Lecture 1: image display and representation

Transcription

1 Learning Objectives: General concepts of visual perception and continuous and discrete images Review concepts of sampling, convolution, spatial resolution, contrast resolution, and dynamic range through examples 1. Assignment Activate your CAE account. CAE accounts URL: Link: activating your CAE account I. Imaging Science (in this class) A. Blend of: i. Imaging physics 1. Image acquisition and reconstruction a. e.g. CT projection and back projection 2. Factors governing image quality a. Point response function (blurring) => Deterministic b. Signal-to-noise ratio => Stochastic ii. Digital image processing 1. Image display and interpretation a. Window/level; detection of lesions i. Blend of deterministic and stochastic factors 2. Measurement and modeling a. Derived quantitative parameters => depend on image quality factors i. Must be validated => hopefully related to disease diagnosis/prognosis or progression/staging II. Continuous vs. Discrete A. A continuous system behaves similarly at all resolutions i. Continuous structure retained at different scales ii. Analog signals and systems are continuous in both time and amplitude B. In practice we observe and interpret images using tools that approximate continuous systems i. Film and silver halide: AgCl crystals embedded in an emulsion layer mounted on a chemically stable film base (Fig. 1): (Castleman, Digital Image Processing )

2 Light photon energy photodecomposition to silver ions. The image is developed by using solvents to remove the emulsion and remaining silver halide. ii. Retina of the eye: Figure 3a (Wandell, Foundations of Vision) Figure 3b Rods are specialized cells in the retina intensity sensitive. Cones are specialized cells distributed more sparsely color sensitive. Cones are further classified by the color spectral sensitivity (Fig. 3a) into S, L, and M types (Fig 3b). Flicker-Fusion Threshold physiological refresh rate. Image display or frame rates that exceed this threshold cannot be perceived. In most people this is ~16 Hz for the Fovea (for peripheral vision, the threshold is much higher). Most image display rates television, computer monitors, movies display at 30 Hz. iii. Television and Computer Monitors 1. Cathode ray tube (CRT): CRT Display National television standards committee (NTSC): 1. 2 fields/frame (solid and dotted at left) a. Interlaced vs. Progressive scanning fields/s 3. ~500 lines/frame 4. ~67 us/line 5. Transmission bandwidth is 4.5 MHz Review Concept: What is the available matrix along each line (i.e. the matrix resolution of the display)? 4.5 MHz 67 us/line = ~300 pixels /line 150 cycles/line

3 Figure 4 (Wandell, Foundations of Vision) Red, green and blue phosphors coating the inside of the CRT yield color display (Fig. 4). The transfer function for the net power spectral density (PSD) is given by: er Total PSD = [M1 M2 M3] e ; For each pixel t g PSD = e r m 1 +e g m 2 +e b m 3. eb M1 = column vector of power spectral density for red phosphor M2 = for green phosphor M3 = for blue phosphor Review Concept: Recall that PSD is the power per unit frequency and is also the FT of the autocorrelation function. Is this superposition of 1D transfer functions a convolution process? Yes, it can be characterized in this way. It is a linear superposition of the convolution of the beam location with the auto-correlation functions of each phosphor. Is it a continuous or discrete convolution? R r (t) Scaled pixel color and intensity. T[ ]=k gauss r (m) kr r (t); It is an analog transfer function because the PSD s are continuous functions and so are their autocorrelation functions. Therefore it is best represented as a continuous convolution. We assume here that the electron beam intensities are represented by constants independent of spectral frequency, but this is not necessarily true in general.

4 Note that the CRT is calibrated so that the brightness, used to characterize the visual perception of intensity, has a linear dependence on the pixel value in the color look up table used to determine the electron beam intensities. How are these electron beam intensities encoded in the display? Digital look up table. Consider an 8 bit monochrome or gray scale digital image (Fig 5a) and a 2 bit binary image (Fig 5b): Figure 5a Figure 5b For the 8 bit monochrome image, a single 8 bit value determines the intensity of the electron beam. For the RGB image, an 8 bit integer determines the intensity for each electron beam directed at the red, green, and blue phosphors. Review Concept: Dynamic range is a characteristic of a system defined by the range between the smallest and largest possible values. The dynamic range for the 8 bit gray scale image and the RGB image is 1 to 256. Maximum intensity = [ ] to [ ] in binary representation = 2 8 = 256 gray levels in decimal representation. In truth there is a practical difference between dynamic range and bit depth (i.e. 8 bits in the example above) if only part of the range is used. For example, a binary image is just 0 s and 1 s and thus would have a dynamic range of 2 levels even if the bit depth of the binary image is 8. This difference has ramifications for the concepts of image compression and quantization noise. If the information is an image is using only a fraction of the bit-depth, we can represent that information without loss using a variety of image compression (or for video COmpression/DECompression (CODEC)) algorithms. If the opposite is true, that is say an analog signal has inadequate gain to take advantage of the full dynamic range or bit-depth of the image, the signal can suffer from quantization noise. Imagine we tried to encode the gray scale

5 image in (Fig 5a) with only 2 bits? Then we would get a severe loss of information, essentially the binary image shown in (Fig 5b). Now consider a 24bit RGB image (Fig 6a; 8 bits per color channel) and an indexed color image (Fig. 6b): Figure 6a: 24bit RGB. Size ~1 MB. Figure 6b: Indexed Image (256 levels). Size 330 KB Review Concept: Contrast resolution defines the smallest scale of intensity change that can be depicted normalized by the dynamic range. For the 8 bit gray scale image (without noise) this is 1/256. The equivalent concept for the color RGB image is color resolution. Note that 1/( ) = 1/16.8 million color levels. Thus, RGB color images have exquisite color resolution. Another color image format is an indexed image where, for example, a color look up table with a finite bit-depth (e.g. 8 bit for Figure 6b) is used to define the (e.g. 256 levels for Figure 6b) color levels in a color image. An indexed color image doesn t require any more bits to encode than a monochrome image but the color resolution is restricted to the bit depth or only 256 color levels.