Spatial filtering using ENVI 5.2

Prof. P. Lewis & Dr. M. Disney

Remote Sensing Unit

Dept. Geography

UCL

Aims

After completing this practical, you should be able to answer the questions: Which type of filter should I use for a given filtering application? What impact will the size and shape of the filter have on the output? You should have some understanding of the process (and issues) of spatial filtering of EO data using Envi.

Advanced use of these notes

Although it is perfectly adequate to simply view the html (webpage) of these notes, there are some additional features in these notes that you can use (in this case, a convolution tool with sliders) if you access them in a different way. The reason this is possible is that these notes are written in an ipython notebook.

To use the notes as a notebook (assuming you have git and python on your computer):

1. Copy all of the notes to your local computer (if for the first time)

    mkdir -p ~/DATA/working
    cd ~/DATA/working
   
    git clone https://github.com/profLewis/geog2021.git
   
    cd geog2021

2. Copy all of the notes to your local computer (if for an update)

    cd ~/DATA/working/geog2021
   
    git reset --hard HEAD
   
    git pull

3. Run the notebook

    ipython notebook SpatialFiltering.ipynb

Contents

[top] [Introduction] [Convolution Filtering] [1D Convolution] [Extras] [Summary]

Data

The datasets you need for this practical are available from:

• ETM-190600
• ETM-190600.HDR
• TM-280589
• TM-280589.HDR

You should download these data and put them in a directory (folder) that you will remember!

The data you will be using are:

• six wavebands of a Landsat TM image over Greater London, imaged on May 28th 1989. The data were obtained from the GLCF which maintains a large database of (freely available) Landsat and other imagery. The data are at an original pixel spacing of 28.5 m, but have been resampled to a 25 m grid here. The data are in a Transverse Mercator projection with OSGB 1936 datum.

• six wavebands (nominally the same wavelengths) of a Landsat ETM image with 25 m spatial resolution, covering the same spatial extent. These data were obtained on June 19th 2000. The data were obtained from Landmap which contains a database available to Universities and other users through an Athens login (done via the institution you are at).

The wavebands are:

1	2	3	4	5	6
450-520 nm	520-600 nm	630-690 nm	760-900 nm	1550-1750 nm	2080-2350 nm

The extent of the imagery is (Lat/Lon):

$$ 51^o 43' 9.23'' North, 0^o 36' 18.37'' West $$

to

$$ 51^o 16' 29.32'' North, 0^o 27' 24.60'' East $$

1. Introduction

In this section, we load the image data we wish to explore.

The purpose of this practical is for you to build on practical 1 and learn about the process of spatial (convolution) filtering.

Note that convolution is a mathematical operation involving the modification of one function by another to produce a third (output) function. In spatial fitering this implies the operation of a filter (one function) on an input image (another function) to produce a filtered image (the output).

The session will be normally run as one two hour supervised practical. You may not complete all tasks in detail in that time, so once you get the hang of how to use the tools, move on to the next section and return later to think more about the remote sensing.

There is a good material for this in text books (e.g. Jensen, Curran etc.) and some of this is online e.g. much of the Jensen material.

First, obtain and then load the TM and ETM images of London that we used in a previous practical.

View the ETM image as a FCC.

2. Convolution filtering

In this section, we use various tools for image convolution.

A description of the various options for convolution and morphology are as envi help pages. You should have a quick read over this if you are not familiar with the types of filter we will be using.

These operations are available via the Toolbox menu:

Apply a high pass filter (the one shown above) to the dataset

Now Display this and the original dataset using 'two vertical views' with the colvolution result in the left.

You should then 'geo-link' the two views, so that moving around or zooming in one view is performed the same for both views.

Make sure you make notes of what you have done and how you have done it so you can recall this later.

Now, find an interesting part of the image, for example Richmond Park, and try to understand how the filter is operating over the features you see.

You might find it easiest to use a greyscale image for this rather than false or real colour.

You may find it useful to examine horizontal or vertical profiles of the original satellite data:

You may need to zoom in to the image to see the detail of the transect, but what you should be interested in examining is the relationship between features in the original dataset and the high-pass dataset.

For instance, looking at the NIR band, for a transect going over Richmond Park we see higher DN over the park than surrounding (urban) areas (why?) in the original data. In the corresponding high pass filtered dataset (below), we see variation in the filtered result around zero, with some 'larger' features (spikes).

Consider carefully the numerical values in the convolution kernel:

-1	-1	-1
-1	8	-1
-1	-1	-1

What does it indicate when there is a positive (or negative) spike in the filtered transect?

Why is there a number 8 in the centre of the filter?

what does the filter produce if the image data are constant? ('flat')

what does the filter produce if the image data show a step change? (see e.g. resevoirs)

3. Convolution

To think some more about this, it can be instructive to consider filtering in one dimension (rather than the two dimensions of an image). To aid this, we can consider some prototype 'shapes' and look at how ther respond under the filtering operation.

Typical example would be step and ramp features.

Two basic operations we can perform are looking at the local average (e.g. mean) or local difference with a convolution operator.

For a local mean over extent 3, we would use

0.333	0.333	0.333

What do the numbers add up to? why is that so

what would a filter of extent 7 look like?

We would expect the local mean to provide some 'smoothing' of the function:

an we can see that this is the case in the illustration (filter width 7) the impact (of smoothing) on the 'clean' signals is mostly negligible (which is an effect we would want), and for the noisy datasets, the noise is reduced.

We can also note some 'edge effects' (e.g. the step at x = 100):

why do these occur?

does the extent of the edge effects depend on the extent of the filter? If so, why

what might be done to mitigate such effects?

A local mean (low pass) filter then, such as that shown above reduces the high frequency components of the signal and retains the low frequency components (so we can 'get rid of' (reduce)) random noise in the signal.

A local mean is effectively a local integration of the signal.

The 'opposite' of this is differentiation, i.e. the difference between one pixel value and the next.

The simplest filter for this is:

1	-1

which we can call a first order difference filter.

what do the values in the filter add up to in this case?

why is this so?

The impact of this is illustrated below.

Think through why it has the impact that we see.

Of what use might such a filter be?

If we convolve the first order differential filter:

1	-1

we get a second order differential filter

1	-2	1

Whereas the first filter represents the 'rate of change' (e.g. slope) of the signal, the second order filter gives the rate of change of the rate of change (rate of change of slope).

what do the values in the filter add up to in this case?

why is this so?

To illustrate this:

At first sight, this might look quite similar to the result of the first order differential.

However, if we look more closely:

we see e.g. that the 'edge' of the step edge is mapped to a 'zero crossing' in this case, rather than a local maximum as was the case for the first order filter.

The peak of the ramp shows a small negative value in the second order differential data: why is this so?

What would the result look like if we were to replace the step and ramp functions by one minus step and one minus ramp?

As a final example, let us consider what happens if we smooth (low pass) and then differentiate (high pass):

Applying two filters to an image/signal has the same effect as convolving the two filters together and then applying this.

We see that convolving a filter of extent 2 with one of extent 3 gives a new filter of extent 4. Why is this so?

To demonstrate, in the plots below, we first convolve the step and ramp with filter 1 (what type of filter is this?) (blue line), then convolve this with filter 2 (what type of filter is this?) (green line). Applying the combined filter to the data, we get the dashed red line (which is the same as the green line).

Thinking through these graphs should re-inforrce what you have learned about spatial convolution in the lectures. You should be able to describe what the impact of different forms of filter on such prototype functions would be. You should then be able to translate this knowledge back to examining the image data.

Go back to the envi session and examine the impact of first and second order differential and smoothing filters on the image data

Relate what you see (e.g. in looking in detail at transects) to the impacts on the prototype shapes

Of what use might all of this be?

4. Extras

If you run these notes as an ipython notebook, then this shows an interactive tool to see the impact of filtering.

You can use the tool to explore the trade-offs you need to consider when filtering: e.g. a wider smoothing filter will suppress a higher level of noise (i.e. do more smoothing) than a narrow filter. However, with a wider filter, you are likely to suffer from greater 'edge effects'.

5. Summary

The main aim of this practical is to reinforce your understanding of convolution operationsd using the image processing software tool envi.

In this practical, we have loaded Landsat images of London and and examined the application of high and low pass filters.

[top] [Introduction] [Convolution Filtering] [1D Convolution] [Extras] [Summary]