# Morphological Image Processing

**Morphological Image Processing**

- The word
*morphology*commonly denotes a branch of biology that deals with the form and structure of animals and plants. - We use the same word here in the context of
*mathematical morphology*as a tool for extracting image components that are useful in the representation and description of region shape, such as boundaries, skeletons, and the convex hull. - We are interested also in morphological techniques for pre- or post processing, such as morphological filtering, thinning, and pruning.
- In mathematics, the
**convex hull**or**convex**envelope or**convex**closure of a set X of points in the Euclidean plane or in a Euclidean space (or, more generally, in an affine space over the reals) is the smallest**convex**set that contains X

*Structuring Elements*

*Structuring Elements*

*structuring elements***(SEs)**: small sets or subimages used to probe an image under study for properties of interest.

**Example (How SE works on an image)**

- Create a new set by running
**B**over**A**so that the origin of**B**visits every element of**A**. At each location of the origin of**B**if**B**is completely contained in**A**, mark that location as a member of the new set (shown shaded); else mark it as not being a member of the new set (shown not shaded). - Eroded image is the result

**B is completely contained in A **means that A and B are completely overlapping

**Erosion and Dilation**

- We begin the discussion of morphology by studying two operations
*Erosion**Dilation*- These operations are fundamental to morphological processing.
- In fact, many of the morphological algorithms discussed in this chapter are based on these two primitive operations

**Erosion**

**Dilation**

- A
**⊕ B** - Reverse process of Erosion
- The element is marked in output when SE is overlapping partially or completely.

##### Example

- One of the simplest applications of dilation is for bridging gaps.
- Fig shows the same image with broken characters that we studied in
- The maximum length of the breaks is known to be two pixels.

**Opening and Closing**

Ø** Opening** generally smoothes the contour of an object, breaks narrow isthmuses, and eliminates thin protrusions.

Ø**A ****o**** B **= ( **A⊖B **) **⊕ B**

Ø

Ø** Closing** also tends to smooth sections of contours but, as opposed to opening, it generally fuses narrow breaks and long thin gulfs, eliminates small holes, and fills gaps in the contour.

Ø**A** **.** **B** = ( **A**** ⊕ ****B** ) **⊖ ****B**

**Opening**

**Closing**

**Opening**

**The Hit-or-Miss Transformation**

- The morphological hit-or-miss transform is a basic tool for shape detection
- This concept is introduced with the aid of Fig. 9.12, which shows a set consisting of three shapes (subsets), denoted C, D and E
- The shading in Figs. 9.12(a) through (c) indicates the original sets, whereas the shading in Figs. 9.12(d) and (e) indicates the result of morphological operations.
- The objective is to find the location of one of the shapes, say,D.

**Hole Filling**

- A
*hole*may be defined as a background region surrounded by a connected border of foreground pixels. - To develop an algorithm based on dilation, complementation, and intersection for filling holes in an image.
- Let A denote a set whose elements are 8-connected boundaries, each boundary enclosing a background region (i.e., a hole).
- Given a point in each hole, the objective is to fill all the holes with 1s.

- We begin by forming an array, X0 , of 0s (the same size as the array containing A), except at the locations in corresponding to the given point in each hole, which we set to 1.
- Then, the following procedure fills all the holes with 1s

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