Handbook of Machine Vision - Rilegato

Rilegato

ISBN 10: 3527405844 ISBN 13: 9783527405848

Casa editrice: Vch Verlagsgesellschaft Mbh, 2006

Riassunto

With the demands of quality management and process control in an industrial environment machine vision is becoming an important issue. This handbook of machine vision is written by experts from leading companies in this field. It goes through all aspects of image acquisition and image processing. From the viewpoint of the industrial application the authors also elucidate in topics like illumination or camera calibration. Attention is paid to all hardware aspects, starting from lenses and camera systems to camera-computer interfaces. Besides the detailed hardware descriptions the necessary software is discussed with equal profoundness. This includes sections on digital image basics as well as image analysis and image processing. Finally the user is introduced to general aspects of industrial applications of machine vision, such as case studies and strategies for the conception of complete machine vision systems. With this handbook the reader will be enabled not only to understand up to date systems for machine vision but will also be qualified for the planning and evaluation of such technology.

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Informazioni sull?autore

Alexander Hornberg is Professor for Physics and Photonics at the University of Applied Sciences Esslingen, Germany. He holds a degree in physics and a doctorate in mathematics from the University of Karlsruhe. He started his professional career as development and software engineer for a major industry manufacturer (DUNLOP) in 1989. In 1992 he returned to higher education at the University of Applied Sciences Ulm. Since 1997 he has been working in the field of machine vision at the Technical University of Applied Sciences Esslingen.

Dalla quarta di copertina

With the demands made of quality management and process control within an industrial environment, machine vision is becoming an increasingly important issue. Written by experts from leading companies operating in the field, this handbook covers all aspects of image acquisition and image processing.
The authors approach the subject in terms of industrial applications, elucidating such topics as illumination and camera calibration. Throughout, they concentrate on all hardware aspects, ranging from lenses and camera
systems to camera-computer interfaces, as well as discussing the necessary software in equal detail.

Equipped with this handbook, readers will not only be able to understand the latest systems for machine vision but will also be qualified to plan and evaluate such technology.

Estratto. © Ristampato con autorizzazione. Tutti i diritti riservati.

Handbook of Machine Vision

John Wiley & Sons

Copyright © 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
All right reserved.
ISBN: 978-3-527-40584-8

Chapter One

Processing of Information in the Human Visual System

Prof. Dr. F. Schaeffel, University of Tbingen

1.1 Preface

To gather as much necessary information as possible of the visual world, and neglect as much unnecessary information as possible, the visual system has undergone an impressive optimization in the course of evolution which is fascinating, in each detail that is examined. A few aspects will be described in this chapter. Similar limitations may exist in machine vision, and comparisons to the solutions developed in the visual system in the course of 5 billion years of evolution might provide some insights.

1.2 Design and Structure of the Eye

As in any camera, the first step in vision is the projection of the visual scene on an array of photodetectors. In the vertebrate camera eye, this is achieved by the cornea and lens in the eye (Fig. 1.1) which transmit the light in the visible part of the spectrum, 400 nm to 780 nm, by 60 to 70%. Another 20-30% are lost due to scattering in the ocular media. Only about 10% are finally absorbed by the photoreceptor pigment. Due to the content of proteins, both cornea and lens absorb in the ultraviolet and due to the water content, the transmission is blocked in the far infrared. The cornea consists of a thick central layer, the stroma, which is sandwiched between two semipermeable membranes (total thickness about 0.5mm). It is composed of collagen fibrils with mucopolysaccharides filling the space between the fibrils. Water content is tightly regulated to 75-80%, and clouding occurs if it changes beyond these limits. The crystalline lens is built up from proteins, called crystallines, which periphery have high solubility, but in the center they are largely insoluble. The vertebrate lens is characterized by its continuous growth throughout life, with the older cells residing in the central core, the nucleus. With age, the lens becomes increasingly rigid and immobile and the ability to change its shape and focal length to accommodate for close viewing distances disappears - a disturbing experience for people around 45 who now need reading glasses (presbyopia). Accommodation is an active neuromuscular deformation of the crystalline lens that changes focal length from about 53mm to about 32mm in young adults.

Both media have higher refractive index as the water-like solutions in which they are embedded (tear film - on the corneal surface, aqueous - the liquid in the anterior chamber between the cornea and the lens, and vitreous humor - the gelly-like material filling the vitreous chamber between the lens and retina, Fig. 1.1). Due to their almost spherically curved surfaces, the anterior cornea and both surfaces of the lens have positive refractive power with an optical focal length of together about 22.6mm. This matches almost perfectly (with a tolerance about 1/10 of a Millimeter) the distance from the first principal plane (Fig. 1.1, H) to the photoreceptor layer in the retina. Accordingly, the projected image from a distant object is in focus when accommodation is relaxed. This optimal optical condition is called emmetropia but, in about 30% of the industrialized population, the eye has grown too long so that the image is in front of the retina even with accommodation completely relaxed (myopia).

The projected image is first analyzed by the retina in the back of the eye. For developmental reasons, the retina in all vertebrate eyes is inverted. This means that the photoreceptor cells, located at the backside of the retina, are pointing away from the incoming light. Therefore, the light has to pass through the retina (about a fifth of a millimeter thick) before it can be detected. To reduce scatter, the retina is highly translucent, and the nerve fibers that cross on the vitreal side, from where the light comes in, to the optic nerve head are not surrounded by myelin, a fat-containing sheet that normally insulates spiking axons (see below). Scattering in retinal tissue still seems to be a problem since, in the region of highest spatial resolution, the fovea, the cells are pushed to the side. Accordingly, the fovea in the vertebrate eye can be recognized as a pit. However, many vertebrates don not have a fovea; they have then lower visual acuity but their acuity can remain similar over large regions of the visual field, which is then usually either combined with high motion sensitivity (i.e., rabbit) or high light sensitivity at dusk (crepuscular mammals). It is striking that the retina in all vertebrates has a similar three-layered structure (Fig. 1.9), with similar thickness. This makes it likely that the functional constraints were similar. The function of the retina will be described below.

The optical axis of the eye is not perfectly defined because the cornea and lens are not perfectly rotationally symmetrical and also are not centered on one axis. Nevertheless, even though one could imagine that the image quality is best close to the optical axis, it turns out that the human fovea is not centered in the globe (Fig. 1.2). In fact, it is displaced to the temporal retina by the angle [kappa], ranging in different subjects from 0 to about 11 but highly correlated in both eyes. Apparently, a few degree away from the optical axis, the optical image quality is still good enough to not limit visual acuity in the fovea.

1.3 Optical Aberrations and Consequences for Visual Performance

One could imagine that the optical quality of the cornea and lens must limit the visual acuity since the biological material is mechanically not as stable and the surfaces are much more variable than in technical glass lenses. However, this is not true. At day light pupil sizes < 2.5mm are the optics of the human eye close to the diffraction limit (further improvement is physically not possible due to the wave properties of light). An eye is said to be diffraction limited when the ratio of the area under its MTF (Fig. 1.3) and the area under the diffraction-limited MTF (Strehl ratio) is higher than 0.8 (Rayleigh criterion). With a 2mm pupil, diffraction cuts off all spatial frequencies higher than 62 cyc/ - a limit that is very close to the maximal behavioral resolution achieved by human subjects. By the way, diffraction-limited optics is achieved only in some birds and primates, although it has been recently claimed that also the alert cat is diffraction-limited. A number of tricks are used to reduce the aberrations that are inherent in spherical surfaces: the corneal surface is, in fact, clearly aspheric, flattening out to the periphery, and the vertebrate lens is always a gradient index structure, with the refractive index continuously increasing from the periphery to the center. Therefore, peripheral rays are bent less than central rays, which compensates for the steeper angles that rays encounter if they hit a spherical surface in the periphery. The gradient index of the lens reduces its spherical aberration from more than 12 diopters (for an assumed homogenous lens) to less than 1 diopter (gradient index lens). Furthermore, the optical aberrations seem to be under tight control (although it remains uncertain whether this control is visual). The remaining aberrations of cornea and lens tend to cancel each other and this is true, at least, for astigmatism , horizontal coma and spherical aberration. However, aberrations have also advantages: they increase the depth of field by 0.3 D, apparently without reducing visual acuity; there is no strong correlation between the amount of aberrations of subjects and their letter acuity. They also reduce the required precision of accommodation , in particular, during reading. It is questionable whether optical correction of higher order aberrations by refractive surgery or individually designed spectacle lenses would further improve acuity for high contrast letters in young subjects, creating an eagle's eye. It is however clear that an extended MTF can enhance the contrast sensitivity at high spatial frequencies. Correcting aberrations might also be useful in older subjects, since it is known that the monochromatic aberrations increase by a factor of 2 with age. Aberrations may also be useful for other reasons; they could provide directionality cues for accommodation and, perhaps, for emmetropization.

In a healthy emmetropic young eye, the optical modulation transfer function (Fig. 1.3) appears to be adapted to the sampling interval of the photoreceptors.

The contrast modulation reaches zero at spatial frequencies of around 60 cyc/, and the foveal photoreceptor sampling interval is in the range of 2 m. Since one degree in the visual field is mapped on a 0.29mm linear distance on the retina, the highest detectable spatial frequency could be about 290/4 m or about 70 cyc/. The modulation transfer function (MTF) shows that the contrast of these high spatial frequencies in the retinal image is approaching zero (Fig. 1.3). With defocus, the MTF drops rapidly. Interestingly, it does not stop at zero modulation transfer, but rather continues to oscillate (although with low amplitude) around the abscissa. This gives rise to the so-called spurious resolution ; defocused gratings can still be detected beyond the cutoff spatial frequency, although in part with reversed contrast (Fig. 1.4).

The sampling interval of the photoreceptors increases rapidly over the first few degrees away from the fovea and visual acuity declines (Fig. 1.5), both because rods are added to the lattice which increases the distances between individual cones and because their cone diameters increase. In addition, many cones converge on one ganglion cell. Furthermore, only the foveal cones have private lines to a single ganglion cell (Fig. 1.9).

Because the optical quality does not decline as fast in the periphery as the spatial resolution of the neural network, the retinal image is undersampled. If the receptor mosaic would be regular, like in the fovea, stripes that are narrower than the resolution limit would cause spatial illusions (moir patterns , Fig. 1.6). Since the receptor mosaic is not so regular in the peripheral retina, this causes just spatial noise. Moir patterns are, however, visible in the fovea if a grating is imaged which is beyond the resolution limit. This can be done by presenting two laser beams in the pupil, which show interference.

Moire patterns are explained from the Shannon's sampling theorem which states that regularly spaced samples can only be resolved when the sampling rate is equal to or higher than twice the highest spatial frequency - to resolve the samples, between each receptor that is stimulated there must be one that is not stimulated. The highest spatial frequency that can be resolved by the photoreceptor mosaic (Nyquist limit) is half the sampling frequency. In the fovea, the highest possible spatial sampling was achieved. Higher photoreceptor densities are not possible for the following reason: because the inner segments of the photoreceptors have higher refractive indices than their environment, they act as light guides. But if they become very thin, they show properties of waveguides. When their diameter approaches the wavelength of the light, energy starts to leak out, causing increased optical crosstalk to neighboring photoreceptors. As it is, about 5% of the energy is lost which seems acceptable. But if the thickness (and the sampling interval) is further reduced to 1 m, already 50% is lost.

Since the photoreceptor sampling interval cannot be decreased, the only way to increase visual acuity is then to enlarge the globe and, accordingly, the PND and the retinal image. This solution was adopted by the eagle eye, with an axial length of 36 mm, and the highest spatial acuity in the animal kingdom (grating acuity 135 cyc/).

1.4 Chromatic Aberration

In addition to the monochromatic aberrations (those aberrations that persist in monochromatic light) there is also chromatic aberration which results from dispersion of the optical media, i.e., the fact that the refractive index is wavelength dependent. In technical optical systems, lenses with different refractive indices are combined in such a way that the focal length does not vary much across the visible spectrum. In natural eyes, no attempt was made to optically balance chromatic aberration. Neural image processing makes it possible that we are not aware of the chromatic image degradation under normal viewing conditions, and there are morphological adaptations in the retina in addition. Inspection of the chromatic aberration function in the human eye (Fig. 1.7A) shows that a large dioptric change occurs in the blue end of the spectrum(about 1 D from 570 to 450 nm)while the change is smaller in the red end (about 0.5 D from 570 to 680 nm). We have three cone photopigments, absorbing either at long wavelengths (L cones, peak absorption typically at 565 nm), at middle wavelengths (M cones, typically at 535 nm), or at short wavelengths (S cones, typically at 440 nm). The dioptric difference between L and M cones is small (about 0.2 D) but the dioptric differences to the S cones are significant (> 1 D). It is, therefore, impossible to see sharply with all three cone types at the same time (Fig. 1.7C). A white point of light is, therefore, imaged in the fovea as a circle with a diameter of up to 100 cones diameters, with a 6mm pupil. Perhaps as a consequence, the S cone system was removed from the high acuity region of the central 0.5 of the fovea (the foveola); one cannot focus them anyway and they would only occupy space that is better used to pack the M and L cones more densely, to achieve best sampling. High acuity tasks are then performed only with the combined L and M cones. The blue information is continuously filled in because small eye movements make it possible to stimulate the parafoveal S cones. Therefore, this scotoma is normally not visible, similar to the blind spot, where the optic nerve leaves the eye - surprising, given that the blind spot has about five times the diameter of the fovea. Nevertheless, a small blue spot viewed on yellow background from a distance appears black, and a blue field of about 440 nm that is sinusoidally modulated at a few Hertz makes the blue scotoma in the fovea visible as a star-shaped black pattern. Also in the periphery, the S cones sample more coarsely than the L and M cones and reach a spatial resolution of maximally 5-6 cyc/ in the parafoveal region at about 2 away from the fovea. The dispersion of the ocular media does not only produce different focal planes for each wavelength (longitudinal chromatic aberration ), but also different image magnifications (transverse chromatic aberration ). Accordingly, a point on an object's surface is imaged in the different focal planes along a line only in the achromatic axis of the eye (which can be psychophysically determined; Fig. 1.7B). Even a few degrees away from the achromatic axis, the blue light emerging from an object point will be focused more closer to achromatic axis than the red. In particular, since the fovea is usually neither in the optical nor in the achromatic axis (see above), the images for red and blue are also laterally displaced with respect to each other. With a difference in image magnification of 3%, a [kappa] of 3.5, and a linear image magnification of 290m per deg, the linear displacement would be 3.5 290 0.03 m or about 30m, which is about the distance from one S cone to the next. Human subjects are not aware of this difference in magnification and the rescaling of the blue versus the red image by neural processing seems to occur without effort.

(Continues...)

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Dettagli dell'edizione

• Editore: Vch Verlagsgesellschaft Mbh
• Data di pubblicazione: 2006
• Lingua: Inglese
• ISBN 10: 3527405844
• ISBN 13: 9783527405848
• Rilegatura: Copertina rigida
• Numero edizione: 1
• Numero di pagine: 798
• Redattore: Hornberg Alexander
• Contatto del produttore: non disponibile
• Persona responsabile: non disponibile