（27） Open operation, close operation, morphological gradient, top hat, black hat

First, the main purpose of morphology is to obtain object topology and result information , Through some operations of objects and structural elements , Get the more essential form of the object , The main applications in image processing are ：

（1） Use the basic operations of morphology to observe and process the image , So as to improve the image quality

（2） Describe and define various geometric parameters and features of the image, such as area 、 Perimeter 、 connected 、 Particle size 、 Skeleton and directivity

1、 Open operation

The operation is realized by first etching the image and then expanding , The principle expression is as follows ：                                  

dst=open(src,element)=dilate(erode(src,element))

It can exclude small lumps ( Suppose the object is brighter than the background ), The result of the open operation deletes the object area that cannot contain structural elements , Smoothed the outline of the object , Broke the narrow connection , Removed the small protrusions , As shown in the figure below ： The image on the left is the original image , The figure on the right is the result of the open operation conversion , You can find that the white space at the corner of the letter disappears .

2、 Closed operation

Mathematically, closed operation is the result of expansion and then corrosion , The principle expression is as follows ：

dst=close(src,element)=erode(dilate(src,element))

It can exclude small black holes ( Black areas ), It can smooth the outline of the object , But unlike the open operation, the closed operation generally connects narrow gaps to form slender bends , And fill holes smaller than structural elements .

3、 Morphological gradient

The morphological gradient is the difference between the expansion diagram and the corrosion diagram , The operation principle expression is as follows ：

dst=morph(src,element)=dilate(src,element)-erode(src,element)

Morphological gradient operation can preserve the edge contour of the object

4、 Top hat

The top hat operation is the difference between the original image and the result of the open operation , The principle expression is as follows ：

dst=tophat(src,element)=src-open(src,element)

The result of the open operation is to enlarge the crack or locally reduce the brightness of the area , Therefore, the effect image obtained by subtracting the calculated image from the original image can highlight the area brighter than the area around the outline of the original image , And this operation is related to the size of the selected core . The top hat operation is often used to separate the plates that are lit next to each other , When an image has a large background and small objects are regular , The top hat operation can be used for background extraction .

5、 Black hat

Black hat operation is the difference between the result of closed operation and the original image , The principle expression is as follows ：

dst=blackhat(src,element)=close(src,element)-src

The effect image after black hat operation highlights the darker area than the area around the outline of the original image , This operation is also related to the selected core size . So the black hat operation is used to separate the patches darker than the adjacent points , The rendering has a very perfect outline .