CHAPTER 13. Image Processing and AnalysisCHAPTER 13. Image Processing and AnalysisMicroscopists have traditionally used photography to document microscopic observations and enhance contrast. However, photography is limited to single frames and it takes a relatively long time to see your results. By the time you print the photograph, the specimen will probably be dead and unavailable for taking better pictures. Video and digital processing allows instant feedback, and it can be done with a series of images that make up a time course in real time. Measurements on the image, or image analysis, can be done on video images with high temporal and spatial resolution. Thus the coupling of signal processing with video and digital microscopy allows us to improve the temporal and spatial resolution as well as extract a tremendous amount of quantitative data from the image(s).1. Analog Image ProcessingAn analog video camera transforms an optical signal into an electrical signal. The intensity information of a two dimensional image is stored in the amplitude of the electrical signal and the positional information is stored, along with the sync signals, in the length of the electrical signal.Once we have a video output signal in the form of an electrical signal we can use all the technologyavailable in electrical amplifiers to enhance the image. Analog image enhancement allows us to manipulate the gray levels in the image in order to maximize the contrast necessary to resolve a given detail. Contrast is defined as the difference in brightness or color of two nearby points in an image.For simplicity, consider that the object is a stepped gray wedge where the contrast between each step is equal. Imagine the video output signal that arises from this object. We can amplify the signal with a linear amplifier where the output signal is proportional to the input signal. Imagine that the amplifier has a gain of 1.0. Then the contrast of the video image is the same as the contrastof the optical image focused on the video camera. When the gain is set to a level greater than 1, we can increase the contrast of the low contrast details which include the very small details that lose contrast due to the process of video scanning. When we set the gain to a level less than 1, we eliminate the low contrast details and increase the visibility of the high contrast details which include the low spatial frequency regions. The following equation relates the output signal (in volts)to the input signal (in volts):output signal = m(input signal)where m is the gain of the linear amplifier.326We can also amplify the video output signal with a nonlinear amplifier. The degree of nonlinearity is characterized by the gamma of the amplifier. A linear amplifier has a gamma of 1.0. With a nonlinear amplifier the output signal is related to the input signal according to the following function:output signal = (input signal) where  represents the gamma of the amplifier.When gamma is greater than 1, the above function is exponentially increasing and the contrast between the brighter regions of the image is expanded. When gamma is less than 1, the above function increases rapidly at low input voltages and then begins to level off thus the contrast in the darker regions of the image is enhanced. 327We can decrease the brightness of the image by adding negative voltages to the video signal. In doing this we redefine the threshold voltage of a video signal, so that any signal below the thresholdvoltage will appear black. Normally signal voltages of 0 volts produce a black image. By adding a negative voltage of 0.5 volts to the video signal, we can make all the input values less than 0.5 volts, black. By changing the baseline, we can increase the contrast between two points.output signal = input signal – bwhere b is the offset voltage.By varying the gain, the gamma and the offset, we can selectively increase the contrast of any given region of interest in the image. The output signal will be related to the input signal by the following equation:328output signal = m(input signal) - bWe can reverse the polarity of the video signal and cause the bright regions to become dark and the dark regions to become bright. The polarity control causes the input signal to be multiplied by –1 and then -0.7 V is subtracted from the product. In this way, bright regions with an input signal of +0.7 volts give an output signal of 0 volts, and dark regions with an input voltage of 0 volts give anoutput signal of 0.7 volts. The polarity control allows us to see different details in a manner analogous to how a negative high phase contrast objective brings out different details than a positive low phase contrast objective.329It is also possible to pass the signal through amplifiers with more than one stage so that details of almost any contrast can be brought out in a background of a given contrast. Thenoutput signal = m2[m1(input signal)1 - b1]2 - b2330By now you must be thinking that we can create anything we want in a video image so that we can easily "cheat" and there may be no relationship between the image and the object. However, remember back to the time we discussed aberrations. In an optical image produced by a single lens we get chromatic and spherical aberrations. We then keep adding lens elements to correct the aberrations produced in the original imaging lens of the objective. Moreover, the objective lens can be considered to be an analog computer that does inverse Fourier transforms, although not perfectly. Therefore, when we use a single lens to make an image we have a distortion of reality. We can correct the distortions either optically or electronically. Both types of corrections are not "cheating" as long as we take Plato’s advice and understand the relationship between the object andthe image. This is the reality of distortion. You should be more like the line than the squiggle in TheDot and the Line (Juster, 1963). You may have the experience of using an equalizer with your stereo so that you can match the characteristics of the recorded sounds with the acoustic properties of your room or car.We can also use an analog image processor to enhance the contrast of transparent objects by creating a pseudo-relief image. We do this by differentiating the video input signal.331Differentiating the video input signal will brighten one side and darken the other side of the image of an object with a gradient in optical path