken as -1

So now we know about the hierarchy style used in OpenCV, we can check into Contour Retrieval Modes
in OpenCV with the help of same image given above. ie what do flags like cv.RETR_LIST,
cv.RETR_TREE, cv.RETR_CCOMP, cv.RETR_EXTERNAL etc mean?

Contour Retrieval Mode
----------------------

### 1. RETR_LIST

This is the simplest of the four flags (from explanation point of view). It simply retrieves all the
contours, but doesn't create any parent-child relationship. **Parents and kids are equal under this
rule, and they are just contours**. ie they all belongs to same hierarchy level.

So here, 3rd and 4th term in hierarchy array is always -1. But obviously, Next and Previous terms
will have their corresponding values. Just check it yourself and verify it.

Below is the result I got, and each row is hierarchy details of corresponding contour. For eg, first
row corresponds to contour 0. Next contour is contour 1. So Next = 1. There is no previous contour,
so Previous = -1. And the remaining two, as told before, it is -1.
@code{.py}
>>> hierarchy
array([[[ 1, -1, -1, -1],
        [ 2,  0, -1, -1],
        [ 3,  1, -1, -1],
        [ 4,  2, -1, -1],
        [ 5,  3, -1, -1],
        [ 6,  4, -1, -1],
        [ 7,  5, -1, -1],
        [-1,  6, -1, -1]]])
@endcode
This is the good choice to use in your code, if you are not using any hierarchy features.

### 2. RETR_EXTERNAL

If you use this flag, it returns only extreme outer flags. All child contours are left behind. **We
can say, under this law, Only the eldest in every family is taken care of. It doesn't care about
other members of the family :)**.

So, in our image, how many extreme outer contours are there? ie at hierarchy-0 level?. Only 3, ie
contours 0,1,2, right? Now try to find the contours using this flag. Here also, values given to each
element is same as above. Compare it with above result. Below is what I got :
@code{.py}
>>> hierarchy
array([[[ 1, -1, -1, -1],
        [ 2,  0, -1, -1],
        [-1,  1, -1, -1]]])
@endcode
You can use this flag if you want to extract only the outer contours. It might be useful in some
cases.

### 3. RETR_CCOMP

This flag retrieves all the contours and arranges them to a 2-level hierarchy. ie external contours
of the object (ie its boundary) are placed in hierarchy-1. And the contours of holes inside object
(if any) is placed in hierarchy-2. If any object inside it, its contour is placed again in
hierarchy-1 only. And its hole in hierarchy-2 and so on.

Just consider the image of a "big white zero" on a black background. Outer circle of zero belongs to
first hierarchy, and inner circle of zero belongs to second hierarchy.

We can explain it with a simple image. Here I have labelled the order of contours in red color and
the hierarchy they belongs to, in green color (either 1 or 2). The order is same as the order OpenCV
detects contours.

![image](images/ccomp_hierarchy.png)

So consider first contour, ie contour-0. It is hierarchy-1. It has two holes, contours 1&2, and they
belong to hierarchy-2. So for contour-0, Next contour in same hierarchy level is contour-3. And
there is no previous one. And its first is child is contour-1 in hierarchy-2. It has no parent,
because it is in hierarchy-1. So its hierarchy array is [3,-1,1,-1]

Now take contour-1. It is in hierarchy-2. Next one in same hierarchy (under the parenthood of
contour-1) is contour-2. No previous one. No child, but parent is contour-0. So array is
[2,-1,-1,0].

Similarly contour-2 : It is in hierarchy-2. There is not next contour in same hierarchy under
contour-0. So no Next. Previous is contour-1. No child, parent is contour-0. So array is
[-1,1,-1,0].

Contour - 3 : Next in hierarchy-1 is contour-5. Previous is contour-0. Child is contour-4 and no
parent. So array is [5,0,4,-1].

Contour - 4 : It is in hierarchy 2 under contour-3 and it has no sibling. So no next, no previous,
no child, parent is contour-3. So array is [-1,-1,-1,3].

Remaining you can fill up. This is the final answer I got:
@code{.py}
>>> hierarchy
array([[[ 3, -1,  1, -1],
        [ 2, -1, -1,  0],
        [-1,  1, -1,  0],
        [ 5,  0,  4, -1],
        [-1, -1, -1,  3],
        [ 7,  3,  6, -1],
        [-1, -1, -1,  5],
        [ 8,  5, -1, -1],
        [-1,  7, -1, -1]]])
@endcode

### 4. RETR_TREE

And this is the final guy, Mr.Perfect. It retrieves all the contours and creates a full family
hierarchy list. **It even tells, who is the grandpa, father, son, grandson and even beyond... :)**.

For example, I took above image, rewrite the code for cv.RETR_TREE, reorder the contours as per the
result given by OpenCV and analyze it. Again, red letters give the contour number and green letters
give the hierarchy order.

![image](images/tree_hierarchy.png)

Take contour-0 : It is in hierarchy-0. Next contour in same hierarchy is contour-7. No previous
contours. Child is contour-1. And no parent. So array is [7,-1,1,-1].

Take contour-2 : It is in hierarchy-1. No contour in same level. No previous one. Child is
contour-3. Parent is contour-1. So array is [-1,-1,3,1].

And remaining, try yourself. Below is the full answer:
@code{.py}
>>> hierarchy
array([[[ 7, -1,  1, -1],
        [-1, -1,  2,  0],
        [-1, -1,  3,  1],
        [-1, -1,  4,  2],
        [-1, -1,  5,  3],
        [ 6, -1, -1,  4],
        [-1,  5, -1,  4],
        [ 8,  0, -1, -1],
        [-1,  7, -1, -1]]])
@endcode
