Calibration of a Terrestrial Laser Scanner - Institute of Geodesy and ...

74 4. Static Laser Scanning4.1.2 Mixed PixelDue to beam divergence, the laser beam is spread out during propagation.Depending on the range andthe beam divergence, the laser beam creates a characteristic footprint when hitting objects.to be scanned and the deflection of the laser beam maycause the footprintbelong to only one object but to two or more objectssituated at different distances. Thecannot be identified with one of these objects since the range is measured by integratingThe situationto hit a surface that does notreflected energyover the entirefootprint, as characterized by the projected spot. This phenomenon is referred to as mixed pixels, whichcan be anywhere along the line of sight [Hebert and Krotkov, 1992]. The detected ranges from such mixedpixels are somewhere in between, behind or in front of the surfaces.The interpretation for the existence of such mixed pixels is described by [Hebert and Krotkov, 1992]. If onesurface occludes a second surface, the laser beam is reflected by both objects. The geometricallocation ofthe resulting mixed pixel is obtained according to a description of the range and the intensity as a complexnumber with the vector componentsv I+4>i (4.3)=where I is the intensity or magnitude, which depends on several parameters, e.g.the reflectivityof thematerial, the range, and the angle of incidence, and is the phase, which is proportional to the range. Theresulting elements of a mixed pixel caused by two reflections v\ and v2 is calculated byv = vi + V2 = h + h + (i + 2)*- (4.4)The addition of two vectors results in a new vector, with a phase that can be anywhere, dependingon theratio of the lengths and depending on the phase angles. Considering the difference in the phase angles Aof the two objects,a distinction can be made between(1)=A (f>2 -4>1< 7T(2)=A (f>2 -4>1> 7TThe first one results in a mixed pixel with a phase, i.e. the range, between the phaseof the individualcomponents. The second one produces a mixed pixel with a phase that is either greater than or less than thephase of both individual components, depending on the ratio of the intensity values. Figure4.1 visualizesthe effects of mixed pixels with respect to phase angles and intensity values. The left part shows case (1)and the right one shows case (2). For (2) a case differentiation is necessary to decide whether the mixedpixel is closer or farther than the object.object.The right figure shows the mixed pixel,which is closer than theThe elimination of mixed pixels is proposed to be carried out by applying a median filter to the rangeimage [Hebert and Krotkov, 1992]. Most of the pixels should be detected since they appear only along thedirection of edges. The mixed pixels are often isolated pixels in 3D spaceand thus, can be removed easierin 3D space than in 2D images, e.g. range images. The elimination of mixed pixels is onlysuccessful ifthese pixels are far from objects. In contrast, if mixed pixels occur cumulatively near the vicinity of objects,they can rarely be removed automatically.elimination of such mixed pixels can be improved.However, in combination with images,The appearance of mixed pixels can be avoided with a small beam divergence.the identification andThe smaller the beamdivergence, the less the probability that more than one object will be hit by the laser beam. Furthermore,the problem of mixed pixels is related to laser measurement systems using AMCW techniqueand cannot be