FROM PIXEL TO TERRAIN MODEL: EXPERIMENTAL INVESTIGATIONS

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1 FROM PIXEL TO TERRAIN MODEL: EXPERIMENTAL INVESTIGATIONS Yu.F.Knizhnikov, V.I.Kravtsova Laboratory of Aerospace methods, Faculty of Geography, Moscow State University, Moscow, Russia Commission VII KEYWORDS: Digital, Imagery, Stereoscopic, Observations, Measurements, Accuracy, Pixel, Experimental ABSTRACT: Stereoscopic terrain models, constructed from photographs, have been in use for more than 100 years. They formed the basis for compilation of contour lines in topographic maps. This is likely to continue in the era of digital technologies. So the investigation of metric features of a digital stereoscopic model is valuable for the modern photogrammetry. We should also note that the widely used automatic stereoscopic measurements will be always rationally integrated with visual human-assisted measurements. Investigations in this area are conducted at the Laboratory of Aerospace Methods of Lomonosov Moscow State University in two directions: study of the influence of discretization on the formation of stereoscopic model; and study of influence of different factors on the accuracy of stereoscopic model measurements. The first direction implies research of discrete stereomodel formation at micro-level, namely the investigation of the influence of images pixel structure on geometric properties of the stereomodel. The main method used here is the construction of graphic stereogramms for different positions of an image in relation to the pixel matrix and their stereoscopic observations for control. Experiments have shown that pixel discretization of images may lead to horizontal and vertical distortion of stereomodel s points for up to 1-2 pixels. The second direction includes experimental investigations of digital stereomodel metric properties by computer measurements of a real pair of stereo pictures (photo-theodolite images), digitized with different pixel sizes. The influence of various factors on the accuracy of visual computer measurements of a digital stereomodel has been experimentally investigated. The factors are the pixel size of initial digital image, screen resolution, additional zooming, representation quality of the stereomodel, the frequency of onscreen image regeneration, and six methods of computer stereomodel observations. It was found that investigated factors have little influence on the visual stereo-measurements accuracy. This allows to put forward a psycho-physical hypothesis of stereoscopic measurements, namely that the dependence of measurements accuracy on the physical characteristics of stereomodel is subject to the Weber-Feсhner law. 1. INTRODUCTION Stereoscopic terrain models, constructed from photographs, have been in use for more than 100 years. They formed the basis for compilation of contour lines in topographic maps. This is likely to continue in the era of digital technologies. So the investigation of metric features of a digital stereoscopic model is valuable for the modern photogrammetry. We are also confident that the widely used automatic stereoscopic measurements will be always rationally integrated with visual human-assisted measurements. Investigations in this area are conducted at the Laboratory of Aerospace Methods of Lomonosov Moscow State University in two directions: study of the influence of discretization on the formation of stereoscopic model; and study of influence of different factors on the accuracy of stereoscopic model measurements. 2. METHODS AND MATERIALS The investigations of pixel discretization influence on the geometric properties of stereomodel at micro-level were carried out with the suggested method of graphic formation of stereogrammes and their analysis. Stereogramms are drawn pictures, which simulate discrete images of compact and linear objects, structure lines of relief (terrain), plane elements and simple forms of relief. Peculiarities of discrete (pixel) image depend on the position of the original analog image in relation to the pixel matrix, therefore the changes of image objects due to shifts of the matrix were investigated. Stereoscopic stereomodel observations were used for control. The evaluation of metric properties of a digital stereomodel provides for the investigation of main factors influencing the accuracy of stereoscopic computer measurements. These factors are: the size of pixel of the initial digital image pix c ; the size of pixel of screen pix d, and consequently the zoom-in factor ϑ of the screen image ( ϑ = pix d / pixc ); additional (scaling) zoom factor η = pix id / pixd, where pix id is pixel size of the screen image; representation quality of the stereomodel; frequency of on-screen image regeneration; various methods of computer observations of stereomodel. A real pair of high-quality stereo pictures (photo-theodolite negatives), with resolution R=50 mm -1, was chosen as initial analogue images. They were carefully measured in 24 specially selected points with a precision optical-mechanical Stecometer stereocomparator (C.Zeiss). For formation of digital images the same original negatives were digitized on a photogrammetric Ultrascan-Vexcel scanner with pixel sizes pix c 5, 10, 20, 40 and 80 µm. This allowed creating stereomodels with small-size (less than µm) and big-size pixels. The measurements of these digital stereomodels in the same 24 points with controlled changes of the investigated factors were carried out using a computer KSK stereocomparator produced by the Russian company IBIK. Experimental technique secures the determination of mean squared errors of stereoscopic measurements m v with an estimated accuracy of 15% or better.

2 3. RESULTS OF THE INVESTIGATION OF PIXEL DISCRETIZATION INFLUENCE ON THE STEREOMODEL PROPERTIES 3.1. Compact objects Subpixel objects are the most sensitive to position of their images in relation to the pixel matrix (Figure 1). Stereogrammes in Figure 2 (this and other stereogrammes should be observed stereoscopically) shows the changes in height ratio of three compact objects for different positions of their images in relation to pixel matrix. For this reason the heights of objects in the stereomodel may be distorted for the value of difference of longitudinal parallaxes: p=1pix Linear objects Linear objects, subpixel in width, parallel to the initial plane and oriented along the matrix columns, are represented as lines in the discrete image. But shift of the image position in relation to pixel matrix changes the ratio of line heights (Figure 3). I II Figure 1. Image of a group of subpixel objects (a) and its transformation when shifted in relation to the pixel matrix (b). Initial objects are shown in black, their representation in pixel form - by hatching III Figure 3. I Initial stereogramme of three linear objects with subpixel width. II Discretized stereogramme of the same objects under two various positions of pixel matrix (with shift of 0.5 pix). III The same stereogrammes without pixel grid Linear objects, parallel to the initial plane and oriented at angle to matrix columns, are represented in the discrete stereomodel as a line oriented series of elements, displaced at various heights (Figure 4a), or with various inclinations to the initial plane of stereogramme (Figure 4b, c) in dependence of line width. Figure 2. I Stereogrammes of three compact subpixel objects under two various positions of pixel matrix (with shift of 0.5 pix). II The same stereogrammes without pixel grid The pixel representation of linear objects, inclined to the initial plane and oriented at angle to matrix columns, is the most complex they are represented as intricate line oriented series of elements with various heights and with various inclinations to the initial plane (Figure 5).

3 If the structure line falls near the edge of a pixel column, then the brightness of the resulting pixel line is near to that of nearest slope. As a result such structure line is perceived as dislodged towards opposite slope (Figure 6c,d). Thus, the gorisontal position of a structure line may be distorted by 1 pix, as a result of pixel discretization. Figure 4. Graphic 3-D representation of a discrete stereomodel representation for linear objects of various width and orientation in relation to matrix columns. Objects are parallel to the initial plane. А width <1pix, angle 30 о ; B width 1pix, angle 15 о ; C width >1pix, angle 45 о Structure line inclined to the initial plane (Figure 7a) is represented in the stereomodel as a chain of adjoining elements, with heights gradually changing in accordance with the structure line inclination (Figure 7b). Image shifts of various size in relation to the pixel matrix (for shifts of 0.25 pix, 0.75 pix, Figure 7c and f), can cause breaks in the chain or changes in heights of some elements in relation to initial heights at size corresponding to p=1pix (for shift of 0.50 pix). So heights of certain points of a structure line are distorted, and structure line obtains an uneven profile with peaks and depressions instead of a smooth line (Figure 7 d). Figure 5. Graphic 3-D representation of a linear object, inclined to the initial plane and varying in width: a - <1pix; b - 1pix; c - 2pix I II III IV 3.3. Structure lines of relief The relief is represented in the stereomodel as an aggregate of various inclined planes, lines of their intersection (structure lines) and feature points at location of their joining. Structure lines are represented as boundaries between illuminated and shaded slopes. If a structure line, parallel to initial plane, coincides with the matrix line (the boundary between adjoining pixel columns) during discretisation, then a strongly pronounced ridge is represented in stereomodel (Figure 6a). If such structure line falls in the middle of pixel column, then it is represented as strip 1 pix wide, with intermediate brightness; in the stereomodel such a line represents a narrow plane surface extending along the ridge (Figure 6b). Figure.7. I Stereogramme of a structure line, inclined to the initial plane, and results of its discretisation for various positions in relation to pixel matrix. II Differences of longitudinal parallaxes for points of the line. III Profiles of the structure line in pixel representation. IV 3-D representation of the structure line 3.4. Plane elements Figure 6. Stereogramme of a structure line, parallel to the initial plane and oriented along matrix columns (a) and results of its discretisation for various positions in relation to pixel matrix (b-d) Plane plots with inclination along the basis line were investigated. The basis was determined from the changes of differences in longitudinal parallaxes of consequent points. Inclined plane is represented in stereomodel as a series of parallel strips, which are perpendicular to the basis line and characterized by gradual changes of strip heights. Variable

4 brightness is assigned to consequent strips in left and right images of stereogramme in Figure 8 for better identification. As Figure 8 shows, the shift of image in relation to pixel matrix by over 0.5 pix may cause changes of strips heights, meaning also changes of plane height, which correspond to p=2pix if both images of the stereogramme are shifted and p=1pix if one of stereogramme images is shifted. Counter shift of the images causes the increase of height, but divergent shift causes the decrease of heights. 4. THE ACCURACY OF DIGITAL STEREOMODEL MEASUREMENTS The following results were derived from experiments investigating the accuracy of visual computer measurements of digital stereomodel. Figure 8. Stereogrammes of inclined plane, marked by parallel strips (a) and results of the both images displacement in relation to pixel matrix by 0.5 pix at various directions: counter displacement (b) and displacement in opposite sites (c) 3.5. Elementary forms of relief The described regularities of stereo discretisation for structure lines and plane elements of relief formation allow to determine possible displacements of stereomodel: distortion of slope crossections (Figure 9); disappearance of micro-relief forms; flattening of relief; disappearance of ridges and valleys (banks and narrows); appearance of banks in place of narrows; changes in ratio of peaks heights (Figure 10). Figure 10. Stereogramme of two pyramidal peaks of equal height (а) and results of left image shift by 0.5 pix in relation to pixel matrix during discretisation (only one peak is remaining) (b) 4.1. The accuracy of measurements of digital stereomodels with various pixel size pix c (influence of zoom-in factor ϑ on the accuracy) The results of this experiment (Figure 11) testify to the general rectilinear dependence of stereoscopic measurements accuracy on the digital image pixel size. However the increase of stereoscopic measurements error is observed in the area of small-size pixels; this is caused by the decrease of observed quality of the stereomodel as a result of excessive zooming. Figure 11. Graph of the dependence of stereoobservations mean squared error (in micrometers and pixels) on the pixel size of digital stereomodel pix c Figure 9. Transformation of a slope crossection, marked by a series of parallel strips, formed by subpixel elements. Discretisation turned a linear gradually inclined slope into a concave slope 4.2. The influence of scaling zoom factor η A double increase of the scaling zoom factor for a stereomodel with large-size pixels doubles the accuracy of stereoscopic measurements, but there is almost not influence on the

5 measurement accuracy for stereomodels with small-size pixels (Figures 12, 13). The increase of the scaling zoom factor η leads to appearance of the pixel structure in the stereomodel; it has the strongest influence at boundaries of areas with various brightness, where it forms a specific pixel fringe, and lesser influence in monotonous areas of the image. In general the appropriate reconstruction of stereomodel geometry takes place, which may be named stereogeneralization; its regularities has not yet been investigated. The highest accuracy of stereomeasurements is reached not for the most common pixel size pix d = 0.3 мм, but for a size 1.5 times larger. This allows to decrease considerably the demand to the volume of necessary videoinformation. However, in general the pixel size of screen image has weak influence on to the accuracy of computer stereomeasurements. If the pixel size pix d changes by the factor of 3, this results in change of the mean squared error of stereoscopic observations only by 30% of its value Influence of visual quality of the images on the accuracy of computer stereomeasurements Stereomodels for this experiment were created by degrading the visual quality of initial images with photographic method (contratyping 6 times) and software method (degradation of image with a smoothing circle 60 micron in radius) (Figure 15). In general the visual quality of images has weak influence on the accuracy of visual measurements. The degradation of visual quality of images significally influences the accuracy of measurements only for stereomodels with small-size pixels. Figure 12. Dependence of the accuracy of stereoscopic observations m v of digital stereomodels with various pixel sizes for various screen scaling zoom factor η Figure 13. Influence of scaling zoom factor η on the accuracy of measurements of a model with various pixel size 4.3. The dependence of measurements accuracy on the screen resolution pix d The results of the experiments testify to the fact that stereoscopic measurements have specific demands to screen resolution (Figure 14). Figure 15. The accuracy of computer measurements of various stereomodels: 1 original model, 2 contratype model (R = 7 mm -1 ), 3 fuzzy model (R = 50 mm -1 ) 4.5. Frequency of on-screen image regeneration Even change of the image regeneration frequency by 2 times does not significally influence the accuracy of stereomeasurements both for linear and frame images separation methods; however it leads to discomfort during observations Various methods of computer observations of stereomodel and accuracy of computer stereomeasurements Six methods of computer stereoobservations were investigated: without stereo-spectacles; with prizm stereospectacles; with binoculars; with shutter LCD stereo-spectacles; with anaglyph spectacles. Figure 14. Dependence of stereo observation mean average squared errors ratio m v to mv on screen resolution ( m v i stereoobservation error for pix d = 0.3 mm, m v for pix d = 0.61, 0.49, 0.46, 0.39, 0.19 and 0.18) Experimental measurements had shown that the method of stereomodel computer observation does not play a significant role in the accuracy of computer stereomeasurements. All investigated methods may be assessed as practically equal in accuracy. However it does not means that the visual quality of stereomodels is equal. As follows from subjective experts evaluations, stereomodels, formed with prizm stereospectacles,

6 without spectacles and frame stereomodels are characterized by the best quality. CONCLUSIONS As a result of graphic construction of stereogrammes, their analysis and stereoobservations, it has been discovered that significant distortions of digital stereomodels are possible under discretisation; they reach 1-2 pix in horisontal direction and the value corresponding to p=2pix in height. The results of experiments on evaluation of the accuracy of digital stereomodel measurements testify that stereoscopic model has good metric stability. The connection between errors of stereoobservations and physical properties of stereomodel (resolution, sharpness, contrast) has a character of psychophysical dependence. So the investigated experimental results allow to put forward a psycho-physical hypothesis of stereoscopic measurements: namely that the dependence of visual measurements accuracy (reaction to stimul) from physical characteristic of stereomodel (stimul) appears to be logaritmic, meaning that it submits to the general psychophysical Weber-Fechner law. REFERENCES Knizhnikov Yu.F., Kravtsova V.I., Baldina E.A. et al Digital stereoscopic terrain model. Ed. by Knizhnikov Yu.F. Moscow: Scientific World. 244 p. (in Russian) ACKNOWLEDGEMENTS The investigations were carried out under the support of Russian Foundation of Basic Research (grant ).

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