This is an old revision of the document!
Spatial Wavelet Analysis (SWA)
Mexican-hat Wavelet Analysis
Wavelets have been used across a wide range of scientific disciplines from medical imaging to astronomy, to identify the size, shape, and location of individual objects of interest. Spatial wavelet analysis is an image processing techniques that has considerable potential to objectively and automatically quantify ecologically relevant objects at multiple scales across large landscapes. The image analysis method can be applied to any type of digital imagery, for example aerial photography, LiDAR (Light Detection and Ranging) or satellite images.
The technique can be explained in four simple steps: 1) Selection of a wavelet function that is similar in shape to the objects of interest in the image. We selected the Mexican Hat Wavelet because it has a shape that is similar to the western juniper trees in our aerial photos. 2) The wavelet is passed across the image and every time the wavelet crosses an object of similar size and shape a high score is recorded in a tabular database. Mathematically this is based on convolution of the wavelet function and the intensity (pixel values) of the object in the image. We used the Matlab software to conduct the analysis. 3) Wavelets of different sizes are passed across the image and the wavelet with the size most similar to the object receives the highest score. 4) Locations with wavelet scores and the size the wavelet that recorded the highest score are reported in the final output table, providing the user with a good approximation of the size and location of image objects.
The output is an ASCII file listing the diameter and spatial location (X and Y coordinates at the object center) for objects detected by the wavelet analysis algorithm. GIS software is needed to display the output data spatially. All objects are represented by a circle when the Mexican Hat wavelet is used, however other wavelet shapes could potentially identify objects of different shapes.
Spatial wavelet analysis has been used successfully to quantify the crown diameter and location of individual juniper trees in a matrix of grassland or shrub steppe. Analysis of temporal sequences of photographs can provide information about rates of juniper expansion into steppe vegetation. Expansion rates in different biophysical settings and under a variety of human caused or natural disturbance regimes can be estimated.
Wavelet analysis can, with the use of allometric relationships relating the crown diameter of individual juniper trees to biomass, help quantify the above ground woody biomass contained within an area or estimate changes in above ground woody biomass over time if data from different time periods are compared.
Spatial wavelet analysis can be applied to any type of digital imagery, for example aerial photography, LiDAR (Light Detection and Ranging) or satellite images. Images must be converted to ASCII files for processing in the MATLAB software.
Spatial wavelet analysis has been conducted on a Windows XP workstation using the MATLAB software from The MathWorks (http://www.mathworks.com/products/matlab/). ArcGIS from ESRI is helpful in displaying the results and calculating caopy cover and a spreadsheet software such as Microsoft Excel is needed to summarize data and use allometric equations to compute biomass for individual plants.
Aerial photographs of a western juniper/sagebrush steppe landscape (15 ha). The dark dots are juniper plants in the matrix of sagebrush steppe. Upper left: Original black & white aerial photograph at 1-m resolution from 1939. Upper right: Original aerial photograph of the same area in 1998. Lower left: Projectedjuniper plant radii derived from wavelet analysis for the 1939 photograph, Lower right: Projected juniper plant radii derived from wavelet analysis for the 1998 photograph. The juniper canopy cover estimated from the 1939 photograph is 2.7% using wavelet analysis, and 7.3% in 1998 using the wavelet technique.
You must have an account and be logged in to post or reply to the discussion topics below. Click here to login or register for the site.