# Questions tagged [morphological-operations]

Non-linear operators in Mathematical Morphology is the theory of using algebraic structure of lattices and geometrical analysis of structures, based on set theory, topology, and random functions. operators: Erosion, Dilation, Opening and Closing. Reconstruction filters, Connected filters, granulometries, watershed transformation, levelling, alternating sequential filters(ASFS), Duality, Idempotent filters, hierarchical analysis.

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### Texture Analysis and Statistic Models

Let's assume we have a random binary texture image $X(i,j)$ that comes from a Markov-Gibbs model with zero boundary conditions. The probability distribution Gibbs function is: Pr(X)=\frac{1}{Z}\exp(-...
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### Erosion compotition rule $\left ( f \ominus g \right ) \ominus h = f \ominus \left (g \oplus h \right )$

I want to prove that erosion of a signal by a function $g$ followed by erosion with another function $h$ is equivalent to erosion of the signal by the dilation of the two functions (Erosion property): ...
28 views

### How to partition collagen into separate fibers?

I have a picture representing collagen fibers of a tissue: Image is binary consisting of a background (pixels with value 0) and white collagen (pixels with value 1). A zoomed in section of an image ...
21 views

### Amount of pixel eroded

Is there a definite relation between the kernel size and shape of a morphology change and the amount of pixels added or removed? I have a case where I have a segmented image, and I need to remove x ...
145 views

### Fast morphological erosion/dilation with variable window sizes

I want to perform the following operation on an image: consider a square window around every pixel, find the maximum value in this window, and replace the central pixel value with this maximum value. ...
414 views

### Morphology - Why does the concept of opening and closing images exist when we already have erosion and dilation?

If we consider the closing operation of an image, we first dilate the image and then erode it. So, first we expand the foreground (white pixels) and and then we take away some part of the foreground. ...
72 views

### How does reconstruction function relate to watershed segmentation?

I'm trying to understand how watershed work by reading The Morphological Approach to Segmentation: The Watershed Transformation S. Beucher and F. Meyer This document mentions the reconstruction ...
1k views

### removing vertical lines in grayscale images by thickness

Suppose we have a grayscale image that contains vertical lines. Now suppose that not all vertical lines are the same, some of them have different thickness. Question is, is there a way, in MATLAB or ...
455 views

### Counting pixel connectivity groups

How many 4-connected and 8-connected components are present in the binary image below? Using definition of connectivities from the same textbook "A connected component is a group of pixels that are ...
348 views

### Algo Name: Detecting Elongated Shape in 2D Image by Convolution with Directed Lines

IĀ am detecting a shape with roughly known orientation (obtained by using Hough line transform) in thresholded binary image by convolving the image with line with that orientation, and counting the ...
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I'm trying to implement the Adaptive Morphological Edge-Linking Algorithm (Frank Y. Shih, Image Processing and Pattern Recognition: Fundamentals and Techniques, section 5.5.2 OR Article link). The ...
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### Morphological transformations for images with discrete values

I have a series of images in which the pixels take integer values corresponding to a classification. I'd like to try some morphological transformations (e.g. erosion, dilation) to remove noise and ...
730 views

### Granulometry by morphological opening and closing

I am trying to understand granulometry. I understand that it deals with determining the size distribution of particles in an image and uses the principles of opening and closing. I have a smoothed ...
977 views

### Segmentation of overlapping noisy parallelograms in a binary image

Edited. Previously this question was named "Segmentation of overlapping pulses in a binary spectrogram" and it was stated in slightly different way. I'm apologise to those users, who were affected by ...
271 views

To obtain the gradient from an image, one can use a linear filter that for example is derrived from the derrivative of a gaussian. Then convolving the image with this linear filter gives you the ...
527 views

### Gap Filling Contours / Lines

I have the following image: and I would like to fill in its contours (i.e. I would like to gap fill the lines in this image). I have tried a morphological closing, but using a rectangular kernel of ...
88 views

### Using morphological operations for color images processing

Have you ever seen any articles about using morphological-like technique for denoising color images?
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### OCR (optical character recognition) for Indian languages - segmentation

Can any one help me in how to extract a table from the whole document image and segment it? I have done segmentation for the document image which has only text by using the projection profile. So ...
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### Best way to remove unwanted region from image

I am finding the techniques to remove unwanted regions (small dots) from image. I have an image that includes object and some unwanted region (small dots- see first image). I want to remove it. Hence, ...
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### Computations in Grayscale morphology dilation

I red this link, but unfortunately i still don't understand the process... By the way, Dilation process is performed by laying the structuring element H on the image I and sliding it across the image ...
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### Decomposition of **3D** structuring elements for morphological operations

I am struggling to implement a mathematical morphology toolset in an image processing package. I base my implementation on what I saw in MATLAB, and on several papers on the subject. There seems to ...
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### Uneven background subtraction: Rolling ball vs Disk tophat

A classical technique in still images (e.g. fluorescence microscopy images) to remove uneven illumination and isolate bright blobs is to use morphological operation such as the top-hat transform. For ...
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### OpenCV: Problem at creating a Skeleton of Lines

I need to get the lines from a photographie of a sheet of paper. While recherching, I came along this, where one answer referred to this blog entry. Now I am having trouble with this approach. I have ...
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### Erosion in image

I don't if I am posting my question in the correct place. I have tried hard to solved it but I am unsuccessful. I have an structuring element shown below: ...
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### Image processing: how do I erode on boundary and dilate inside boundary?

I have an image that I am trying to process: I want two seamingly contradictory effects: I want to remove "holes" inside "the blob". That is I want all pixels inside the blob to be solid red. I want ...
6k views

### Find branches in skeleton image using matlab

I have a skeleton image. I am able to detect branchpoints, endpoints and able to label image using BWMorph, BWLabel. Now I want to differntiate between skeleton center line and branches. In short I ...
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### Grayscale morphology

Hello I've been trying to understand the grayscale dilation operation using the following example, but my results are different. \$I = \begin{pmatrix} \bf{5} & 2 & 4 \\ 1 & -3 & 1 \end{...
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### Shape of structuring elements for morphological gradients

I am looking to understand recommended shapes of structuring elements used in calculating morphological gradients. According to Pierre Soille: Morphological Image Analysis: Only symmetric ...
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### OpenCV/C++ connect nearby contours based on distance between them

I have to connect nearby contours in an image based on the distance between them which specifies if the contours are to be connected. Now there's a question already on the same problem here https://...
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### On the de-noising of time-frequency images

I am wondering what techniques might be available for 'de-noising' the following example time-frequency image that was created using Welch's method. The following plot was created from a robotic ...
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### How to: pixel packs in an image to representative point coordinates (x,y)

Let's have an image (gray-scale or even binary) as shown on the following figure at the left hand side, the goal is to generate a list of points i.e., coordinates in the form of (x,y) for each pack of ...
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### Erosion and dilation in images

I don't know if I am posting in the correct place. I wanted to ask about dilation and erosion in bitmaps. I have as a homework to implement in a programming language these morphological operations but ...