In the previous blogs, we discuss two fundamental morphological operations – Erosion and Dilation. Both have their own advantages and disadvantages. For instance, erosion is useful in removing salt noise and structures of a certain shape but at the same time, if holes or gaps are present in the object, this tends to amplify them. So, what we want is something that removes the structures or fills holes/gaps without affecting the remaining foreground parts.

One plausible solution is to combine erosion and dilation operation. So, for instance, let’s take the case of noise removal. Like we discussed that the erosion will remove the salt noise but at the same time will shrink the foreground region also. To counter this, we apply dilation operation using the same structuring element. Because noise is removed, so dilation will only work on the shrunk foreground area and revert it back to the original. This process of applying erosion followed by dilation is known as Opening and in this blog, we will discuss this method in detail.

So, why is the name Opening? Because this opens up the gap between the objects connected by thin protrusions that are of size less than that of the structuring element. Below is the image where the bridge is 2 pixels wide while the SE is 3 pixels wide.

Now, let’s formulate the opening operation in terms of a set operation. The opening of binary image A by the structuring element B is defined as the erosion of A by B, followed by the dilation of the result by B. This can be stated using any of the two expressions as shown below

The second one states that the opening is the union of all the translations of SE B that fits into A. There is an interesting property associated with the opening known as idempotence. This simply states that if an image has been opened once, performing the subsequent opening operation with the same SE will have no effect on that image. This is because after opening the new boundaries created are such that the SE always fits inside them. Now, let’s discuss another operation – closing that is a dual of opening operation.

Closing

This is the just the reverse of Opening i.e Dilation followed by Erosion. Because this closes the holes/gaps present in the object while keeping the initial object size the same. That’s why the name Closing. Now, let’s formulate this in terms of a set operation.

Actual implementation involves rotating the SE by 180 degrees before performing dilation and erosion. But since our SE is mostly symmetric, we usually don’t care. Similar to the opening, this operator is also idempotent. Unlike opening, this fuses narrow breaks or bridges between the objects. Generally, good for removing pepper noise but not salt noise.

Now, let’s discuss how to implement these using OpenCV-Python. For Opening, one way is to first apply erosion and then dilation using the builtin functions we discussed earlier. Similarly, for closing also. Fortunately, OpenCV provides another function that directly implements these operations as shown below.

Here, src is the input image with any number of channels( all will be processed independently) and the kernel is the structuring element whose origin is defined by the anchor (default (-1,-1)). Don’t know why the iterations argument is given because the opening and closing are idempotent operators. You can create the SE using cv2.getStructuringElement() or simply using numpy. It is sometimes useful to pad the image to account for the boundary pixels or if the image is of non-regular shape and this can be done using the “borderType” and “borderValue” arguments. The “op” argument specifies which type of morphological operation to apply. Following are the types available.

• MORPH_OPEN – an opening operation
• MORPH_CLOSE – a closing operation
• MORPH_GRADIENT – a morphological gradient
• MORPH_TOPHAT – “top hat”
• MORPH_BLACKHAT – “black hat”

Below is an example where we open and close the image with the rectangular SE.

In the next blog, we will discuss other morphological operators like morphological gradient, top hat, etc. Hope you enjoy reading.

If you have any doubt/suggestion please feel free to ask and I will do my best to help or improve myself. Good-bye until next time.