Digital Images

A basic image capture system – review

The fundamental properties of the digital photographic image.

 Monochrome Images

Color Images

 Sampling

Quantisation

Following picture gives an idea how 3D-optical measurement methods can be divided into active and

passive methods.

Image captured by a camera or other kind of imaging instrument

A basic image capture system contains a lens and a detector. Film detects far more visual information than is possible with a digital system.

With digital photography, the detector is a solid state image sensor called a charge coupled device...CCD for short.

On an area array CCD, a matrix of hundreds of thousands of microscopic photocells creates pixels by sensing the light intensity of small portions of the film image.

To capture images in color, red, green and blue filters are placed over the photocells.

Film scanners often use three linear array image sensors covered with red, green and blue filters.

Each linear image sensor, containing thousands of photocells, is moved across the film to capture the image one-line-at-a-time.

Digital imaging products like Photo CD, enable us to capture and store film images electronically, then process them on the computer, much like we process text and drawings. A film image is represented electronically by continuous analog wave forms. A digital image is represented by digital values derived from sampling the analog image.

Analog values are continuous. Digital values are discrete electronic pulses that have been translated into strings of zeros and ones the only digits in a binary numbering system.

What is an Image?

Value – f(x,y,z, ,t)

(0,0)

The pattern is defined is a coordinate system whose origin is conventionally defined as the upper-left corner of the image .

We can describe the pattern by a function f(x,y).

 Color Images

Color images can be represented by an intensity function C(x,y,) which depends on the wavelength of the reflected light.

(so, for fixed , C(x,y,) represents a monochrome image)

0 < C(x,y,) <=Cmax = constant

The brightness response of a human observer to an image will therefore be dVyxCyxf ))(),,,(),(

where V() is the response factor of the human eye at frequency . V() is called the relative luminous efficiency function of the visual system . In the human eye, three types of sensors have been identified and associated mainly with red, green and blue lights. We, therefore, have three brightness response functions.

dVyxCyxf RR ))(),,,(),( dVyxCyxf GG ))(),,,(),( dVyxCyxf BB ))(),,,(),(

Question :

What is the difference between luminance and brightness?

Answer:

Luminance of an object is its absolute intensity.

Brightness is its perceived luminance, which depends on the luminance of the surrounding.

Question

Why are luminance and brightness different?

Answer:

Because our perception is sensitive to luminance contrast rather than absolute luminance.

Example :car headlights bother front car driver much more at might ( when it’s dark ) than in the day time .

Luminance of headlights is the same, it’s only the perceived luminance

( brighness) that differs from night ( dark) to daytime (light)

Monochrome Image

For monochrome image , the value of the function at any pair of coordinates x, and y is the intensity of the light detected at that point. For fixed value of (x,y), f(x,y) is proportional to the grey level of the image at that point .

(black=)0=< f(x,y) < =fmax = constant

Why ?

“> =” because light intensity is a real positive quantity .

“<= fmax” since in all practical imaging systems, the physical system imposes some restrictions on the maximum intensity level of an image.

Digital Image Definitions A digital image f[m,n] described in a 2D discrete space is derived from an analog image f(x,y) in a 2D continuous space through a sampling process that is frequently referred to as digitization.

The 2D continuous image f(x,y) is divided into N rows and M columns. The intersection of a row and a column is termed a pixel. The value assigned to the integer coordinates [m,n] with {m=0,1,2,...,M-1} and {n=0,1,2,...,N-1} is

f[m,n]. The value assigned to every pixel is the average brightness in the pixel rounded to the nearest integer value. The process of representing the amplitude of the 2D signal at a given coordinate as an integer value with L different gray levels is usually referred to as amplitude quantization or simply quantization.

 

Sampling and Quantisation

For standard video signals, both processes are usually carried out by a single piece of hardware, known as an analogue to digital converter ( ADC)

 Sampling

Sampling is the process of measuring the value of the image function f(x,y) at discrete intervals in space. Each sample corresponds to a small square area of the image, known as a pixel. A digital image is a two-dimensional array of these pixels. Pixels are indexed by x and y coordinates, with x and y taking integer values.

The spatial resolution of an image is the physical size of a pixel in that image.

Image Quality

The quality of a raster image is determined at capture by two factors: spatial resolution and brightness resolution.

The pixel size is determined by the rate at which the scanner samples the image. A long sampling interval produces an image low in spatial resolution. A shorter interval produces higher spatial resolution.

Dense sampling will produce a high resolution image in which there are many pixels.

Coarse sampling will produce a low resolution image in which there are few pixels.

 

CCD with few photocells, samples at low resolution.

At extremely low resolution, pixels can be seen with the unaided eye. This is called pixelization.

CCD with more photocells, samples at higher spatial resolution.

In this kind of image individual pixels can no longer be seen.

Nyquist criterion

The sampling that we choose for an image should satisfy the Nyquist criterion. The sampling frequency should be at least double the highest spatial frequency found in the image. fs =2fmax

If we sample an image coarsely, such that the Nyquist criterion is not met, then the image may suffer from the effects of aliasing.

Consequently, the sampling process is normally preceded by anti-aliasing .This is a filtering operation designed to remove frequencies that exceed half the sampling rate achieved by the analogue to digital converter (ADC).

Another way to state this is that the sampling interval should be no larger than one-half the cycle intervals ( called the Nyquist sampling intervals)

2cycle

s

xx

Sampling pattern Sampling pattern does not have to be rectangular pattern. The rectangular patterns are uniform, with the result that one part of an image is as important as any other part

A Log-polar sampling pattern has some interesting and useful properties .

The pixels of this array are sectors with a fixed angular size and a radial size that increases logarithmically with increasing distance from the center.

This gives high resolution near the center of the array and low resolution in the periphery.

Attentive visual strategy !

 Quantisation

The process of quatisation involves replacing a continuously varying f(x,y) with a discrete set of quantisation levels. Conventionally, a set of n quatisation levels comprises the integers 0,1,….n-1. O and n-1 are usually diplaed or printed as black and white, respectively, with intermediate levels rendered in various shades of grey. The collective term for all the grey levels, ranging from blak to white , is a greyscale.

For convenient , the number of grey levels, n , is usually an integral power of two.

n=2b

where b is the number of bits used for quantisation.

Quantisation

The brightness or color value of each pixel is defined by one bit or by a group of bits. The more bits used, the higher the brightness resolution.

                            

An 8-bit gray-scale image displays 256 levels of brightness.

Each pixel is black, white or one of 254 shades of gray.

A 1-bit image can have only 2 values, black or white.

1-bit images simulate grays by grouping black and white pixels. This process is called dithering or halftoning.

A higher resolution 12-bit medical image provides more than 4000 brightness levels.

In a 24-bit image, each pixel is described by three 8-bit sets of numbers representing the brightness values for red, green and blue.

High resolution 24-bit images display 16.7 million colors.

Each pixel in a 24-bit image has one of 256 brightness values for red, green and blue.

How many bits do we need to store an image?

For number of bits b, we need to store an image of size N x N with 2m different grey levels is :

b=N x N x m

So for a typical 512 x 512 image with 256 grey levels (m=8) we need 2,097,152 bits. That is why we often try to reduce m and N without significant loss in the quality of the picture.

 What is meant by image resolution?

The resolution of an image expresses how much detail we can see in it and clearly depends on both N and m.

Keeping m constant and decreasing N results in the checkerboard effect.

Keeping N constant and reducing m results in false contouring.

 

Common Values Parameter Symbol Typical values

Rows N 256,512,525,625,1024,1035

Columns M 256,512,768,1024,1320

Gray Levels L 2,64,256,1024,4096,16384

Table 1: Common values of digital image parameters

Quite frequently we see cases of M=N=2K where {K = 8,9,10}. This can be motivated by digital circuitry or by the use of certain algorithms such as the (fast) Fourier transform (see Section 3.3).

The number of distinct gray levels is usually a power of 2, that is, L=2B where B is the number of bits in the binary representation of the brightness levels. When B>1 we speak of a gray-level image; when B=1 we speak of a binary image. In a binary image there are just two gray levels which can be referred to, for example, as "black" and "white" or "0" and "1".

Review The quality of a scanned image is determined by pixel size, or spatial resolution; and by pixel depth, or brightness resolution.

This relates to the two basic steps in the digital capture process: In step one, sampling determines pixel size and brightness value. In step two, quantization determines pixel depth.

When a scanner samples the photographic image, it divides the image into pixels. The size of pixels depends upon the number of photocells.

In addition to spatial and brightness resolution, other factors influencing the quality of a scanned image are dynamic range, noise and artifacts.

Dynamic range indicates how well the scanner can differentiate between light levels. Film excels at distinguishing small changes in light level, while digital capture systems have limited brightness range.

To accurately render highlights and shadows, scanner exposure must be controlled precisely. With low dynamic range, shadows lose detail and saturated areas are washed out .

Noise is another factor. The information captured by a sensor contains both image data and noise. Noise appears as small, random variations in brightness or color.

Sensor sites with low signal-to-noise ratio, introduce noise.

Sensor sites with high signal-to-noise ratio represent the image accurately.

Artifacts, another factor in digital image capture, are distortions, such as the moiré pattern that occurs when an image is undersampled.

The sampling rate should be based on the spatial frequency of the image. Spatial frequency is the rate at which the brightness of the image changes.

For example, the teeth in this photo show slow changes in brightness levels, or a low spatial frequency. The hair shows rapid changes in brightness levels, or a high spatial frequency.

To eliminate moiré in this photo, the sampling rate should be twice as high as the spatial frequency of the hair. In other words, pixels should be small enough so that each detail is represented on two pixels.

Conclusions sampling - measuring f(x,y) at discrete intervals in space

- resolution - area of input that one pixel represents

- dense sampling => high resolution image

- sparse sampling => low resolution image

- must consider the spatial frequencies in the input

- rapid changes in f(x,y) => high frequency

- gradual changes in f(x,y) => low frequency

- aliasing - artifacts in the image due to inadequate sampling rate

- Nyquist criterion - sampling frequency should be twice the highest spatial frequency in the input

- we can filter the input before sampling to ensure the Nyquist criterion is met

- gaussian spot intensity distribution of display devices can introduce aliasing

- sampling pattern does not have to be rectilinear - e.g. log-polar sampling

Conclusions

quantization - mapping f(x,y) to a discrete set of values

- number of gray levels is 2b where b is the number of bits used to represent a gray level

- 0 = black, ..., 2b-1 = white

- grayscale - the entire range of values

- edge detection processing in the human eye allows us to discern more gray levels