1 imaging seeing invisible things orecap equations for wave travel oexamine a range of digital...

1 IMAGING Seeing invisible things oRecap equations for wave travel oExamine a range of digital images oExplain what is meant by image resolution

Pixel Pixels are the tiny building blocks from which a digital image is built.

Resolution Smallest discernible feature or smallest detectable difference. Resolution = image dimension/number of pixels

Current is kept constant so a record on the up and down motion is a record of the surface. Scanning tunnelling microscope.

Ultrasound imaging Explain principles of the technique Calculate key parameters such as horizontal and vertical resolution, minimum pulse duration, maximum pulse rate

Principles of Ultrasound Key things to know about: How is it generated? Why the need for short pulses? Why the need for high frequency? What information do we gain from: The pulse-echo times The reflected intensity

Ultrasound pulse sequence showing two pulses being sent out by the probe. The listening time is much longer than the duration of a pulse.

4-D ultrasound is similar, except that the images are constructed rapidly to give almost real-time information. 3-D ultrasound sends sound pulses in at different angles. A computer algorithm constructs a highly detailed image from the reflections.

Ultrasound is also used to detect cracks in objects such as aeroplane components and rails. How does it work? Why is it preferable to using x rays?

There are only 10 types of people in the world. ..those who understand binary numbers ..and those who dont. Can you explain this rather lame joke?

Information in digital images Explain how information is stored in digital images Use binary arithmetic to work out the values stored for each pixel Compute the amount of information in an image in bits and bytes

Each Pixel is represented by a number

00000000000 00000000000 00000000000 00000000000 00044400000 002102553520000 002121303420000 00223246720000 00044400000 00000000000 00000000000 Each pixel is assigned a byte of info = 2 8 = 256 alternatives = 256 levels of grey

DecimalBinary 00 11 2 311 4 5101 Binary All 0s and 1s

DecimalBinary 00 11 210 311 4100 5101 Binary All 0s and 1s

Bits and Bytes One Bit of information = 0 or 1 (two possibilities) Eight Bits of information = 256 possibilities. (8 bits = 1 byte) HOW? There are 256 alternative arrangements of 8 bits. (each bit is either 1 or 0)

There is 0/1 alternative for each position One 0/1 choice = One bit In 8 bit data there are eight 0/1 alternatives Eight bits = eight 0/1 choices = One byte There are 2 8 = 256 alternatives or 0-255 Number of alternatives = 2 I Where I is the number of bits. e.g. 16 bit computer uses 2 16 = 65536

Each pixel is assigned a byte of info 00000001 = A 00000010 = B. 10010010 = &

Bits and Bytes N = number of alternatives l = number of bits N= 2 8 = 256 In general: N = 2 l log 2 N= l

Amount of data in image = no. of pixels x bits per pixel

Questions: 120S Logarithms and Powers The response of the eye (and ear) to light (and sound) intensity is logarithmic not linear. A logarithm is just another name for the power (or exponent or index lots of different names for the same idea!) that the constant ratio is raised to. 1.We can choose convenient ratios to consider: take a constant ratio of x 10. Write out a series of intensity values starting with 1 with this constant ratio property. 2. If you haven't done so, repeat question 1, writing out the series using scientific notation and powers of ten. 3. What is happening to the power of ten (its index), or logarithm to base 10? The base is just the initial constant ratio we chose to work with; any number will do. (Base 2 gives binary, base 10 gives log10, base e (e = 2.718...) gives the natural log e (written ln).

Questions: 120S Logarithms and Powers 4. Using your calculator, record log10 of the series 1, 10, 100, 1000, 10000 etc. What do you notice? 5. Sketch a graph of the series of intensities plotted on the y-axis, against the powers of ten or log10 plotted on the x-axis. This graph is logarithmic in shape (we say it grows exponentially). Now plot the graph on a log scale (non-linear), i.e. log10 (series) on y-axis against the powers of ten on the x-axis. What has the log scale done to the exponentially growing data? You will use log scales for representing quantities that vary enormously, and for testing for logarithmic or exponential variations.

Questions: 120S Logarithms and Powers 6. If you have followed these steps so far, you have in fact learnt to master the scale for the measurement of sound intensity ratios, the bel scale (after Alexander Graham Bell) where: number of bels = log10 (I 2 / I 1 ) or more commonly the sound level in decibels (1 dB = 0.1 B) is given by number of decibels = 10 log10 (I 2 / I 1 ) A sound that is on the threshold of audible intensity is 10 -12 W m -2 (like hearing a pin drop). This is taken as the baseline intensity I 1. A painful sound (like a jet taking off) has an intensity of about 10 W m -2. What is the sound level of the jet in bels and dB?

Image processing Process a range of digital images to extract the maximum amount of useful information Explain how the processing algorithms work

Image processing algorithms Smoothing Noise removal Edge detection Change brightness Change contrast

Image processing algorithms Smoothing Noise removal Edge detection Change brightness Change contrast For each of the image processing algorithms: 1.Describe its effect on an image. 2.Explain how the algorithm operates on the data. 3.Describe a situation where it might be useful. 4.Discuss any drawbacks of the algorithm. The Mars Face

111333 111333 111333 111333 111333 111333 Smoothing out sharp edges Replace each pixel by the mean of it and its eight neighbours

112233 112233 112233 112233 112233 112233 Resulting in....

Image before sharpening

Image after sharpening

333333 336333 333333 333133 343333 333333 Removing Noise Replace each pixel by the median of its value and those of its neighbours

333333 333333 333333 333333 333333 333333 Resulting in...

Finding Edges Laplace Rule -1x +4x-1x Subtract the N, S, E and W neighbours from 4x the value of each pixel.

Finding Edges Laplace Rule Result if there is an edge. -1x +4x-1x Subtract the N, S, E and W neighbours from 4x the value of each pixel.

Finding edges with the Laplace Rule If there is no edge but a gradient then the Laplace rule simply smooths the data

Improving Contrast How might we make image brighter? How might we improve the contrast? 444 424 444 Decimal numbers of image

Improving Contrast 444 424 444 888 848 888 888 868 888 +4 x2 Adding fixed positive value makes image brighter Multiplying by fixed value increases contrast and makes brighter.

A histogram analysis showing how many pixels there are in an image that have a particular number of pixel values is very useful in explaining how the contrast and brightness algorithms work.

Starter: Match up the image processing technique with the algorithm that describes how it is applied to the data A Smoothing B Noise removal C Edge detection D Change brightness E Change contrast 1.Subtract N,S,E,W neighbours from 4 times value of pixel. 2.Multiply all pixel values by a constant factor. 3.Add a fixed value to all pixel values. 4.Replace each pixel value by the median of its value and those of its neighbours 5.Replace each pixel value by the mean of its value and those of its neighbours

Making images using lenses Recap relationship between light rays and waves Investigate properties of converging lenses Solve problems using 1/v = 1/u+1/f

The King of all Imagers: The Eye. 100 million rods 5-10 photons are required to trigger a response.

Nerve Fibres

Refractive index Refractive index(n) = Speed of light in vacuum Speed of light in material The refractive index of glass is 1.5 Q1. What happens to the speed, frequency and wavelength of light waves when they pass from air into glass? Hint: use the equation above, the equation speed = frequency x wavelength and if you are stuck, see page 21 of the textbook Q2. The larger the refractive index of a material, the more light will bend when it enters the material at an angle. Use this fact to explain why the makers of spectacle lenses prefer to use glass with a higher refractive index.

Long Focal LengthShort Focal Length

Fish eye lens

How lenses shape light. v v focus

A lens modifies the curvature of the wave by 1/f v v f focus

v v f f is the focal length 1 / f = the power of the lens measured in dioptre e.g. If focal length f = 50mm Power = 1 / 50 x10 -3 = 20 dioptre f

v v If the object is close to the lens

If we have a object near to the lens NEGATIVE POSITIVE

1 = 1 + 1 v u f The lens changes the curvature of the incoming wave by 1/f

Question 1: What is the distance of the object from the lens? v = 0.8m f = 0.31m

Question 2: What is the focal length? v = 0.65m u = 0.45m

Question 3: What is the distance of the image from the lens? f = 0.21m u = 0.3m

m = image height = image distance object height object distance Magnification by a lens m = v/u

What is the focal length of the lens? u (m) v (m) -0.220.99 -0.280.52 -0.330.40 -0.400.33 -0.490.29 -0.550.27

You could just substitute individual values of u and v into the equation 1/v = 1/u + 1/f, but there is a better way: Plot 1/v against 1/u, and then note where the line cuts the y- axis. This corresponds to 1/u = 0, in other words the source is very far from the lens. The line cuts the y-axis where 1/v = 1/f, so f can be determined.

1/v = 1/u + 1/f When 1/u = 0 (object very far from lens), 1/v = 1/f

Try these: Questions on Page 25. Homework Summary Questions on page 27

1 imaging seeing invisible things orecap equations for wave travel oexamine a range of digital...

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