CS代考 BMEN90021, Lecture set 1, Image Operations

Medical Imaging
Medical Imaging Semester 1, 2022
Prof Leigh Johnston
A/Prof Kathryn Stok

Lectures & tutorials – all classes will be recorded and available on Canvas.
Mondays Tuesdays Wednesdays
15:15 – 16:15 10:00 – 11:00
14:15 – 15:15
All times listed above are either lectures or tutorials, therefore there will be three classes every week.
4 workshops spread across the semester First workshop will be in Week 3.
Refer to subject schedule on Canvas.
© University of Melbourne 2 BMEN90021, Lecture set 1, Image Operations

Timetable continued…
Imaging lab visits
Mid-semester test
A few imaging lab visits will be scheduled throughout the semester,
to see imaging systems in practice.
Lab visits are not compulsory or assessable.
Tuesday 26 April (Week 8).
© University of Melbourne 3 BMEN90021, Lecture set 1, Image Operations

Assessment
One mid-semester examination of one hour duration (10%).
Attendance and participation in four laboratory classes in Weeks 2 to 12, working in groups of two, each with a written assignment of approximately 750 words. 18-20 hours of work (30% total);
One end-of-semester examination of three hours duration Hurdle requirement: Students must pass end of semester
examination to pass the subject.
From University of Melbourne’s Assessment Policy (MPF1326):
“Students who do not satisfy the hurdle requirements in any subject will fail that subject, even if they have obtained more than 50% of the marks available by the completion other components of assessment.”
© University of Melbourne 4 BMEN90021, Lecture set 1, Image Operations

Subject overview (handbook)
This subject introduces students to the engineering, physics and physiology of medical imaging, including the history and progression of medical imaging modalities as well as emerging imaging technologies in clinical and research practise. reconstruction methods;
Topics include:
Image metrics including signal-to-noise and contrast-to-noise ratios, image resolution, image operations including convolution, filtering and edge detection;
Biophysical principles of X-ray, CT, PET, SPECT, MRI and ultrasound, and the mathematics of image reconstruction for each modality, including filtered backprojection and Fourier reconstruction methods;
This material is complemented by the use of software tools (e.g. MATLAB) for data simulation, modelling, image manipulation and reconstruction.
© University of Melbourne 5 BMEN90021, Lecture set 1, Image Operations

Objectives (handbook)
Having completed this unit the student should be able to:
• Describe the principles of the modalities of medical imaging systems
• Describe the physics and physiology fundamental to these imaging systems
• Apply the mathematics of each imaging modality
• Compute image reconstructions using back-projection methods
• Compute image reconstructions using fourier transform methods
• Identify basic causes of image contrast and artefacts
• Describe clinical applications of each imaging modality
• Apply their knowledge to understanding emerging medical imaging technologies.
© University of Melbourne 6 BMEN90021, Lecture set 1, Image Operations

• • • • • •
Other modalities (if time permits)
Outline of topics
Image operations, metrics & analysis
Computed Tomography
Ultrasound
Magnetic Resonance Imaging
Nuclear Medicine
Scintigraphy SPECT PET
© University of Melbourne 7
BMEN90021, Lecture set 1, Image Operations

Fundamentals of Medical Imaging, 2nd ed. by
Cambridge University Press 2009
Available from online booksellers,
also in e-book form from Book Depository (and others).
Webpage: http://www.cambridge.org/uk/stm/suetens/index.asp
Exercises and solutions — for extension: LMS
These are not necessarily representative of exam questions.
Additionally: Introduction to Biomedical Imaging by , IEEE Press 2003
© University of Melbourne 8 BMEN90021, Lecture set 1, Image Operations

Lecture 1: Introduction
Medical imaging is a fusion of engineering, physics and
physiology.
What is an image?
How is an image stored?
How is an image manipulated?
Before jumping into radiography, need to understand the basics:
First, a quick look at scanners…
© University of Melbourne 9 BMEN90021, Lecture set 1, Image Operations

Medical imaging scanners
!X-ray (dms-egy.com)
!CT (radiology-equipment.com)
!PET/CT (unimelb.edu.au)
!NIRS (phys.org)
!MEG (oobject.com)
!SPECT (cnx.org)
!MRI (monash.edu)
!Ultrasound (gehealthcare.com)
© University of Melbourne
BMEN90021, Lecture set 1, Image Operations

Digital image = a matrix • X-ray radiography film
A (near-)continuum of intensities in 2-d space Physiology is naturally continuous!
• In the computer era, images are stored digitally.
An image is a matrix of intensity values.
Easiest to understand in a Matlab example
Grayscale images are 2-d matrices RGB colour images are 3-d matrices
Standard image formats jpg, tif, gif, png
Medical image formats
Scanner manufacturer dependent
“.dicom”: Digital Imaging and Communications in Medicine
colenta.at
© University of Melbourne 11 BMEN90021, Lecture set 1, Image Operations

Properties of digital images
• Gray value is assigned to each grid point (or colour vector assigned to each grid point if image is RGB)
• Grid points are termed “pixels” (picture-elements) • In 3-d, grid points are “voxels” (volume-elements)
© University of Melbourne 12 BMEN90021, Lecture set 1, Image Operations

Quantization
Conversion from analog to discrete values (digital) =
sampling via quantization:
The more gray values, the smoother looking the image.
Medical images: traditionally 4096 intensity values (= 12 bits per pixel)
© University of Melbourne 13 BMEN90021, Lecture set 1, Image Operations

Image operations
A digital image, I, attributes a gray value (brightness) to
each pixel (i,j).
A “gray level transformation”:
I0(i, j) = g(I(i, j))
Main use: Increase contrast in some regions of an image.
Original intensity
© University of Melbourne 14 BMEN90021, Lecture set 1, Image Operations
New intensity

Image operations
Windowing: choose a window of intensity levels
Contrast outside window is lost
OrigIninteanl sinitytensity
© University of Melbourne 15 BMEN90021, Lecture set 1, Image Operations
New intensity

Image operations
Thresholding: Intensities up to a threshold value are set to zero, while those above the threshold value are set to a maximal value:
OInritgeinsailtyintensity
© University of Melbourne 16 BMEN90021, Lecture set 1, Image Operations
New intensity

Histograms
Equivalently an empirical probability density function.
An image histogram is a frequency plot of all intensities in the image, regardless of position.
Original intensity Intensity
© University of Melbourne 17 BMEN90021, Lecture set 1, Image Operations
New intensity

Histogram exercise…
Plot the histogram of the image intensities for the image below, where black = 0, white = 255.
© University of Melbourne 18 BMEN90021, Lecture set 1, Image Operations

Result of windows
Original image
Two different window functions
(solid & dashed lines). Which produces which image below?
© University of Melbourne 19
BMEN90021, Lecture set 1, Image Operations
New intensity

Multi-image operations
I+(i, j) = I1(i, j) + I2(i, j) I(i, j) = I1(i, j) I2(i, j)
Images can be added and subtracted pixelwise:
The average image of a set of n images is:
I a v ( i , j ) = n1 ( I 1 ( i , j ) + . . . + I n ( i , j ) ) .
repeated 6 times & averaged
Example: MRI acquisition (Scan time: 3 minutes)
Same MRI acquisition, (Scan time: 18 minutes)
© University of Melbourne 20
BMEN90021, Lecture set 1, Image Operations

Multi-image operations
X-ray image after injection of a contrast
Mask image of same region before contrast
agent administered.
Subtraction of two images & contrast
enhancement.
© University of Melbourne 21 BMEN90021, Lecture set 1, Image Operations

Linear filters
A linear, shift-invariant transformation of an image
Convolution
© University of Melbourne 22 BMEN90021, Lecture set 1, Image Operations

Convolution in steps
Define the filter, for example a 3 x 3 filter:
Step 1: Flipping
Colour the pixels for ease of visualisation
– Flip filter in Left-Right direction
– Flip resultant filter in Up-Down direction
© University of Melbourne 23 BMEN90021, Lecture set 1, Image Operations

Convolution in steps
• Step 2: Repeat for every pixel in the image,
– Place flipped filter over the image, centred at that pixel.
2 3 4 5 6 7
© University of Melbourne
24 BMEN90021, Lecture set 1, Image Operations

Convolution in steps
• Step 2: Repeat for every pixel in the image,
– Place flipped filter over the image, centred at that pixel.
• eg. The pixel (3,4)
2 3 4 5 6 7
© University of Melbourne
25 BMEN90021, Lecture set 1, Image Operations

Convolution in steps
• Step 2: Repeat for every pixel in the image,
– Place flipped filter over the image, centred at that pixel.
• eg. The pixel (3,4)
© University of Melbourne
26 BMEN90021, Lecture set 1, Image Operations

Convolution in steps
• Step 2: Repeat for every pixel in the image,
– Place flipped filter over the image, centred at that pixel.
• eg. The pixel (3,4)
– Multiply filter intensities by image intensities, pixel-by-pixel, and sum the result:
I’(3,4) = x I(2,3) + x I(2,4) + … + x I(4,5)
© University of Melbourne 27 BMEN90021, Lecture set 1, Image Operations

Convolution in steps
• Step 2: Repeat for every pixel in the image,
– Place flipped filter over the image, centred at that pixel.
• eg. Next, the pixel (3,5)…
– Multiply filter intensities by image intensities, pixel-by-pixel, and sum the result:
I’(3,5) = x I(2,4) + x I(2,5) + … + x I(4,6)
© University of Melbourne 28 BMEN90021, Lecture set 1, Image Operations

Convolution in steps
• Step 2: Repeat for every pixel in the image, I0(i, j) = I(i, j) ⇤ f
=XXf(m,n)I(im,jn), 8i,j mn
Original image, I New image, I’
© University of Melbourne 29 BMEN90021, Lecture set 1, Image Operations

Convolution: at the edges?
• MATLAB has three ways of dealing with the edges.
– 1. ‘Full’ convolution, which means new image is bigger than the original.
– 2. ‘Same’, which means new image is the same size as the original.
– 3. ‘Valid’, which returns a smaller image: all those pixels not affected by edges.
• Preference for ‘same’, as the output image stays the same size.
© University of Melbourne 30 BMEN90021, Lecture set 1, Image Operations

Low-pass linear filters
The averaging filter makes an image more smooth and removes some noise.
eg. Gaussian filter
A ‘softer’ way to smooth is to weight the centre of the filter more than the edges.
Attenuates high frequency information Therefore this is a “low-pass filter”.
© University of Melbourne 31 BMEN90021, Lecture set 1, Image Operations

High-pass linear filters
A high-pass filter is easily created by subtracting a low-pass filtered image from the original image.
© University of Melbourne 32 BMEN90021, Lecture set 1, Image Operations

Unsharp masking
An image can be written as a sum of low- and high- pass filter outputs:
I = g ⇤ I + (I g ⇤ I).
Unsharp masking highlights the high frequency parts
For some α > 0,
I = g ⇤ I + (1 + )(I g ⇤ I) = I + (I g ⇤ I)
= (1 + )I g ⇤ I
© University of Melbourne 33 BMEN90021, Lecture set 1, Image Operations

Nonlinear filters
When denoising with a linear filter (eg. Gaussian), the image becomes blurry.
Denoising & keeping edge information is better done with a median filter.
Original Gaussian Median
© University of Melbourne 35 BMEN90021, Lecture set 1, Image Operations

Geometric operations
Affine (not technically linear!) transformations
Scaling, translation, rotation and shear
http://www.bobpowell.net/transformations.htm
© University of Melbourne 37 BMEN90021, Lecture set 1, Image Operations

程序代写 CS代考加微信: powcoder QQ: 1823890830 Email: powcoder@163.com

Related Posts