Morphology Restoration

Morphological image processing Image Restoration

SPEECH AND IMAGE PROCESSING LAB Morphological image processing & Image restoration Nishil. B. S. Nisha J. S.

Nishil. B. S.Nisha J. S.

SPEECH AND IMAGE PROCESSING LAB Morphological image processing

Morphological image processing Image Restoration

Morphological image processing Structuring element Morhological operations

Morphological image processing

What is morphological image processing ? A broad set of image processing operations that process images based on shapes

Nishil. B. S.Nisha J. S.

SPEECH AND IMAGE PROCESSING LAB Morphological image processing

Morphological image processing Image Restoration

Morphological image processing Structuring element Morhological operations

Morphological image processing

Applications of Morphological image processing Extraction of image components eg. Boundaries, skeletons etc. Geometric measurements eg. Object location, orientation ,area ,perimeter Morphological smoothing To compute the morphological gradient of an image To compensate uneven background illumination Granulometry

Nishil. B. S.Nisha J. S.

SPEECH AND IMAGE PROCESSING LAB Morphological image processing

Morphological image processing Image Restoration

Morphological image processing Structuring element Morhological operations

Morphological image processing

Value of each pixel in the output image is based on the neighbouring pixels in the input image Morphological operations require an image and a structuring element Size and shape of the neighbours depends on the structuring element

Basic morphological operations Erosion Dilation

Nishil. B. S.Nisha J. S.

SPEECH AND IMAGE PROCESSING LAB Morphological image processing

Morphological image processing Image Restoration

Morphological image processing Structuring element Morhological operations

Structuring element

Matrix consisting of only 0’s and 1’s Can have any arbitrary shape and size Pixels with values of 1 define the neighborhood Origin of structuring element identifies the pixel of interest Matlab syntax strel(shape, parameters)

Nishil. B. S.Nisha J. S.

SPEECH AND IMAGE PROCESSING LAB Morphological image processing

Morphological image processing Image Restoration

Morphological image processing Structuring element Morhological operations

Dilation

Grows or thickens objects in a binary image Manner and extent of thickening controlled by the structuring element Rule for dilation The value of the output pixel is the maximum value of all the pixels in the input pixel’s neighborhood Matlab syntax imdilate(original image, structuring element)

Nishil. B. S.Nisha J. S.

SPEECH AND IMAGE PROCESSING LAB Morphological image processing

Morphological image processing Image Restoration

Morphological image processing Structuring element Morhological operations

Illustration of dilation of binary image

Nishil. B. S.Nisha J. S.

SPEECH AND IMAGE PROCESSING LAB Morphological image processing

Morphological image processing Image Restoration

Morphological image processing Structuring element Morhological operations

Illustration of dilation of greyscale image

Nishil. B. S.Nisha J. S.

SPEECH AND IMAGE PROCESSING LAB Morphological image processing

Morphological image processing Image Restoration

Morphological image processing Structuring element Morhological operations

Erosion

Shrinks or thins objects in a binary image Manner and extent of shrinking controlled by the structuring element Rule for erosion The value of the output pixel is the minimum value of all the pixels in the input pixel’s neighborhood Matlab syntax imerode(original image, structuring element)

Nishil. B. S.Nisha J. S.

SPEECH AND IMAGE PROCESSING LAB Morphological image processing

Morphological image processing Image Restoration

Morphological image processing Structuring element Morhological operations

Illustration of erosion of binary image

Nishil. B. S.Nisha J. S.

SPEECH AND IMAGE PROCESSING LAB Morphological image processing

Morphological image processing Image Restoration

Morphological image processing Structuring element Morhological operations

Morphological Opening

Erosion followed by dilation Smoothens object contours Breaks thin connections between objects Removes thin protrusions matlab syntax imopen(original image, structuring element)

Nishil. B. S.Nisha J. S.

SPEECH AND IMAGE PROCESSING LAB Morphological image processing

Morphological image processing Image Restoration

Morphological image processing Structuring element Morhological operations

Illustration of opening a binary image

Nishil. B. S.Nisha J. S.

SPEECH AND IMAGE PROCESSING LAB Morphological image processing

Morphological image processing Image Restoration

Morphological image processing Structuring element Morhological operations

Illustration of opening a binary image

Nishil. B. S.Nisha J. S.

SPEECH AND IMAGE PROCESSING LAB Morphological image processing

Morphological image processing Image Restoration

Morphological image processing Structuring element Morhological operations

Morphological Closing

Dilation followed by erosion Joins narrow breaks Fills long thin gulfs Fills holes smaller than the structuring element matlab syntax imclose(original image, structuring element)

Nishil. B. S.Nisha J. S.

SPEECH AND IMAGE PROCESSING LAB Morphological image processing

Morphological image processing Image Restoration

Morphological image processing Structuring element Morhological operations

Illustration of closing a binary image

Nishil. B. S.Nisha J. S.

SPEECH AND IMAGE PROCESSING LAB Morphological image processing

Morphological image processing Image Restoration

Morphological image processing Structuring element Morhological operations

Hit or Miss Transformation Used to identify specified configurations of pixels Steps involved in Hit or Miss Transformation 1 2

3

4

Input image is eroded with a structuring element B1 Complement of input image is the eroded using a structuring element B2 Logical AND operation is performed on images obtained from step 1 and 2 Output image consists of 1 in all locations that match the pixels in B1

matlab syntax bwhitmiss(original image, B1, B2)

Nishil. B. S.Nisha J. S.

SPEECH AND IMAGE PROCESSING LAB Morphological image processing

Morphological image processing Image Restoration

Morphological image processing Structuring element Morhological operations

Illustration of Hit or Miss Transformation of a binary image

Nishil. B. S.Nisha J. S.

SPEECH AND IMAGE PROCESSING LAB Morphological image processing

Morphological image processing Image Restoration

Morphological image processing Structuring element Morhological operations

Illustration of Hit or Miss Transformation of a binary image

Nishil. B. S.Nisha J. S.

SPEECH AND IMAGE PROCESSING LAB Morphological image processing

Morphological image processing Image Restoration

Morphological image processing Structuring element Morhological operations

Skeletonization

Skeletonization Reduce all objects in an image to lines without changing the essential structure of the image matlab syntax bwmorph(original image, ‘skel’, inf)

Nishil. B. S.Nisha J. S.

SPEECH AND IMAGE PROCESSING LAB Morphological image processing

Morphological image processing Image Restoration

Morphological image processing Structuring element Morhological operations

Illustration of Skeletonization of a binary image

Nishil. B. S.Nisha J. S.

SPEECH AND IMAGE PROCESSING LAB Morphological image processing

Morphological image processing Image Restoration

Morphological image processing Structuring element Morhological operations

Perimeter Determination

Determines the perimeter pixels of the objects in a binary image A pixel is considered a perimeter pixel if it satisfies both of these criteria: The pixel is on One (or more) of the pixels in its neighborhood is off

matlab syntax bwperim(image)

Nishil. B. S.Nisha J. S.

SPEECH AND IMAGE PROCESSING LAB Morphological image processing

Morphological image processing Image Restoration

Morphological image processing Structuring element Morhological operations

Illustration of Perimeterisation of a binary image

Nishil. B. S.Nisha J. S.

SPEECH AND IMAGE PROCESSING LAB Morphological image processing

Morphological image processing Image Restoration

Morphological image processing Structuring element Morhological operations

Labeling Connected Components Method to identify objects in a binary image Pixels in each different object are assigned a unique integer Type of the chosen connectivity affects the number of objects found in an image Definition of object Set of pixels in a binary image that form a connected group is called an object or a connected component matlab syntax [L num] = bwlabel(image,connectivity) L = label matrix num = total number of objects

Nishil. B. S.Nisha J. S.

SPEECH AND IMAGE PROCESSING LAB Morphological image processing

Morphological image processing Image Restoration

Morphological image processing Structuring element Morhological operations

Labeling Connected Components Pixel Connectivity Connectivity defines which pixels are connected to other pixels Standard 2D connectivities are : 4-connected 8-connected

Custom connectivities can also be specified

Nishil. B. S.Nisha J. S.

SPEECH AND IMAGE PROCESSING LAB Morphological image processing

Morphological image processing Image Restoration

Morphological image processing Structuring element Morhological operations

Illustration of Labeling of a binary image

Nishil. B. S.Nisha J. S.

SPEECH AND IMAGE PROCESSING LAB Morphological image processing

Morphological image processing Image Restoration

Morphological image processing Structuring element Morhological operations

Morpholgical Reconstruction Repeated dilations of an image Morphological transformation involving two images and a structuring element One image, the marker is the starting point of transformation Other image, the mask constrains the transformation Morpholgical Reconstruction Algorithm Initialize h1 to be the marker image Create the structuring element: B = ones(3) Repeat: hk+1 = (hk dilationB) ∩ mask until hk+1 = hk . matlab syntax imreconstruct(marker, mask) Nishil. B. S.Nisha J. S.

SPEECH AND IMAGE PROCESSING LAB Morphological image processing

Morphological image processing Image Restoration

Morphological image processing Structuring element Morhological operations

Illustration of Morpholgical Reconstruction

Nishil. B. S.Nisha J. S.

SPEECH AND IMAGE PROCESSING LAB Morphological image processing

Morphological image processing Image Restoration

Image degradation Degradation model Image restoration techniques

Image Restoration

Image Restoration Recovering the desired or perfect image from a degraded version.

Nishil. B. S.Nisha J. S.

SPEECH AND IMAGE PROCESSING LAB Morphological image processing

Morphological image processing Image Restoration

Image degradation Degradation model Image restoration techniques

Image degradation

causes of Image degradation 1 2 3 4

degradation due to sensor noise Blur due to camera misfocus Degradation due to camera motion Degradation due to random atmospheric turbulence

Nishil. B. S.Nisha J. S.

SPEECH AND IMAGE PROCESSING LAB Morphological image processing

Morphological image processing Image Restoration

Image degradation Degradation model Image restoration techniques

Degradation model

Degradation function together with an additive noise term operates on an input image to produce degraded image g (x, y ) = h(x, y ) ∗ f (x, y ) + η(x, y ) f(x,y) h(x,y) η(x, y ) g(x,y)

Original true image Degradation function, also called PSF(Point Spread Function) Additive noise Degraded image

Nishil. B. S.Nisha J. S.

SPEECH AND IMAGE PROCESSING LAB Morphological image processing

Morphological image processing Image Restoration

Image degradation Degradation model Image restoration techniques

Degradation model cont..

Figure: Degradation model

Nishil. B. S.Nisha J. S.

SPEECH AND IMAGE PROCESSING LAB Morphological image processing

Morphological image processing Image Restoration

Image degradation Degradation model Image restoration techniques

Image blurring

A form of bandwidth reduction of the image due to imperfect image formation process Caused by relative motion between the camera and the original scene, or by optical system, which is out of focus PSF of motion blur is characterized by two parameters namely, blur direction and blur length matlab syntax fspecial(’motion’, blur length, blur angle)

Nishil. B. S.Nisha J. S.

SPEECH AND IMAGE PROCESSING LAB Morphological image processing

Morphological image processing Image Restoration

Image degradation Degradation model Image restoration techniques

Example of blurred image

Figure: Original and blurred image

Nishil. B. S.Nisha J. S.

SPEECH AND IMAGE PROCESSING LAB Morphological image processing

Morphological image processing Image Restoration

Image degradation Degradation model Image restoration techniques

Image restoration techniques

1 2 3 4

Inverse filtering Wiener filtering Lucy Richardson Algorithm Blind deconvolution

Nishil. B. S.Nisha J. S.

SPEECH AND IMAGE PROCESSING LAB Morphological image processing

Morphological image processing Image Restoration

Image degradation Degradation model Image restoration techniques

Inverse Filtering

This is a very basic restoration filter Restoration is done using the inverse of degradation function G (u, v ) Fb (x, y ) = H(u, v ) This filter generally gives poor results matlab syntax deconvwnr(degraded image, PSF)

Nishil. B. S.Nisha J. S.

SPEECH AND IMAGE PROCESSING LAB Morphological image processing

Morphological image processing Image Restoration

Image degradation Degradation model Image restoration techniques

Wiener Filtering Used for restoring images in the presence of blur as well as noise Seeks an estimate fˆ that minimises the statistical error function e 2 = E (f − fˆ)2 Wiener filter function is given by : " Fˆ (x, y ) = G (u, v )

2

|H(u, v )|

#

2

H(u, v ) |H(u, v )| + Sn (u, v )/Sf (u, v )

Sn = noise power spectrum Sf = power spectrum of undegraded image

Nishil. B. S.Nisha J. S.

SPEECH AND IMAGE PROCESSING LAB Morphological image processing

Morphological image processing Image Restoration

Image degradation Degradation model Image restoration techniques

wiener filtering

features This filter gives descent results It is quite fast matlab syntax deconvwnr(degraded image, psf,nspr) nspr = Noise to signal power ratio deconwnr(degraded image,psf, nacorr, facorr) nacorr = Noise autocorrrelation function facorr= Undegraded image autocorrelation function

Nishil. B. S.Nisha J. S.

SPEECH AND IMAGE PROCESSING LAB Morphological image processing

Morphological image processing Image Restoration

Image degradation Degradation model Image restoration techniques

Lucy - Richardson Algorithm

Iterative non-linear image restoration technique Used when only the PSF is known This algorithm maximises the liklihood function Features Reduce the effect of noise amplification Accounts for nonuniform image quality Reduces Camera read-out noise

Nishil. B. S.Nisha J. S.

SPEECH AND IMAGE PROCESSING LAB Morphological image processing

Morphological image processing Image Restoration

Image degradation Degradation model Image restoration techniques

matlab syntax deconvlucy(degraded image, psf,numit, dampar, weight) numit = Number of iterations dampar = Threshold deviation weight = weight to be assigned to each pixel

Nishil. B. S.Nisha J. S.

SPEECH AND IMAGE PROCESSING LAB Morphological image processing

Morphological image processing Image Restoration

Image degradation Degradation model Image restoration techniques

Blind deconvolution

Image restoration not based on the specific knowledge of PSF Based on maximum liklihood estimation Restores the image and the PSF simultaneously using an iterative process similar to the Lucy-Richardson algorithm matlab syntax deconvblind(degraded image, intpsf) intpsf = Initial PSF

Nishil. B. S.Nisha J. S.

SPEECH AND IMAGE PROCESSING LAB Morphological image processing

Morphological image processing Image Restoration

Image degradation Degradation model Image restoration techniques

References

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Rafael C. Gonzalez, Richard E. Woods & Steven L. Eddins,“Digital image processing using matlab”, Pearson Education Inc. Anil K. Jain, “Fundamentals of digital image processing”, Prentice-Hall Inc. www.prenhall.com/gonzalezwoods www.mathworks.com

Nishil. B. S.Nisha J. S.

SPEECH AND IMAGE PROCESSING LAB Morphological image processing