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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