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The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008 
V(LH r ) + V(HL r ) + V(HH r ) < 
V(LH r+] ) + V(HL r+i ) + V(HH r+i ) 
scanner: DELTA SCAN 
scanning resolution: 12 pm and 14 pm (respectively 
for medium and small scale) 
GSD: 12 cm (medium) and 36 cm (small scale), 
photo capturing: October 2003 (medium) and June 
2006 (small scale). 
where V(LH r ), V(HL r ), V(HH r ), V(LH^, V(HL^0, V(HH r+x ) 
= variance of detail components on level r and level 
r+1 of decomposition 
V(I) [%] 
Level of decomposition 
Figure 2. The illustration of equation of relative variance 
preservation by wavelet decomposition 
The speed of the relative variance growing is connected with 
the density and power of edges. In other words the growing of 
speed depends of scale and image contents. 
Images from digital camera: 
• camera type: DMC (Z/I Imaging), 
focal length 120 mm, 
■ pixel size: 12 pm, 
■ photo scale: 1:12 000 (medium) and 1:38000 (small), 
• GDS=14 cm (medium) and 46 cm (small scale), 
■ photo capturing: October 2007 (medium) and 
September 2007 (small scale). 
The images were taken and delivered in TIFF format without 
compression by MGGP AERO company from Tamow, Poland 
(http://www.mggpaero.com). 
The images were selected in pair which were composed of 
analogue and digital image. An example of pair in medium and 
small scale is showed in Figures 3 and 4 respectively. 
For image with noise the following rule was established: Figure 3. The pair of analogue and digital images in medium 
scale 
V(LH X ) + V(HL X ) + V(HH X ) > 
V(LH 2 ) + V(HL 2 ) + V(HH 2l ) 
Therefore the equation (5) is useful for comparing multi-level 
wavelets transform of different aerial images taken from 
analogue and digital cameras. 
4. THE USEFULLNESS OF WAVELET FOR NOISE 
DETECTION - PRACTICAL STUDY 
4.1 The research data 
For the research a set of aerial images taken by two cameras, 
analog and digital photogrammetric, was used. The main 
characteristic of the research data are described below: 
Images from analogue camera: 
■ camera type LMK1000 (Zeiss Jena), 
• lens type LAMEGON, 
• focal length 153mm, 
• film: AGFA Aviphot Color XI00, 
developing process: C-41, 
photo scale: 1:10 000 (medium) and 1:26000 (small), 
Figure 4. The pair of analogue and digital images in small scale 
4.2 The research method and tools 
For each pair of photographs, corresponding fragments of the 
same contents were selected. That task was more challenging 
for photos in a smaller scale, as the analogue photographs were 
taken in 2003, and the digital ones in 2007. As far as possible, 
fragments of uniform land use were selected, e.g. buildings, 
parking lots, fields, forests. That made it possible to observe 
how the land use affected the wavelet transform. 25 fragments 
of images altogether were selected for the tests in the medium