Image&Analysis&& && TheBasics&& - The University …sdb/PHYS871/PHYS871-Image...PHYS871(Clinical(Imaging(Applicaons(/(Image(Analysis(—(The(Basics( 1 Image&Analysis&& && TheBasics&&!

PHYS871 Clinical Imaging Applica4ons / Image Analysis — The Basics 1

Image Analysis The Basics

Dr Steve Barre6 April 2016

Image Analysis The Basics

PHYS871 Clinical Imaging ApplicaBons


IntroducBon

Image Processing

Image Analysis

Kernel Filters Rank Filters

Fourier Techniques Par4cle Analysis

Fourier Filters

Specialist Solu4ons


Image Display

/ Image Display

An image is a 2-‐dimensional collec4on of pixel values that can be displayed or printed by assigning a shade of grey (or colour) to every pixel value.


Image Display An image is a 2-‐dimensional collec4on of pixel values that can be displayed or printed by assigning a shade of grey (or colour) to every pixel value.

/ Image Display


SpaBal CalibraBon For image analysis to produce meaningful results, the spa4al calibra4on of the image must be known. If the data acquisi4on parameters can be read from the image (or parameter) file then the spa4al calibra4on of the image can be determined.

For simplicity and clarity, spa4al calibra4on will not be indicated on subsequent images.

/ Image Display / Calibra4on


SPM Image Display With Scanning Probe Microscope images there is no guarantee that the sample surface is level (so that the z values of the image are, on average, the same across the image).

Raw image data A[er compensa4ng for 4lt

/ SPM Image Display


SPM Image Display By trea4ng each scan line of an SPM image independently, anomalous jumps in the apparent height of the image (produced, for example, in STMs by abrupt changes in the tunnelling condi4ons) can be corrected for.

Raw image Compensated for 4lt Line-‐by-‐line compensa4on

/ SPM Image Display


Image Processing Image processing means changing all or some of the pixel values in an image, usually with the aim of making some feature(s) of the image more easily ‘visible’.

The most trivial example would include changing the colour used to represent each pixel value — the look-‐up table (LUT).

default greyscale increased contrast

/ Image Processing / LUT


Image Processing The LUT does not have to be a linear, or even monotonic. A non-‐linear mapping between pixel value and displayed colour can o[en reveal unexpected detail in the image.

default greyscale zebra greyscale

/ Image Processing / LUT


Image Processing Changing the LUT is reversible, as it is only the mapping between pixel values and display colours that is changed.

Taking a differen4al – replacing each pixel with the value of the local differen4al of the surface with respect to some direc4on – is irreversible in the sense that integra4ng doesn’t (necessarily) get you your original image back.

greys → z values greys → ∂z/∂x values

/ Image Processing


Kernel Filters Processing is o[en carried out using a kernel filter which uses an n x n matrix of numbers. The kernel matrix is applied to every pixel in an image in turn.

The elements of the kernel matrix are mul4plica4on values that are applied to a target pixel and its neighbouring pixels. The target pixel is replaced with the normalised sum of these products, and then the process is repeated for the next (overlapping) set of pixels.

1 1 1

1 1 1

1 1 1

Central value in matrix aligned with target pixel

1 1 1

1 1 1

1 1 1

/ Image Processing / Kernel Filters


Kernel Filters The simplest kernel filters use 3 x 3 matrices...

1 1 1

1 4 1

1 1 1

smooth

-‐1 -‐1 -‐1

-‐1 9 -‐1

-‐1 -‐1 -‐ 1

sharpen

-‐2 -‐1 0

-‐1 0 1

0 1 2

gradient

original image



Kernel Filters An edge detec4on filter (or Sobel filter) does exactly what it says it does.

original image Sobel filtered

[ Note that the image was pre-‐processed so that the filter picked out the islands clearly. Also, the filtered image had the contrast increased and the background grey filled in. ]



Rank Filters Processing using a rank filter uses the same idea of an n x n neighbourhood of pixel values, but without the matrix of numbers used with kernel filters.

1 2 3 4 5 6 7 8 9

/ Image Processing / Rank Filters


Rank Filters Rank filters can be used to remove isolated pixels that are significantly brighter or darker than their neighbours. A median filter can be a very effec4ve noise reduc4on filter.

image + ar4ficial noise median filtered

/ Image Processing / Rank Filters


Fourier Filters Processing using Fourier filters involves calcula4on of the image’s frequency components.

IFFT

FFT

/ Image Processing / Fourier Filters


Fourier Filters Here’s an easy way to ‘clean’ a surface.

original image Fourier filtered



Fourier Filters Even when the signal–to–noise ra4o is lousy, Fourier filtering can extract the signal.

original image

signal

noise



Fourier Filters Fourier filters can be even more powerful if the symmetry of the surface is exploited.

FFT

IFFT Select Fourier components with 10 -‐ fold symmetry



Fourier Filters Although features lacking 10 -‐ fold rota4onal symmetry (such as the randomly dispersed contamina4on) have been effec4vely removed from the image, the correspondence between the original image and the Fourier filtered image can s4ll be seen.

original image Fourier filtered



Image Analysis Image analysis means extrac4ng quan4ta4ve informa4on that is derived from the pixel values in an image.

Rather than being used as an intermediate step in image processing, the FFT can be a valuable source of quan4ta4ve informa4on.

original image Fourier transform strongest components

The FFT maxima occur at a spa4al frequency of 2.33 per µm (→ period = 0.43 µm).

/ Image Analysis


ParBcle Analysis The name par4cle analysis should not be taken too literally. The ‘par4cles’ can be any features that can be separated from the background by thresholding.

original image thresholded

Note that an image may require pre-‐processing to ensure that the intensity (height) of features of interest are above a threshold and all ‘background clumer’ is below.

/ Par4cle Analysis


Thresholding Thresholding will not work effec4vely if the features of interest are on a varying background.

Senng the threshold at the appropriate level may require some care.

/ Par4cle Analysis / Thresholding


ParBcle Analysis

Mean nearest neighbour distance = 13 ± 5 nm Nearest neighbour lies in azimuthal direc4on 83° (anisotropy = 0.19)

... ... ... ... ... ... ... ... ... ... ... ...

... ... ... ... ... ... ... ... ... ... ... ...

... ... ... ... ... ... ... ... ... ... ... ...

Size Area Height

/ Par4cle Analysis


Specialist Analysis When “seeing the wood for the trees”, or in this case the adsorbate for the substrate, computers can find the task much harder than an eye/brain combina4on.

The property of the DNA strands that allows them to be separated from the background clumer is their curvature (the second differen4al of height wrt transverse distance).

/ Specialist Analysis / Enhancing DNA


Specialist Analysis

0.25

1.18

Can the extent of ‘entanglement’ be quan4fied?

/ Specialist Analysis / Enhancing DNA


Image Analysis If you'd like to know more about the principles behind digital image processing and image analysis, or maybe you want to get your teeth into some of the maths, then try…

/ Further Reading

The examples used have been drawn from the field of earth sciences rather than medical sciences, but the same principles apply.

ISBN: 978-‐3-‐642-‐10342-‐1 DOI: 10.1007/978-‐3-‐642-‐10343-‐8 eBook: hmp://link.springer.com.ezproxy.liv.ac.uk/book/10.1007/978-‐3-‐642-‐10343-‐8


Acknowledgements

Johanne Holly Meningitis Fund

Liverpool School of Tropical Medicine

Caltech Czech Academy of Sciences Washington State University University of Würzburg

Thanks to

for use of their SEM, SFM and STM images and to

for supporting image analysis projects

Image&Analysis&& && TheBasics&& - The University …sdb/PHYS871/PHYS871-Image...PHYS871(Clinical(Imaging(Applicaons(/(Image(Analysis(—(The(Basics( 1 Image&Analysis&& && TheBasics&&!

Documents