Object tracking with subpixel accuracy often needs targets with special shapes, which include random dot patterns, circular objects or targets with irregular contours. Unfortunately, in majority of real applications no such objects are found or cannot be attached to the region of interest and non-optimal objects must be used. Among those, we will analyze here the performance of rectangular objects that may be common in natural or artificial targets. Object tracking has been performed through the two most common methods that appear in the literature: centroid calculation and cross-correlation with peak interpolation. Numerical simulations show that tracking results for such objects are highly dependent of the object orientation with respect to the direction of movement. This is due to the interference of the object borders and the sensor and how is the subpixel information obtained. Best results are obtained for object orientations from 5 to 30 deg with respect to the normal to the displacement directions. Experimental results confirm the simulations and allow us to establish that, although object alignment provides a better image on the sensor with sharper borders, this situation is not desirable for accurate subpixel tracking, with accuracies varying from accuracies of 0.08 px (RMS error) with aligned objects to 0.02px with a misaligned target.
Some materials undergo an hygric expansion when they are soaked. In porous rocks, this effect is enhanced by the pore space that allows the water to reach every part of its volume and to hydrate the most of their swelling parts. This enlargement has negative structural consequences in the vicinity since adjacent elements will support some compressions or displacements. Recently image-based methods have arisen in this field due to their advantages versus traditional methods. Among all image processing methods, digital image correlation (DIC) is one of the most used in all areas. In this work, we propose a new methodology based on DIC for the calculation of the hygric expansion of materials. We use porous sandstone, with dimensions 14x14x30 mm to measure its hygric swelling using an industrial digital camera and a telecentric objective. We took one image every 5 minutes to characterize the whole swelling process. Due the large magnification, the whole 14 mm length of one contour was not in the image and therefore we lost the image scale reference. To solve this, a 1951 USAF test was used to calibrate the imagen. The telecentric objective and a narrow deep of field allowed to have the specimen surface exactly on the same plane that the USAF test was during the calibration. The image was pointed to one corner of the specimen, to obtain information not only of its vertical displacement due to its expansion but also of its horizontal movement. Preliminary results show that the proposed methodology provides reliable information of the hygric swelling using a non-contact methodology, with an accuracy of 1 micron.
A technique for obtaining subpixel resolution when tracking through cross-correlation consists of interpolating the obtained function and then refine the peak location. Although the technique provides accurate location results, the peak is always biased towards the closest integer coordinate. This effect is known as peak-locking error and is a major limit to the experimental accuracy of this calculation technique. This error may be different depending on the algorithm used to fit and interpolate the correlation peak but no systematic analysis was found in the literature. In our study we explore the three most common interpolation methods: thin-plate splines, second-order polynomial fit and Gaussian fit together with the influence of the extent of local interpolation area around the peak. Additionally, we have checked the influence of the image blurring on the results, since it is reported as one effective method to reduce the peak-locking error. Finally, the optimal adjustment found is the Gaussian fit with no blur and a neighborhood around the correlation peak of 11x11 pixels.
The study of the blink can provide a lot of information regarding ocular surface health, cognitive status, psychological health, human neurological disorders, etc. Blinking can be classified as spontaneous, reflex and voluntary. Between the reflex blinks, direct and consensual reflex can be categorized, being direct that from the eye that is being stimulated and by consensual the other one. A system to evaluate of spontaneous and reflex to light blinking is proposed using a led flash and a high-speed camera that records the blinking of each eye. The LED flash only illuminated one eye and alternated arbitrarily. The light intensity diffused by the eye is almost constant when the eyelid is open but changes when the eyelid closes until reaching a maximum peak, and so does the intensity that was registered by the camera. This variation is directly related to the variation of the eyelid position. Several parameters characterizing the blinks have been defined from the fitting of the blink curve to an exponentially modified Gaussian function. Sequences of 60 seconds of 9 subjects blinking were recorded. Results show that there are no significant differences between reflex and spontaneous blinking, however, significant differences between direct and consensual reflex blinking have been found.
We present a purposeful initiative to open new grounds for teaching Geometrical Optics. It is based on the creation of an innovative education networking involving academic staff from three Spanish universities linked together around Optics. Nowadays, students demand online resources such as innovative multimedia tools for complementing the understanding of their studies. Geometrical Optics relies on basics of light phenomena like reflection and refraction and the use of simple optical elements such as mirrors, prisms, lenses, and fibers. The mathematical treatment is simple and the equations are not too complicated. But from our long time experience in teaching to undergraduate students, we realize that important concepts are missed by these students because they do not work ray tracing as they should do. Moreover, Geometrical Optics laboratory is crucial by providing many short Optics experiments and thus stimulating students interest in the study of such a topic. Multimedia applications help teachers to cover those student demands. In that sense, our educational networking shares and develops online materials based on 1) video-tutorials of laboratory experiences and of ray tracing exercises, 2) different online platforms for student self-examinations and 3) computer assisted geometrical optics exercises. That will result in interesting educational synergies and promote student autonomy for learning Optics.
Subpixel methods increase the accuracy and efficiency of image detectors, processing units, and algorithms and provide very cost-effective systems for object tracking. A recently proposed method permits micropixel and submicropixel accuracies providing certain design constraints on the target are met. In this paper, we explore the use of Costas arrays - permutation matrices with ideal auto-ambiguity properties - for the design of such targets.
Retinal image quality is usually analysed through different parameters typical from instrumental optics, i.e, PSF, MTF
and wavefront aberrations. Although these parameters are important, they are hard to translate to visual quality
parameters since human vision exhibits some tolerance to certain aberrations. This is particularly important in postsurgery
eyes, where non-common aberration are induced and their effects on the final image quality is not clear.
Natural images usually show a strong dependency between one point and its neighbourhood. This fact helps to the image
interpretation and should be considered when determining the final image quality. The aim of this work is to propose an
objective index which allows comparing natural images on the retina and, from them, to obtain relevant information abut
the visual quality of a particular subject.
To this end, we propose a individual eye modelling. The morphological data of the subject's eye are considered and the
light propagation through the ocular media is calculated by means of a Fourier-transform-based method. The retinal PSF
so obtained is convolved with the natural scene under consideration and the obtained image is compared with the ideal
one by using the structural similarity index. The technique is applied on 2 eyes with a multifocal corneal profile
(PresbyLasik) and can be used to determine the real extension of the achieved pseudoaccomodation.
We present a new algorithm to process captured images of reflected Placido rings. Up to our knowledge, conventional
topographers transform from Cartesian to polar coordinates and vice-versa, thus extrapolating corneal data and
introducing noise and image artefacts. Moreover, captured data are processed by the device according to proprietary
algorithms and offering a final map of corneal curvature. Corneal topography images consists of concentric rings of
approximately elliptical shape. Our proposal consists of considering the information that provides each separate ring. A
snake-annealing-like method permits identifying the ring even with discontinuities due to eye-lashes and reflections. By
analysing the geometrical parameters of rings (centre, semi-axis and orientation), one can obtain information about small
morphological micro-fluctuations and local astigmatisms. These parameters can be obtained with sub-pixel accuracy so
the method results of high precision. The method can be easily adapted to work on any topographer, so that it can
provide additional information about the cornea at no additional cost.
The behaviour of a construction safety net and its supporting structure was monitored with a high speed camera and
image processing techniques. A 75 kg cylinder was used to simulate a falling human body from a higher location in a
sloped surface of a building under construction. The cylinder rolled down over a ramp until it reaches the net. The
behaviour of the net and its supporting structure was analysed through the movement of the cylinder once it reaches the
net. The impact was captured from a lateral side with a high speed camera working at 512 frames per second. In order to
obtain the cylinder position each frame of the sequence was binarized. Through morphological image processing the
contour of the cylinder was isolated from the background and with a Hough transform the presence of the circle was
detected. With this, forces and accelerations applying on the net and the supporting structure have been described,
together with the trajectory of the cylinder. All the experiment has been done in a real structure in outdoors location.
Difficulties found in the preparation on the experiment and in extracting the final cylinder contour are described and
some recommendations are giving for future implementations.
Analysis of vibrations and displacements is a hot topic in structural engineering. Video cameras can provide good
accuracy at reasonable cost. Proper system configuration and adequate image processing algorithms provide a reliable
method for measuring vibrations and displacements in structures. In this communication we propose using a pocket
camera (Casio) for measuring small vibrations and displacements. Low end cameras can acquire high speed video
sequences at very low resolutions. Nevertheless, many applications do not need precise replication of the scene, but
detecting its relative position. By using targets with known geometrical shapes we are able to mathematically obtain
subpixel information about its position and thus increase the system resolution. The proposal is demonstrated by using
circular and elliptic targets on moving bodies The used method combines image processing and least squares fitting and
the obtained accuracy multiplies by 10 the original resolution. Results form the low-end camera (400 euros) working at
224×168 px are compared with those obtained with a high-end camera (10000 euros) with a spatial resolution of 800×560 px.
Although the low-end camera introduces a lot of noise in the detected trajectory, we obtained that results are comparable.
Thus for particular applications, low-end pocket cameras can be a real alternative to more sophisticated and expensive
Videokeratometers and Scheimpflug cameras permit accurate estimation of corneal surfaces. From height data it is possible to adjust analytical surfaces that will be later used for aberration calculation. Zernike polynomials are often used as adjusting polynomials, but they have shown to be not precise when describing highly irregular surfaces. We propose a combined zonal and modal method that allows an accurate reconstruction of corneal surfaces from height data, diminishing the influence of smooth areas over irregular zones and vice versa. The surface fitting error is decreased in the considered cases, mainly in the central region, which is more important optically. Therefore, the method can be established as an accurate resampling technique.
A sequence of videokeratoscopic images was registered using commercially available instrument E300 at a rate of 50
fps. During the 20 seconds measurement, subject's head was fixed strongly. Acquired images were analyzed for
detecting fixational eye movements and corneal surface deformation. For this purpose two rings were extracted from
each frame and the ellipses were fitted to them, using least square method. The time series of the ellipses geometrical
parameters were considered: minor and major axes length as well as the ellipses center and the orientation. The
frequency spectra of mentioned parameters were obtained by application of the Fast Fourier Transform. The longitudinal
position of the corneal apex was controlled, thanks to the cone side viewer installed inside the videokeratoscope.
The average amplitude of the variation of the ellipse's axes length is around 20μm and of the orientation of the ellipse
around 0,1 rad. In the signals frequency characteristics, appear the peak corresponding to the heart rate. No clear
relationship was found between the variations of the fitted ellipse parameters and the longitudinal position of the corneal
The fixational eye movements were examined using two different methods. One of them consists of calculating the
correlation function between the first and successive frame of the sequence and searching its maximum. The other is
based on tracking the center of the ellipse fitted to particular ring of the videokeratoscopic image. The accuracy of the
second method found to be higher.
Simple methods proposed in this work can extend the application of videokeratoscopic measurements.
The eye is not a centered system. The line of sight connects the fovea with the center of the pupil and is usually tilted in the temporal direction. Thus, off-axis optical aberrations, mainly coma and oblique astigmatism, are introduced at the fovea. Tabernero et al. [J. Opt. Soc. Am. A 24(10), 3274-3283 (2007)] showed that a horizontal tilt of the crystalline lens generates a horizontal coma aberration that is compensated by the oblique light incidence on the eye. Here we suggest that corneal astigmatism may also play a role in compensation of oblique aberrations, and we propose a simple model to analyze such a possibility. A theoretical Kooijman eye model with a slight (~0.6 D) with-the-rule astigmatism is analyzed. Light rays at different incidence angles to the optical axis are considered, and the corresponding point spread functions (PSFs) at the retina are calculated. A quality criterion is used to determine the incidence angle that provides the narrowest and highest PSF energy peak. We show that the best image is obtained for a tilted incidence angle compatible with mean values of the angle kappa. This suggests that angle kappa, lens tilt, and corneal astigmatism may combine to provide a passive compensation mechanism to minimize aberrations on the fovea.
In this communication, the authors have determined the longitudinal chromatic aberrations in real eyes. The method that has been used combines real data of corneal morphology, central thickness of crystalline lens and biometric measures of axial length together with numerical calculation of the propagation process. The curvature of the crystalline lens has been adjusted to different curvature models and refractive index distributions. The wavelength dependence of all ocular media has been modelled through the Cauchy formula. Propagation through anterior and posterior chambers has been accomplished through numerical calculation of diffraction integral instead of classical ray-tracing approach. This imposes serous restrictions on the number of samples that are needed for a full propagation process. If we are only interested in amplitude calculations the method consists of evaluating propagation from cornea to crystalline lens with a spectrum propagation method. Propagation from the lens to the best image plane is accomplished by a direct calculation of Fresnel integral. With this model, we have obtained the refraction chromatic difference in diopters for several eyes. Results are compared with real measures of the chromatic aberration, showing a good agreement with numerical calculations. The capabilities of the technique have been demonstrated by applying the method to the study of the chromatic aberration of a keratoconus.
Obtention of the phase transmittance of the cornea under the paraxial assumption does not provide accurate estimation of the corneal aberrations for wide apertures of the pupil. On the other hand, exact ray tracing will require a huge amount of calculations and does not provide uniform sampling of the energy distribution at the output. We propose to use a simple approximation that takes into account non-paraxial effects. This approximation allow obtention of a well sampled output plane at no additional computational cost.
The cornea may be considered as the major contributor to the ocular aberrations. For normal corneas working with parallel beams, the best image plane correspond to the image distribution in the focal plane. Working with highly deformed corneas, the focal plane is not well defined and thus further analysis has to be done. Different light distribution propagated from the cornea will be analyzed here. In order to evaluate these patterns we propose three different simple parameters that will provide useful information at low computational cost. The method can be applied in optometry clinics. Since it would be convenient to optimize the image formation process by a correcting lens before performing any surgical process over the cornea.
A new method for the calculation of the Fresnel diffraction patterns through a fast fractional Fourier transform (FRT) is presented. The FRT can be efficiently calculated for any order by using the fast-Fourier transform algorithm. The resemblances between the FRT and the Fresnel integrals allow the use of that algorithm to calculate efficiently the Fresnel integral of any object, with independence of its shape.
The expanding usage of optical communication via optical fibers and the situation of drastic increasing of the data required to be transmitted, urge the exploration of novel systems allowing to transmit high amount of spatial information by fiber with smaller spatial resolution. In this paper, optical encoding and decoding system is suggested for transmitting 1D or 2D images via a single mode fiber. The super resolving system is based on wavelength multiplexing of the input spatial information that is achieved with diffractive optical elements. Preliminary experimental results demonstrate the capabilities of the suggested method for the 1D case.