Image Reconstruction using MATLAB

2D TO 3D IMAGE

RECONSTRUCTION USING

MATLAB

12D TO 3D IMAGE RECONSTRUCTION USING

MATLAB

PRESENTED BY :-

1)SAURAV MONDOL -

2)AJAY KR. PAUL -3)SOUMYO CHAKRAVERTY -4)DEBJIT BAKSHI -

(Dept. of ECE)


MATLAB

UNDER THE GUIDANCE OF :

PROF. OINDRI RAY

DEPT. OF ECE,

MSIT.

2D TO 3D IMAGE RECONSTRUCTION USING MATLAB

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ACKNOWLEDGEMENT

I would like to express my sincere regards to Prof. Oindri Ray,Department of Electronics and Communication Engineering,Meghnad Saha Institute of Technology for her guidance,valuable advice and constructive suggestions for carrying outthis project work.I would like to record my indebtedness to Prof. Chandi Pani,TIC, Dept. of ECE, and Prof. U.Gangopadhyay, Principal,Meghnad Saha Institute of Technology, for providing me withall the facilities that were needed.I would also like to thank all the faculty members of ECEdepartment, MSIT.Finally, my sincere thanks goes to my parents for theirencouragement and support during this project work.


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TECHNICAL OVERVIEW

The main objective of the project is to understand the variousImage Construction techniques and how they are used in variousfields that help us in providing more information about animage. We would proceed by understanding these varioustechniques using MATLAB software. Understanding in details themathematical representations of various images and how topresent these images using MATLAB software.


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CASE1: DETERMINATION OF CRYSTAL PLANE OF A

TEM IMAGE OF SILICON CRYSTAL.

• W. L. Bragg explained this result by modelling the crystal as aset of discrete parallel planes separated by a constantparameter d. It was proposed that the incident X-ray radiationwould produce a Bragg peak if their reflections off the variousplanes interfered constructively. The interference isconstructive when the phase shift is a multiple of 2π; thiscondition can be expressed by Bragg's law:

𝑛𝜆 = 2𝑑𝑠𝑖𝑛𝜃( n=integral value

𝜆=wavelength of X-Ray

d= distance between two base points of a crystal lattice

𝑠𝑖𝑛𝜃= sine of angle between 3 base points)


MATLAB

TEM IMAGE OF Si-

CRYSTAL.

FINDING OUT PARAMETER “d”, USING BRAGGS

LAW

(𝑛𝜆=2𝑑𝑠𝑖𝑛𝜃)

IMAGE RECONSTRUC-TION USING MATLAB 7.0

PLANE PLOTTING

USING MATLAB 7.0 GRAPHIC

TOOLS

CRYSTAL PLANE OF Si-CRYSTAL


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BLOCK DIAGRAM OF THE PROCESS.

FIGURE 1: BLOCK DIAGRAM

CRYSTAL PLANE OF A TEM IMAGE OF SILICON CRYSTAL.

FIGURE 2: (a)TEM image of Si-crystal.(b)Its plane determination in MATLAB plot.


MATLAB

DIFFERENTIAL EQUATIONS

• A differential equation is a mathematical equation for anunknown function of one or several variables that relatesthe values of the function itself and its derivatives ofvarious orders.

• Differential equations play a prominent role in engineering,physics, economics, biology, and other disciplines.

• Differential equations are mathematically studied fromseveral different perspectives, mostly concerned with theirsolutions —the set of functions that satisfy the equation


MATLAB

CASE 2: DETERMINATION OF SURFACE OF

WOUND ON HUMAN SKIN.

• The model is based on conservation laws for the cellular andchemical species and tissue momentum. Thus, the primaryvariables of the model are the cellular densities of fibroblasts,myofibroblasts and collagen, the chemical concentration of amitotic and chemotactic generic growth factor and the ECMdisplacement vector .


MATLAB

BLOCK DIAGRAM OF PROCESS :

DIFFERENTIAL EQUATION OF WOUND ON

HUMAN SKIN

SOLVING THE DIFFERENTIAL

EQUATION USING MATLAB 7.0,WITH

DIFFERENT PARAMETER VALUES

SURFACE PLOTTING OF THE VALUES OBTAINED

FROM DIFFERENTIAL

EQUATION

GRAPHICAL SURFACE REPRESENTATION OF

WOUND


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FIGURE 3: BLOCK DIAGRAM

GRAPHICAL SURFACE OF HUMAN WOUND

ON SKIN.


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FIGURE 4: MATLAB plot showing wound surface in 3D .

The graph above consist of different colour patterns. Each colour pattern determines respective cellular densities .

DIGITAL IMAGE PROCESSING

• Digital image processing is the use of computeralgorithms to perform image processing on digitalimages to provide more details about the originalimage.

• Since images are defined over two dimensions(perhaps more) digital image processing may bemodelled in the form of multidimensionalsystems.

• Image Reconstruction is an integral part in DigitalImage Processing.


MATLAB

IMAGE RECONSTRUCTION

• Image reconstruction techniques are used tocreate 2-D and 3-D images from sets of 1-Dprojections.

• These reconstruction techniques form the basisfor common imaging modalities such as CT, MRI,and PET, and they are useful in medicine, biology,earth science, archaeology, materials science.


MATLAB

EXAMPLES OF IMAGE RECONSTRUCTION :


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FIGURE 5 :a b

c d

e fa)Original Image

b)Image blurred and corrupted by Gaussian Noise.

c) through f) Image b) restored using an algorithm using 5,10,20 and 100 iterations respectively.

FIGURE 6 : a bc d

a) Original Image b) Image blurred

c) Noise Image d) Sum of (b) and (c)


MATLAB

FIGURE 7 : a bc de f

a)Spectrum of specified impulses. b) Corresponding SINE noise pattern in spatial domain c) &d) A similar sequence. e) & f) Two other noise patterns. The dots in a) & c) were enlarged to make them easier to see.


MATLAB

FIGURE 8 : a b

a) Image with Noise power equal to 4

b) Image with noise power equal to 0.4


MATLAB

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2D TO 3D CONVERSION USING IMAGE ENHANCEMENT TECHNIQUES OTHER THAN MATLAB.

• The world of 3D incorporates the third dimension of depth,which can be perceived by the human vision in the form ofbinocular disparity. With an appropriate disparity andcalibration of parameters, a correct 3D perception can berealized.

• An important step in any 3D system is the 3D contentgeneration. Several special cameras have been designed togenerate 3D model directly.

Examples:- 1) Stereoscopic dual-camera2) A depth-range camera


CAMERAS GENERATING 3D MODEL DIRECTLY

FIG 9: STEREOSCOPICDUAL CAMERA FIG 10: DEPTH RANGE CAMERA


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2D TO 3D CONVERSION ALGORITHMS

• Depending on the number of input images, we cancategorize the existing conversion algorithms into twogroups: algorithms based on two or more images andalgorithms based on a single still image.

• In the first case, the two or more input images could betaken either by multiple fixed cameras located atdifferent viewing angles or by a single camera withmoving objects in the scenes. We call the depth cuesused by the first group the multi-ocular depth cues. Thesecond group of depth cues operates on a single stillimage, and they are referred to as the monocular depthcues.


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2D TO 3D CONVERSION ALGORITHMS

FIGURE 11 : CHART SHOWING 2D TO 3D IMAGE CONVERSION ALGORITHMS

NO:

OF

IMAGE INPUTS

ONE IMAGE

DEFOCUS

LINEAR PERSPECTIVE

ATMOSPHERIC SCATTERING

SHADING

PATTERNED TEXTURES

SYMMETRIC PATTERNS

OCCLUSIONS

TWO IMAGES

BINOCULAR DISPERITY

MOTION

DEFOCUS

FOCUS

SILHOUETTE


MULTIOCULAR DEPTH CUE ALGORITHMS

BINOCULAR DISPARITY :

o With two images of the same scene captured from slightlydifferent view points, the binocular disparity can be utilized torecover the depth of an object.

o First, a set of corresponding points in the image pair arefound. Then, by means of the triangulation method, the depthinformation can be retrieved with a high degree of accuracywhen all the parameters of the stereo system are known.


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MOTION :

o The relative motion between the viewing camera and the observedscene provides an important cue to depth perception: near objectsmove faster across the retina than far objects do.

FIGURE 12: MOTION IN MULTIOCULAR DEPTH CUE


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DEFOCUS USING MORE THAN TWO IMAGES

o Depth-from-defocus methods generate a depth map from the degree ofblurring present in the images. In a thin lens system, objects that are in-focus are clearly pictured whilst objects at other distances are defocused,i.e. blurred.

FIGURE 13: DEFOCUS USING MORE THAN TWO IMAGES


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FOCUS :The depth-from-focus requires a series of images of the scenewith different focus levels by varying and registering the distancebetween the camera and the scene.

FIGURE 14 : FOCUS


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SILHOUETTE

A silhouette of an object in an image refers to the contourseparating the object from the background. Shape-from-silhouette methods require multiple views of the scene taken bycameras from different viewpoints.

FIGURE 15: SILHOUETTE IMAGES


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MONOCULAR DEPTH CUE ALGORITHMS

DEFOCUS :The images, with which this group of algorithms works, arerequired to be taken from a fixed camera position and objectposition but using different focal settings.

FIGURE 16: DEFOCUS


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LINEAR PERSPECTIVE :Linear perspective refers to the fact that parallel lines, such as railroad tracks,appear to converge with distance, eventually reaching a vanishing point at thehorizon. The more the lines converge, the farther away they appear to be.

FIGURE 17 (a b) : IMAGES SHOWING LINEAR PERSPECTIVE


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ATMOSPHERIC SCATTERING :

The phenomenon called atmosphere scattering, also known as haze,causes various visual effects: distant objects appear less distinct andmore bluish than objects nearby.

FIGURE 18 (a b) : ATMOSPHERIC SCATERRING


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BILATERAL SYMMETRIC PATTERN :

The idea behind 3D reconstruction based on symmetric patterns is thata single non-frontal image of a bilaterally symmetric object can beviewed as two images of this object from different view angles.

FIGURE 19 : BILATERAL SYMMETRIC PATTERN


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OCCLUSIONS :The principle of depth-from-occlusion algorithms has its roots inthe phenomenon that an object which overlaps or partlyobscures our view of another object is considered to be closer.

FIGURE 20: OCCLUSIONS


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APPLICATION OF ALGORITHMS:


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FIGURE 22 : Shape from texture(From left to right: Original image, Segmented texture region; Surface normals; Depth map;

Reconstructed 3D shape)

FIGURE 21: (a)A 2D image (b) Depth map of image (a)

ADVANTAGES AND DISADVANTAGES OF IMAGE RECONSTRUCTION

ADVANTAGES:

• Provide more information about an Image.• Contrast and Intensity Enhancement.• Removal of external noise from an image.• Provides high resolution form of a low resolution image, etc.

DISADVANTAGES:

• Loss of information can happen during reconstruction from one formto another .

• Increase in memory storage space because of the storage of differentforms of the same image.


MATLAB

CONCLUSION

Image Reconstruction is an important part of Digital ImageProcessing. It helps us in providing various details about animage by enhancing its resolution,contrast,intensity,etc.We havedefined various mathematical operations and plotting functionsof the software and gradually concluded our project by providingMATLAB functions that will help us to solve DifferentialEquations and its plotting, which is the backbone of the ImageReconstruction techniques.


MATLAB

REFERENCES

• Digital Image Processing using MATLAB 2nd Edition –Gonzalez,Woods,Eddins.

• An Introduction to Digital Image Processing – Bill Silver, Chief Technology Officer ,Cognex Corporation, Modular Vision Systems Division.

• Introduction to MATLAB for engineering students - David Houcque,Northwestern University.

• http://www.mathworks.in/help/matlab/math/ordinary-differential-equations.html?s_tid=doc_12b

• http://en.wikipedia.org/wiki/Differential_equation• http://en.wikipedia.org/wiki/Bragg's_law• Wound Model : International Journal of Solids and Structures.• Hassner And Basri: Example based 3d reconstruction model.


MATLAB

THANK YOU


MATLAB

Documents

Image Reconstruction using MATLAB