Computational Biology, Part 21 Biological Imaging I G. Steven Vanni Robert F. Murphy Copyright ...

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Computational Biology, Part 21 Biological Imaging I G. Steven Vanni G. Steven Vanni Robert F. Murphy Robert F. Murphy Copyright Copyright 1998, 2000, 1998, 2000, 2001. 2001. All rights reserved. All rights reserved.

Transcript of Computational Biology, Part 21 Biological Imaging I G. Steven Vanni Robert F. Murphy Copyright ...

Computational Biology, Part 21Biological Imaging I

Computational Biology, Part 21Biological Imaging I

G. Steven Vanni G. Steven Vanni

Robert F. MurphyRobert F. Murphy

Copyright Copyright 1998, 2000, 2001. 1998, 2000, 2001.

All rights reserved.All rights reserved.

Biological imagingBiological imaging Significant advances in the fields of optics and Significant advances in the fields of optics and

electronics in the past two decades have greatly electronics in the past two decades have greatly increased the utility of imaging for addressing increased the utility of imaging for addressing biological questions.biological questions.

These advances permit These advances permit more diverse types of information to be extracted from more diverse types of information to be extracted from

biological specimens biological specimens with greater accuracy with greater accuracy and under more demanding conditions.and under more demanding conditions.

On the following two slides are images On the following two slides are images demonstrating the capabilities of biological demonstrating the capabilities of biological imaging.imaging.

Imaging by Robin DeBiasoImaging by Robin DeBiaso

Timelapse movie of dividing cellTimelapse movie of dividing cell

QuickTime™ and aAnimation decompressor

are needed to see this picture.

Image acquistion and analysis can produce data to test a hypothesisImage acquistion and analysis can produce data to test a hypothesis This experiment supports the hypothesis that the This experiment supports the hypothesis that the

motor protein, myosin II, (high concentration motor protein, myosin II, (high concentration shown in shown in redred) plays a role in separating daughter ) plays a role in separating daughter cells following cell division.cells following cell division.

Imaging by Robin DeBiasoImaging by Robin DeBiaso

Biological specimens present unique Biological specimens present unique challenges and advantageschallenges and advantagesBiological specimens present unique Biological specimens present unique challenges and advantageschallenges and advantages ChallengesChallenges

Controlled environmental conditions are Controlled environmental conditions are required to preserve processes and signals required to preserve processes and signals within a biological specimen.within a biological specimen.

It can be difficult to gain physical access to the It can be difficult to gain physical access to the desired region of a specimen.desired region of a specimen.

AdvantagesAdvantages Biological specimens present unique Biological specimens present unique

opportunities for the use of chemical and opportunities for the use of chemical and molecular biological probes to detect signals.molecular biological probes to detect signals.

Controlled environmental conditionsControlled environmental conditionsControlled environmental conditionsControlled environmental conditions To image living specimens, stringent To image living specimens, stringent

environmental conditions must be maintained not environmental conditions must be maintained not only to keep the specimens alive but also to allow only to keep the specimens alive but also to allow reproducible behavior. Such conditions inlcude:reproducible behavior. Such conditions inlcude: temperaturetemperature partial pressure of specific atmospheric gasespartial pressure of specific atmospheric gases bathing fluid chemistrybathing fluid chemistry

Specimens may be chemicallySpecimens may be chemically fixedfixed to preserve to preserve them for long periods, but then living processes them for long periods, but then living processes can not be observed.can not be observed.

Physical and optical accessibilityPhysical and optical accessibilityPhysical and optical accessibilityPhysical and optical accessibility High magnification (40 to 200X) is often High magnification (40 to 200X) is often

desirable, and this sets limits on how deeply into desirable, and this sets limits on how deeply into the specimen images may be acquired.the specimen images may be acquired.

Typical limits range from 1 mm to 0.1 mm.Typical limits range from 1 mm to 0.1 mm. Given such limits, specimens must be prepared in Given such limits, specimens must be prepared in

ways which allow the optics of the microscope to ways which allow the optics of the microscope to closely approach the area of interest within the closely approach the area of interest within the specimen.specimen.

Additionally, some specimens absorb or scatter the Additionally, some specimens absorb or scatter the signal being detected.signal being detected.

Imaging relies on generating a detectable signal Imaging relies on generating a detectable signal which can be used as a measure of a property of which can be used as a measure of a property of interest in the specimen. interest in the specimen.

This property of interest is the initial signal, but it This property of interest is the initial signal, but it must be must be transducedtransduced or changed through several or changed through several forms before it becomes detectable.forms before it becomes detectable.

Chemical and molecular biological probes Chemical and molecular biological probes may be targeted within a specimenmay be targeted within a specimenChemical and molecular biological probes Chemical and molecular biological probes may be targeted within a specimenmay be targeted within a specimen

For example: A protein may be modified so that For example: A protein may be modified so that when it enters a cell and bumps into another when it enters a cell and bumps into another protein involved in a specific activity, it protein involved in a specific activity, it fluoresces. The original activity was probably not fluoresces. The original activity was probably not detectable, but this newly generated fluorescence detectable, but this newly generated fluorescence signal is detectable.signal is detectable.

Front end of imaging system and detector

SpecimenSpecimenSpecimen may be difficult to see Specimen may be difficult to see except where labeled by probe.except where labeled by probe.

Chemical and molecular biological probes Chemical and molecular biological probes may be targeted within a specimenmay be targeted within a specimenChemical and molecular biological probes Chemical and molecular biological probes may be targeted within a specimenmay be targeted within a specimen

Image Formation and AcquisitionImage Formation and Acquisition Having an understanding of the specimen, the next Having an understanding of the specimen, the next

step is the formation and acquisition of a step is the formation and acquisition of a digital digital imageimage

A two dimensional image plane consists of a A two dimensional image plane consists of a rectangular grid of points, or rectangular grid of points, or pixelspixels

GridSpecimen

Pixel

A digital image plane is acquired by recording a A digital image plane is acquired by recording a digital value proportional to the intensity of light digital value proportional to the intensity of light (or other form of energy) impinging on each (or other form of energy) impinging on each pixelpixel of a of a detectordetector

This intensity usually corresponds to the amount This intensity usually corresponds to the amount of light emitted by or reflected from a of light emitted by or reflected from a corresponding point on a specimencorresponding point on a specimen

0 0 0 2 1 0 0

0 0 0 1 0 0 00 3 7 8 3 0 00 6 8 8 8 2 00 2 8 8 8 4 00 0 4 8 8 3 0

Projection of specimenonto dectector grid

ImageSpecimen

Image Formation and AcquisitionImage Formation and Acquisition

““PixelPixel” ” is used interchangeably to mean:is used interchangeably to mean:““PixelPixel” ” is used interchangeably to mean:is used interchangeably to mean:

One of multiple regions on a detector, each One of multiple regions on a detector, each corresponding to the smallest area from which a corresponding to the smallest area from which a signal can be distinguishedsignal can be distinguished

The numerical value associated with each such The numerical value associated with each such region in a digital image region in a digital image

A region on A region on display devicedisplay device, such as a monitor or , such as a monitor or printerprinter

0 0 0 2 1 0 0

0 0 0 1 0 0 00 3 7 8 3 0 00 6 8 8 8 2 00 2 8 8 8 4 00 0 4 8 8 3 0

Dectector grid Pixel values Display device

7-8

4-6

1-3

0

Pixel

Display of pixel valuesDisplay of pixel values A pixel value is just a number in the data set A pixel value is just a number in the data set

representing a digital image.representing a digital image. Pixel values may be displayed in different ways, Pixel values may be displayed in different ways,

determined by a determined by a look up table (LUT)look up table (LUT)..

0 0 0 2 1 0 0

0 0 0 1 0 0 00 3 7 8 3 0 00 6 8 8 8 2 00 2 8 8 8 4 00 0 4 8 8 3 0

Pixel values Hot to cold

7-8

4-6

1-3

0

Arbitrary

7-8

4-6

1-3

0 Binary

1-8

0

LUT

LUT

LUT

Image FormationImage Formation

Biological images may be acquired via a Biological images may be acquired via a variety of imaging variety of imaging modesmodes or or modalitiesmodalities

Each mode is a combination of an Each mode is a combination of an image image formation system formation system and a and a detectordetector

Image formation systemImage formation system

Sample Image formation system Detector

Optical signal transductionOptical signal transductionOptical signal transductionOptical signal transduction The image formation system further transduces the The image formation system further transduces the

signal emanating from the specimen using optical signal emanating from the specimen using optical and electronic elements.and electronic elements.

For example:For example:Membranes separating cellular Membranes separating cellular

compartments interact with light to change the compartments interact with light to change the light in ways not detectable by eye. Thus, an light in ways not detectable by eye. Thus, an invisible signal describing cellular organization is invisible signal describing cellular organization is hidden in the light. Special optical elements and hidden in the light. Special optical elements and electronics transduce this signal to create intensity electronics transduce this signal to create intensity variation in the light which is detectable by eye.variation in the light which is detectable by eye.

Any image is only a partial recordingAny image is only a partial recording It is important to consider what is or is not being It is important to consider what is or is not being

recorded.recorded. Quality science relies on a careful understanding of Quality science relies on a careful understanding of

the data from which conclusions are drawn.the data from which conclusions are drawn. Any image, digital or not, is an incomplete Any image, digital or not, is an incomplete

recording of a real world specimenrecording of a real world specimen It is incomplete because it records only one channel It is incomplete because it records only one channel

of the available information as determined byof the available information as determined by specimen preparationspecimen preparation selection of imaging system componentsselection of imaging system components detector typedetector type

Any image is a partial recordingAny image is a partial recording Examples of different channels include:Examples of different channels include:

visible light modified by cellular morphologyvisible light modified by cellular morphology visible light modified by the proximity to which a cell visible light modified by the proximity to which a cell

adheres to an underlying substratumadheres to an underlying substratum fluorescence emanating from an activated proteinfluorescence emanating from an activated protein a second wavelength of fluorescence from a different a second wavelength of fluorescence from a different

protein or from a chemical mechanism related to pHprotein or from a chemical mechanism related to pH

And each channel will produce measurements And each channel will produce measurements which more or less accurately address the questions which more or less accurately address the questions being consideredbeing considered

Detector and image typesDetector and image types

While the examples so far have dealt with lightWhile the examples so far have dealt with light microscope images, we will now back up for amicroscope images, we will now back up for a few minutes to consider many different typesfew minutes to consider many different types of images before concentrating again on lightof images before concentrating again on light microscopy.microscopy.

Detector and image typesDetector and image typesIn general, images may be classified according to In general, images may be classified according to

what is being detected:what is being detected: (Visible) light transmission, scattering or emission(Visible) light transmission, scattering or emission

single wavelength, 3 color, or full spectrumsingle wavelength, 3 color, or full spectrum

Electron transmission or scatteringElectron transmission or scattering X-ray transmissionX-ray transmission Radioactive particle emissionRadioactive particle emission Magnetic field perturbationMagnetic field perturbation Physical displacement from “atomic force”Physical displacement from “atomic force”

Comparing types of imagingComparing types of imagingMethod Resolution

(nanometer)Living

specimen?Light 200 or better YesElectron 10 NoMedicalX-ray

1000 orbetter

Yes

X-rayDiffraction

0.1 No

Autoradiography 10 NoFunctionalMRI/NMR

5000 Yes

StructuralNMR

1 No

AFM 1 No

Light microscopyLight microscopyKey concepts are filtration & detection fromKey concepts are filtration & detection from

small specimens (1 cm to 1 um)small specimens (1 cm to 1 um) Optical elements Optical elements filterfilter complex light waves complex light waves

from specimen to generate and detect only the from specimen to generate and detect only the signal of interest, for example:signal of interest, for example:

rhodamine emission at 560 nmrhodamine emission at 560 nm• to locate probes applied to specimento locate probes applied to specimen

phase shifted wavesphase shifted waves• to locate membrane boundaries within specimento locate membrane boundaries within specimen

waves scattered from a specified anglewaves scattered from a specified angle• to determine surface topologyto determine surface topology

LightLight

Light is energy which travels through spaceLight is energy which travels through space It is made of travelling particles or wavesIt is made of travelling particles or waves

This is of interest in two ways:This is of interest in two ways: (1) in transmitted light microscopy(1) in transmitted light microscopy (2) in fluorescence (emitted) light microscopy(2) in fluorescence (emitted) light microscopy

Light has properties which are modified as Light has properties which are modified as it passes through a specimen.it passes through a specimen.

In transmitted light microscopy, light enters In transmitted light microscopy, light enters the specimen, is modified by the specimen the specimen, is modified by the specimen and then passes out and may be detected.and then passes out and may be detected.

Thus if we know how it has been modified, Thus if we know how it has been modified, we can infer something about the specimen.we can infer something about the specimen.

LightLight

Properties of lightProperties of light Wavelength (inverse of frequency)Wavelength (inverse of frequency) Direction of travelDirection of travel PhasePhase

Constructive and destructive interferenceConstructive and destructive interference PolarizationPolarization IntensityIntensity

Ultimate signal sourceUltimate signal source Selected filtration will cause intensity to vary Selected filtration will cause intensity to vary

depending on any of above propertiesdepending on any of above properties

LightLight

In both transmitted and fluorescence light In both transmitted and fluorescence light microscopy, light exits different regions of microscopy, light exits different regions of the specimen.the specimen.

Because of the small wavelengths of light Because of the small wavelengths of light (< 1 um ), it is possible to resolve fine detail (< 1 um ), it is possible to resolve fine detail in a living specimen.in a living specimen.

Light microscopyLight microscopy

The term “Filter” is used very generally.The term “Filter” is used very generally. Typically “filter” means to pass only certain Typically “filter” means to pass only certain

wavelengthswavelengths Thus allowing us to distinguish rhodamine, Thus allowing us to distinguish rhodamine,

fluorescein and white light signals fluorescein and white light signals (examples)(examples)

But more general types of filtering, allow us to But more general types of filtering, allow us to distinguish many changes in the properties of distinguish many changes in the properties of the light passing through a specimenthe light passing through a specimen

Light microscopyLight microscopy To “look at” means to detect at a level To “look at” means to detect at a level

discernible from backgrounddiscernible from background Three primary types of detectorsThree primary types of detectors

human eyehuman eye no digital imageno digital image

CCD or charge coupled deviceCCD or charge coupled device ““work horse” of modern biological imagingwork horse” of modern biological imaging acquires digital image directlyacquires digital image directly

PMT or photomultiplier tubePMT or photomultiplier tube scans to produce digital imagescans to produce digital image

CCD camerasCCD cameras

CCD cameras cost anywhere from $500 to $30,000 CCD cameras cost anywhere from $500 to $30,000 depending on their sensitivity.depending on their sensitivity.

Courtesy of Phometrics, LTD.Courtesy of Phometrics, LTD.

CCD chipsCCD chips

PennyPennyA CCD chip is the actual detector within a CCD A CCD chip is the actual detector within a CCD camera.camera.

Light sources in the objectLight sources in the object Consider a fluorescent specimen made of Consider a fluorescent specimen made of

individual molecules of fluorescent dye.individual molecules of fluorescent dye. Each molecule can emit light.Each molecule can emit light. Each dye molecule may be seen as a vanishingly Each dye molecule may be seen as a vanishingly

small emitter.small emitter. Such an emitter is called a Such an emitter is called a point source.point source. The concept of a point source is useful because a The concept of a point source is useful because a

point is simple to model, and if we know how a point is simple to model, and if we know how a point source is imaged, then we can easily model point source is imaged, then we can easily model a complex specimen as a combination of many a complex specimen as a combination of many points and predict how it will be imaged.points and predict how it will be imaged.

Light sources in the objectLight sources in the object

A specific example might be a microscope A specific example might be a microscope slide containing cells stained with slide containing cells stained with fluorescent dye.fluorescent dye.

In an ideal image, a point source would In an ideal image, a point source would show intensity in only one pixelshow intensity in only one pixel

Idealized Image of Point SourceIdealized Image of Point Source

-3 -2 -1 0 1 2 3-3

-2

-1

0

1

23

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

Intensity

X

Y

In reality, the light from each point in the In reality, the light from each point in the specimen is seen to spread out and affect specimen is seen to spread out and affect many pixels in the image.many pixels in the image.

This “spreading” is an inescapable result of This “spreading” is an inescapable result of the optical properties of the image the optical properties of the image formation system. formation system.

The mathematical description of this The mathematical description of this spreading or blurring process is called a spreading or blurring process is called a point-spread function (PSF)point-spread function (PSF)

Point-spread functionPoint-spread function

Point-spread functionPoint-spread function

The point-spread function (PSF) is The point-spread function (PSF) is determined by the optics of the image determined by the optics of the image formation system, including factors such as formation system, including factors such as the refractive index, diameter and the refractive index, diameter and magnification of its componentsmagnification of its components

The resulting blurred region in the image The resulting blurred region in the image can be approximated by a 2D Gaussian can be approximated by a 2D Gaussian distributiondistribution

Realistic Image of a Point SourceRealistic Image of a Point Source

-3 -2 -1 0 1 2 3-3

-2

-1

0

1

23

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

Intensity

X

Y

This graph shows intensity on the z-axis for a PSF This graph shows intensity on the z-axis for a PSF defined in the X-Y plane.defined in the X-Y plane.

Later we will consider a PSF defined in three Later we will consider a PSF defined in three dimensions. dimensions.

Light sources in the objectLight sources in the object Thus, when a 2D image is acquired, each point in Thus, when a 2D image is acquired, each point in

the specimen will be blurred in all directions and the specimen will be blurred in all directions and will contribute to the recording in many pixels will contribute to the recording in many pixels around that pixel to which it directly correspondsaround that pixel to which it directly corresponds

Introduction to 3D MicroscopyIntroduction to 3D Microscopy The spreading of light from a point source The spreading of light from a point source

actually occurs in three dimensions as will actually occurs in three dimensions as will be shown.be shown.

First, however, it is necessary to understand First, however, it is necessary to understand the three dimensional (3D) nature of the the three dimensional (3D) nature of the object and image as acquired via 3D object and image as acquired via 3D microscopy.microscopy.

When a microscope is focused on When a microscope is focused on a specimen, the detector records a specimen, the detector records an image from a plane. an image from a plane. This is the This is the focal planefocal plane.. Parts of the specimen in the Parts of the specimen in the

focal plane are in the best focal plane are in the best focus.focus.

DetectorDetector

FocalFocalplaneplane

3D Microscopy3D Microscopy

3D data is acquired by combining data from several 3D data is acquired by combining data from several different focal planes into a different focal planes into a stackstack of images. of images.

This is accomplished by changing the distance This is accomplished by changing the distance between the specimen and the microscope’s between the specimen and the microscope’s objective lens objective lens from one image acquisition to the from one image acquisition to the next.next.

ObjectiveObjective

ImageImagestackstack

The next slide shows a real 3D image stack.The next slide shows a real 3D image stack. The specimen is a slice from a fruit fly eye The specimen is a slice from a fruit fly eye

which labeled with a photoreceptor specific which labeled with a photoreceptor specific antibody conjugated to a fluorescent dye.antibody conjugated to a fluorescent dye.

The images were acquired using a The images were acquired using a conventional fluorescence microscope.conventional fluorescence microscope.

The image stack is presented here as a The image stack is presented here as a movie with one acquired image plane per movie with one acquired image plane per movie frame.movie frame.

Real 3D image dataReal 3D image data

Fruit fly photoreceptor cell axonsFruit fly photoreceptor cell axons

Courtesy of Dr. John Pollock

QuickTime™ and aAnimation decompressor

are needed to see this picture.

Now, with a better understanding of what makes Now, with a better understanding of what makes up a 3D image stack, we can better consider how up a 3D image stack, we can better consider how light from a point source spreads out and is light from a point source spreads out and is imaged in three dimensions.imaged in three dimensions.

On the following slide, intensity is shown by On the following slide, intensity is shown by variation in color. variation in color. Warm colors indicate greater intensity.Warm colors indicate greater intensity. All axes indicate real spatial dimensions as All axes indicate real spatial dimensions as

indicated.indicated.

Real 3D image of a point sourceReal 3D image of a point source

Real 3D image of a point sourceReal 3D image of a point source

y z

x x

Courtesy of Image & Graphics Inc.: Courtesy of Image & Graphics Inc.: http://www.imagepro.co.kr/http://www.imagepro.co.kr/

3D Reconstruction3D Reconstructionof Point Spread Function (PSF)of Point Spread Function (PSF)from 0.2 Micron Beadfrom 0.2 Micron Bead

NOTE: Spreading along the Z-axis is more pronounced.NOTE: Spreading along the Z-axis is more pronounced.

Increasing intensityIncreasing intensity

Image FormationImage Formation

Image formation can be described as:Image formation can be described as: the the convolutionconvolution of an array describing the of an array describing the

original specimen or object original specimen or object with a with a functionfunction describing the image formation describing the image formation

system system to yield an acquired image. to yield an acquired image.

Image FormationImage Formation

The mathematical view of convolution The mathematical view of convolution emphasizes that each point in the sample emphasizes that each point in the sample can contribute to each point in the imagecan contribute to each point in the image

There is a mathematical concept which works well to There is a mathematical concept which works well to describe how each point in the specimen or describe how each point in the specimen or objectobject contributes to each point in the image.contributes to each point in the image.

This concept is called a This concept is called a convolutionconvolution and what follows is a and what follows is a graphic description.graphic description.

z’

x’

y’

z

x

y

A few pointsin the object. One example of

a point in the image

The concept of a convolutionThe concept of a convolution

A convolution may be written in somewhat A convolution may be written in somewhat simplified mathematical form as follows:simplified mathematical form as follows:

i(x, y,z) = PSF• o(x',y',z' )dV'∫∫∫

The concept of a convolutionThe concept of a convolution

i(x,y,z) defines the image in its 3D space i(x,y,z) defines the image in its 3D space according to the form of the equation above.according to the form of the equation above.

o(x’,y’,z’) describes the specimen or object.o(x’,y’,z’) describes the specimen or object.

In order to permit a graphic description of In order to permit a graphic description of convolution, the object and the image are convolution, the object and the image are superimposed onto the same graph.superimposed onto the same graph.

The concept of a convolutionThe concept of a convolution

z, z’

x, x’

y, y’

Considering again the PSF, Considering again the PSF, eacheach object point object point would ideally only contribute to one image point, would ideally only contribute to one image point, but actually is detected as being more spread out.but actually is detected as being more spread out.

The concept of a convolutionThe concept of a convolution

z, z’

x, x’

y, y’

z

x

Point Spread FunctionPoint Spread Function(PSF)(PSF)

The concept of a convolutionThe concept of a convolution

By integration, a By integration, a red point red point in in the the image iimage i is defined by the is defined by the sum of the sum of the contributionscontributions from from all all green points green points in the in the object oobject o..

i(x, y, z) = PSF • o(x' , y' , z' )dV'∫∫∫

z, z’

x, x’

y, y’

The concept of a convolutionThe concept of a convolution

By integration, a red point in By integration, a red point in the image i is defined by the the image i is defined by the sum of the contributions from sum of the contributions from all green points in the object o.all green points in the object o.

This This summing of contributions summing of contributions is a is a convolutionconvolution as described as described in the above equation.in the above equation.

i(x, y, z) = PSF • o(x' , y' , z' )dV'∫∫∫

z, z’

x, x’

y, y’

Convolution and the PSFConvolution and the PSF

By integration, a red point in By integration, a red point in the image i is defined by the the image i is defined by the sum of the contributions from sum of the contributions from all green points in the object o.all green points in the object o.

This summing of contributions This summing of contributions is a convolution as described is a convolution as described in the above equation.in the above equation.

i(x, y, z) = PSF(x−x' , y−y' , z−z' ) • o(x' , y' , z' )dV'∫∫∫

z, z’

x, x’

y, y’

Now we consider the Now we consider the parametersparameters of the of the PSFPSF..

Convolution and the PSFConvolution and the PSF

By integration, a red point in By integration, a red point in the image i is defined by the the image i is defined by the sum of the contributions from sum of the contributions from all green points in the object o.all green points in the object o.

This summing of contributions This summing of contributions is a convolution as described is a convolution as described in the above equation.in the above equation.

i(x, y, z) = PSF(x−x' , y−y' , z−z' ) • o(x' , y' , z' )dV'∫∫∫

z, z’

x, x’

y, y’

The The PSFPSF passes less passes less contributioncontribution the further the further separatedseparated the points are. Thus, it is a the points are. Thus, it is a filterfilter..

Convolution and the PSFConvolution and the PSF

By integration, a red point in By integration, a red point in the image i is defined by the the image i is defined by the sum of the contributions from sum of the contributions from all green points in the object o.all green points in the object o.

This summing of contributions This summing of contributions is a convolution as described is a convolution as described in the above equation.in the above equation.

i(x, y, z) = PSF(x−x' , y−y' , z−z' ) • o(x' , y' , z' )dV'∫∫∫

z, z’

x, x’

y, y’

The PSF passes less contribution the further The PSF passes less contribution the further separated the points are. Thus, it is a filter.separated the points are. Thus, it is a filter.

Ideally the Ideally the contributionscontributions would fall off rapidly would fall off rapidly with increasing with increasing separationseparation..

Image FormatsImage Formats There are two general types of image formats.There are two general types of image formats. The format we have been and will continue to The format we have been and will continue to

concentrate on is the concentrate on is the bit map image bit map image composed of composed of pixels filling the image space.pixels filling the image space.

An alternative type of format is the An alternative type of format is the vector image vector image composed of lines or vectors which are defined composed of lines or vectors which are defined only where objects exist in the image space.only where objects exist in the image space.

Bit map imageBit map image Vector imageVector image

Image FormatsImage Formats

An bit map image normally consists of an An bit map image normally consists of an 8-bit or 16-bit value for each pixel.8-bit or 16-bit value for each pixel.

These values are stored as computer files in These values are stored as computer files in various formats.various formats.

Pixel values are normally stored linearly in Pixel values are normally stored linearly in a file with the values for the first row of a file with the values for the first row of pixels followed immediately by the values pixels followed immediately by the values for the second row (etc.).for the second row (etc.).

Image FormatsImage Formats At a minimum, an image format contains:At a minimum, an image format contains:

Image size (# of rows and columns)Image size (# of rows and columns) Number of bits per pixelNumber of bits per pixel Order in which bytes within words are storedOrder in which bytes within words are stored Number of bytes to skip at the beginning of the Number of bytes to skip at the beginning of the

image (the image (the offsetoffset)) The beginning of image files often has a text The beginning of image files often has a text headerheader

that can be skipped if the above values are known.that can be skipped if the above values are known. This header may contain additional descriptive This header may contain additional descriptive

information about the image such as:information about the image such as:• subject of imagesubject of image

• name of person and/or application creating the imagename of person and/or application creating the image

Common Image File FormatsCommon Image File Formats PICTPICT

Originally for MacDrawOriginally for MacDraw Used primarily by Macintosh programsUsed primarily by Macintosh programs Default format for NIH ImageDefault format for NIH Image Readable by Simpletext, WordReadable by Simpletext, Word

Reference: www.shortcourses.com/chapter07.htmReference: www.shortcourses.com/chapter07.htm

Common Image File FormatsCommon Image File Formats TIFF (Tag Image File Format)TIFF (Tag Image File Format)

Originally for scanners and frame grabbersOriginally for scanners and frame grabbers Used extensively on many platformsUsed extensively on many platforms Can be read/written by NIH ImageCan be read/written by NIH Image

Supports lossless compressionSupports lossless compression

Reference: www.shortcourses.com/chapter07.htmReference: www.shortcourses.com/chapter07.htm

Common Image File FormatsCommon Image File Formats JPEG (“jay-peg” Joint Photographic Experts Group)JPEG (“jay-peg” Joint Photographic Experts Group)

Originally referred to a compression method but now Originally referred to a compression method but now refers to the associated file format with or without refers to the associated file format with or without compressioncompression

Most common World Wide Web file formatMost common World Wide Web file format Supports Supports progressiveprogressive display where an image is first display where an image is first

displayed at low resolution and then at higher displayed at low resolution and then at higher resolution.resolution.

Uses a lossy compression techniqueUses a lossy compression technique Optimized for storing photographs and not as good for Optimized for storing photographs and not as good for

line artline art Supports 24-bit colorSupports 24-bit color

Reference: www.shortcourses.com/chapter07.htmReference: www.shortcourses.com/chapter07.htm

Common Image File FormatsCommon Image File Formats GIF (“jiff” Graphics Interchange Format)GIF (“jiff” Graphics Interchange Format)

Also widely used on the WebAlso widely used on the Web Supports progressive displaySupports progressive display

Mostly used for line art as opposed to Mostly used for line art as opposed to photographsphotographs

Only supports 8-bit colorOnly supports 8-bit color

Reference: www.shortcourses.com/chapter07.htmReference: www.shortcourses.com/chapter07.htm

Image Display and ProcessingImage Display and Processing

Next class, we will consider image display Next class, we will consider image display and processing.and processing.

NIH Image is a free program used for image NIH Image is a free program used for image acquisition, display and processing.acquisition, display and processing.