Determining the Accuracy of Measuring the Heights of Objects in the Automatic Processing of Stereo Images

Abstract

Introduction. Currently, information on the spatial description of objects is used in many areas of human activity. One of these types of information are the coordinates of the objects. These data are used in cartography, the construction of digital maps and 3D models, for the operation of the navigation means, etc. There are many software for design and analysis of digital elevation models. These are modules and packages like Spatial Analyst, 3D Analyst, ArcGIS packages, program MapInfo (MapInfo Corp.), Autodesk Map 3D of AutoCAD (Autodesk Inc.) and others. Common to them is build automation of soprovich terrain models, including the combination of the images of the stereopair, what is necessary to measure heights of objects for automated creation of digital elevation models of the earth's surface one of the key quality indicators is the accuracy of determining the heights of objects. The main influence on this indicator provides measurement error of parallax when processing stereosystem.

Obtaining analytical expressions for the accuracy of the determination of the height of the object. To obtain the formula of calculating accuracy of measuring the height of objects used decomposition of the function into a Taylor series. Currently, the standard deviation of measurement errors of height of flight of the aircraft, the basis of stereozone and focal length, usually known with enough high accuracy. The main influence on the accuracy of determining the heights of objects during automatic processing of images is the accuracy of parallax. When measuring parallax, the problem is reduced to the search and discovery of images of the object in the second picture on the image of the object on the first image and measuring its position over images of other objects and noise. Using the formula of Kramer-Rao for the potential measurement accuracy of the image coordinates of the object in the picture, the Fourier transform and the parseval equality proof the identity, the formula obtained accuracy potential of combining stereochemical (measurement of parallax). We used the extreme-correlation combination method, as it can be applied for virtually any signals and systems of measurement.

Analysis of the obtained results. The analysis of the obtained formulas shows that the overlay accuracy of the images deteriorates with the increase of the power spectral density of the noise on the first and second images and reducing the similarity of one image with another and also with the decrease in the effective width of a mutual spectrum spatial stereo. Increasing the value of the basis stereozone error of measurement of heights of objects first improves and then deteriorates. This deterioration is caused by the fact that the images of a stereo pair are obtained from different spatial points and images arise of perspective distortion and the distortion due to relief. Accordingly, as the base of removal increases, these distortions will increase.

Conclusions. The advantage of this approach is the use of finite analytical expression.  It provides the ability to calculate the potential accuracy of defining object heights when building a DMR with modern applications.  The disadvantages include the complexity of calculating the moments of mutual spatial spectrum of stereo images. This approach can be applied when planning the shooting mode and the Earth surface imaging equipment for mapping, 3D models, etc.