The Specified Complexity of Retinal Imagery

An optical image is a very organized and specified collection of information governed by the laws of optics. The formation of an image, and its correct interpretation by sighted living creatures, is a unique example of the great complexity in the living world. While many other functional features of living organisms are extremely complex and point to the handiwork of a designing God, an optical image demonstrates a unique mapping process of the eye-brain system that is very useful to the organism. The transfer of light from an object scene to a visual detection system involving the eye and brain conveys an enormous amount of information. Unless that information is correctly organized into a useful image, however, the exchange of information is degraded and of questionable use. In this paper I examine the “connections” necessary for images to be interpreted correctly. I also address the additional complexity required for the dual-image mapping involved in stereovision. Statistics are presented for “simple eyes” consisting of a few pixels to illustrate the daunting task facing random-chance, purposeless, undirected evolution in the origin of any form of a functional eye. It is concluded that evolutionary processes cannot account for the perception of images by living organisms and that only a creator could produce complex visual systems. * David E. Stoltzmann, Optical Engineering of Minnesota, 368 N. Ninth Street, Bayport, MN, USA 55003-1145, [email protected] Accepted for publication: July 22, 2005 truly remarkable, while correlating two separate images, one from each eye, is astoundingly complex. It is worth examining the intricacy of this image-mapping process to determine if random processes could effectively account for the origin of vision. The object-image mapping process seems to be dealt with sparsely in the literature, if at all. DeYoung (2002) touched on this issue to some extent by describing an insect that has multiple eyes, each of which has a separate retina. The mapping process for that insect’s visual system first needs to invert each retinal image and then combine the various images into one contiguous field of view. For other Creation Research Society Quarterly papers dealing with eyes and vision, consult the references of Crofut and Seaman (1990), Hamilton (1985, 1987a, 1987b, 1988, 1991, 1993), and Sherwin and Armitage (2003). Volume 43, June 2006 5 The Human Eye Compared to Images from Digital Cameras The human eye (Hecht, 2002; Walker, 2000; and Smith, 1990) is roughly a 25-millimeter diameter sphere with a retina that contains about 120 million rods (black and white sensitive receptors) and about 6 million cones (color receptors). The region of greatest acuity is the foveola, which contains about 15,000 cones and is centered in the fovea. Today’s digital cameras use a sensor made up of picture elements called “pixels,” each of which detects light intensity, gray scale, and color. One could think of the structures of the retina in terms of pixels that sample the retinal image, as depicted in Figure 1. By “sample” I mean that the image falling on the retina gets divided into a large number of individual picture elements (pixels), all of which must be reassembled by the brain to reestablish a good image. Thus, the foveola could be thought of as a 125 by 125 pixel camera. At first glance this seems to be a very small number of pixels compared to today’s rather ordinary eight megapixel sensor cameras, which have something on the order of 3500 by 2300 pixels in their field of view (FOV). But the total “pixel” count for the human eye is about 126 megapixels, far beyond the 8-megapixel camera example. The cones of the fovea are individually connected to nerve fibers for highresolution imagery. In this paper I will deal mostly with human eyes, but the basic premise will apply also to other sighted species with various forms of vision, such as compound eyes. The Information Content of the Retinal Image A couple of decades ago, images were analog for the most part, residing on a piece of film, or perhaps projected onto a screen. But with the advent of digital cameras, today’s images are assembled by piecing together a large number of discrete pixels, each pixel making up only a small part of the overall image. When a digital image is finally assembled, the electronic and mathematical process involves a basic form of what is called “image processing” (Berry and Burnell, 2000), where each pixel’s contribution to the final image can be changed or enhanced by many techniques. For example, the intensity of the output from a pixel can be increased, decreased, stretched, changed in color, etc. Noise (dust, scratches, low contrast) can be reduced by a number of mathematical techniques when all of the pixels are combined into a final image. But, no matter how the output from an individual pixel is changed, its precise location in the image itself must be preserved if no distortion (mapping error) is to be tolerated. Thus, image processing involves all of the details needed to first break an analog image apart into digitized components (pixels), perhaps then performing some image enhancement to the signal coming from each pixel, and finally reassembling the pixels in the right order to obtain a faithful representation of the object from which the image was made. In the human visual system, all of this image processing happens on a continuing basis over time. As the eye moves, the field of view changes, the lighting conditions vary, and the chemicals of the retina are continuously altered by the absorbed photons themselves. A ballpark number for the image processing power of the human visual system can be estimated by the critical flicker frequency (CFF), which can be thought of as akin to the number of film frames projected per second by a movie theater projector. A standard TV updates the screen with 30 frames per second, for example. A retinal image digitized by ~100 million rods and cones responding at a modest CFF for a human eye of 10 pictures per second, results in a human image processing system that must deal effectively with ~109 responses per second. In this sense, the old adage is certainly true, that “an image is worth more than a Figure 1. An object scene is viewed by a lens and an inverted image is formed in the focal plane of the lens. In a digital camera, a grid of light-sensitive elements (pixels) divides the image into a matrix. In the human retina, the matrix of rods and cones must be correctly connected to the brain in order for the image to be faithfully restored. 6 Creation Research Society Quarterly thousand words,” and an image from each eye (stereovision) even further compounds the image-processing task. The information transfer from an object scene to a sighted creature’s visual processing system is enormous and perhaps difficult to appreciate when simply calculating the previous approximate numbers. Trying to Make Sense of the Image The real problem for the human visual system is to “wire” the image processor such that the visual information transfer is done correctly to yield a good image by which the perceived scene is a faithful representation of the object (Figure 2a). Figure 2b shows a scrambled version of the same pixels from Figure2a, one of 2500 factorial (2500! = 107411) possible rearrangements or permutations of the 50 by 50 pixel array. An important question for an evolutionist to consider is how likely it is that the correct image arrangement of Figure 2a can be produced by “trial and error” processes in a visual system. Examining the First Principles Only, with No Medical Details In this paper I intend to provide examination of some first-order statistical numbers that help to constrain a visual system in terms of its complexity. The eye itself is not unlike a digital camera in that it samples an image through photoreceptors at a given frame rate, and is connected to an image processing system that attempts to make sense of what is being viewed. My use of terms such as “wired” or “pixel connections,” is merely for descriptive purposes as an actual organic vision system does not function in this precise fashion. A rigorous medical model is not being discussed here because it not only exceeds the purposes of this paper, but also because those additional biochemical and organic details only compound the problem of how an image is formed and has its content ultimately transferred to the brain for processing and interpretation. I will try to reduce a very complicated organic miracle to a much simpler engineering model, which will help demonstrate the complexity of sight based solely on correct image mapping. For the purposes of this paper, a rod or cone (pixel) gets connected to the brain (computer), and an image is nothing more than a collection of pixel connections that establish a FOV. Clearly, a living organism’s visual system does not have pixels or direct wires that connect rods/cones to the brain. Many reference resources for the eye (Anonymous, 2005; Frisby, 1980) are filled with elaborate descriptions of the actual neural pathways and components that contribute to making an image; the reader is directed to these sources. The evolutionary problem can be framed simply in terms of a digital camcorder hooked up to a television monitor. The camera (eye) views an object scene and sends the video information to the display (TV) in a specifically coded sequence such that the digitized images are ultimately organized and displayed as a “good image” on the monitor (the brain). This mapping process, from object scene to displayed image, could produce everything from a “perfect” image having complete correlation from object to image (Figure 2a), to a corrupted image such as the “snow” in Figure 2b, as well as anything in between. The details of the “wiring” of the camera to the processor are not important to the discussion here. I am evaluating only the final mapping of the output image compared to the input object scene in order to determine the quality of the image being presented by the complete system. This “mapping” of object scene to perceived image is the unique feature of a living visual system, and it is this mapping that will be the focus of discussion. Some Statistics for Wiring the Eye by Random Chance A 12-pixel Image The number of possible combinations that an eye-brain system has in connecting all the rod/cone receptors is an astounding and virtually unknowable number. I shall start with a single wire Figure 2. 50 by 50 pixel image of a small section of a topographic map. The correctly digitized (scanned) image is shown in (a), while the scrambled pixels shown in (b) represent one redistribution of the 2500! (1.63x107411) possible permutations of the pixels for this image. 50 by 50 pixels is roughly 1/6th of the foveal FOV for human eyes. Volume 43, June 2006 7 connection and then add additional wires for each additional “pixel” on the retina we wish to connect. Figure 3 shows an example of this kind of “eyebrain” wiring, for the case of 12 wires that need to be connected. The correct connection of wires in the example shown is to have A-a, B-b, ...L-l pairings, such that an “image” that falls on the pixels in the capital letters block gets correctly transmitted to the lower-case block in exactly the right order. There are 12 factorial (12! = 479,001,600) permutations available in trying to make the connections, a task not easily accomplished by chance. Figure 4 shows how an “image” of the letter F would appear for the 12 pixels shown in Figure 3. If the connections are not done right, however, what could be expected for the quality of the image in cases of incorrect wiring? There are almost 500 million permutations possible for the 12 pixels to be wired in different ways. To reduce the permutations to a manageable level, I shall start with some even simpler examples having fewer connections. Some Statistics for Simple “Eyes” Having 1-4 Pixels Figure 5 shows the possible connections for pixel counts ranging from one to four. For one pixel there is only one possible connection that can be made, so the accuracy of the image in this case is 100%. A one-pixel image is not very useful but is accurate in its connections. For two pixels, there are two possible permutations: a correct wiring, and a completely incorrect one. The correct wiring has a 50:50 chance of occurrence. For three pixels, there are 3! = 6 possible permutations, in which only one is correct, three have one correct wire in place, and two are completely wrong. In the case of four pixels, there are 4! = 24 possible permutations. Only one case is completely correct for all four wires; there are six cases where half the wires (two) are right, eight in which only one wire is right, and nine in which none are correct. Examples of 1-11 Pixel “Eyes” Figure 6 shows the results of cases for pixel counts ranging from 1 to 11. The trend is very clear: once the number of pixels starts to become more than just a few, almost all of the random wiring attempts are incorrect. Ignoring the left-most column of M, the first four columns tabulate the same number of permutations previously discussed. In the other seven columns of Figure 6, it becomes apparent that for larger numbers of pixels, the number of incorrectly connected pixels grows rapidly. At seven pixels and upward, very few correctly-wired pixels are added to the list in comparison to the huge number of additional incorrectly wired cases. In Figure 7, the statistics for the case of 11 pixels have been listed and graphed to illustrate the trend of how the numbers are tracking (see Appendix 1 and 2). Where M is the number of correctly wired pixels, in the case of Figure 3. A 12-wire connection example where the same capital letter to lowercase letter is the correct connection, and all others have some level of error. Figure 4. A letter ‘F’ image on the 12 pixels shown in Figure 3. Figure 5. Wiring connection permutations for 1, 2, 3, and 4-pixel “eyes.” 8 Creation Research Society Quarterly M=1 there are a little less than 37% of the available permutations that have no correctly wired pixels. The number of singly wired correct pixels (M=1) is also about 37%. Adding these two percentages results in about 73.5% of the available permutations that have either one or zero correct connections. The percentage of correctly connected pixels falls rapidly as M gets larger, while the sum of the percentages for the incorrectly wired pixels quickly nears 100%, as shown in Figure 7. The percentage of correctly connected pixels is given by: 36.78794/M! percent, a relationship that can be determined empirically by evaluating the tabulated numbers of Figure 6. As M increases, M! in the denominator increases exponentially resulting in a pixilated FOV wherein very few of the pixels are correctly wired. Without the Lord’s designing hand in creating the coded information for correct image mapping, no random or “trial and error” process could have accounted for the phenomenally accurate imagery that sighted creatures have. 11 1 10 1 0 9 1 0 55 8 1 0 45 330 7 1 0 36 24