Lab 3: Image Acquisition and Geometric Correction

Transcription

1 Geography 309 Lab 3 Answer Page 1 Objectives Preparation Lab 3: Image Acquisition and Geometric Correction Due Date: October 22 to introduce you to digital imagery and how it can be displayed and manipulated to explore the concepts of image histograms to become familiar with the procedures and issues involved in searching and downloading digital satellite imagery; to learn how to geometrically correct an image. Re-read Chapter 11 in your text. Prepare a memory stick or personal disk space with 600 Mb of free space. Parts A and B of this Lab may be done at home (you need the 600 Mb of available disk space for Part B). Part C must be done using the licensed version of Geomatica installed at the University. You may have to wait for up to 1 week before your imagery needed in Part B becomes available. You should start Part B of this lab as soon as you can. A. Introduction to Digital Imagery 1 Background A technique I like to use when trying to learn a new image analysis method is to "work it out by hand" and follow a few individual pixel values through the analysis stages. In this manner, I get a deeper understanding of the procedure and the exact nature of its effect on the data. In this lab you will be the "image analysis system" and create a display of some image data. To permit these hand simulations with only paper and pencil, the following simplifications have been made: The picture to be processed is reduced in size to 49 picture elements (pixels), compared to the several millions typical of digital images; A multispectral image often contains from four to 24 spectral channels or bands. For hand simulation purposes, the pseudo images have been designed with only two spectral bands; and The number of intensity levels which may be recorded by a sensor is typically 256 or more. This is impractical to manipulate by hand, so the sample image has merely 10 levels. 1 This section is derived from material presented in the publication Introduction to Digital Images and Digital Image Analysis Techniques by Tom Alföldi

2 Geography 309 Lab 3 Answer Page 2 The manual techniques to be described are very similar to the tasks performed by computer. However, the computer's great speed permits it to handle much larger images with more channels and greater radiometric range. All referenced Figures and Tables are included on the Answer Sheets attached to the end of this Lab. Please use these Answer Sheets to submit your answers. Image Data Arrangement and Presentation Figure 1 shows the data from two bands of a small segment of a satellite scene, with brightness information quantified into 10 levels (from 0 to 9) for each band. One band A is red-sensitive and the other band B covers a portion of the reflective infrared. The format of the data in this figure is called line-interleaved. For the 7 x 7 image represented on this data stream, the first seven numbers correspond to the pixel intensities in the first line of band A, from left to right in the picture. The next seven numbers are for the same first line but of band B data. This is followed by the next seven numbers which are for line No. 2, band A, and so on. For the 7 x 7 picture area, there are 7 lines x 7 pixels x 2 bands = 98 numbers. It is useful to arrange the numbers in a geometrically convenient form. Question 1: Beginning at START in Figure 1a, mark off every seven numbers from left to right, and label the first seven for band A, the second seven for band B, the third seven for band A, and so on. Now, insert the numbers from the data stream into their appropriate geometric position thus: The first seven numbers of band A from Figure 1a are positioned as pixels 1-7 of line No. 1 of the band A matrix in Figure 1b. The next seven numbers from the data stream are for pixels 1-7 of line No. 1 of band B in Figure 1b. Continue in this manner until the two matrices of Figure 1b are filled. Figure 1b shows the basic format of a digital image. Band A and band B represent the same area on the earth's surface, but are coded separately because they represent different portions of the electromagnetic spectrum (or colours of light). The digital or numerical maps constructed in Figure 1b may now be converted into another format that will permit a visual appreciation of the image. A "grey map" is produced to synthesize a visual image from the numbers at hand. When you view greymaps on the screen, each pixel value is assigned to an appropriate display intensity level, where the number of intensity levels shown depends on the radiometric resolution of the imagery and the capabilities of the display device. Real remote sensing images have radiometric resolutions of at least 256 levels and most hardcopy and softcopy display devices can produce images with many more levels than that. The sample data in this exercise have a radiometric resolution of 10 levels (0-9). The display device you will use is a pencil and a sheet of paper. To make the greymap manageable, you will attempt to represent the l0-level image using 3 shades of grey.

3 Geography 309 Lab 3 Answer Page 3 Question 2: For each of the band A and B digital images (Figure 1b), transform the numerical values of each pixel into a shade of grey according to the following convention: Numerical Value Grey Level and sketch these transformed pixels into Figure 2. Note that the smallest intensities are represented as the darkest. Observe that in the completed Figure 2, there are some similar and some dissimilar patterns appearing when bands A and B are compared. Although some environmental spatial patterns are beginning to appear, it is obvious that the grey maps represent much less information than is inherent in the digital maps. One-Dimensional Histograms A one-dimensional histogram offers a graphical representation of the data distribution for a single band. An image histogram shows the number of pixels that have a particular intensity level. This is an abstract, but important concept. Patterns which become evident in histograms may prompt further image investigation and understanding. For example, you may wonder what area of the image corresponds to the most frequently occurring intensity level? Question 3: Using band A from the digital image in Figure 1b, count the number of pixels which have an intensity of zero. Enter this number in the space provided for band 'A' of Figure 3a. Now count the number of times that the intensity level 1 occurs and similarly record it on Figure 3a. Continue for all levels. Check that the sum of these values is 49 (= 7 x 7). Now plot these values as bar charts on the graphs in Figure 3b and join the plotted points with vertical bars, progressing from left to right. Similarly construct the histogram for band B. There are several observations to be made regarding the appearance of these two histograms. First, the fact that the two histograms are significantly different means that there is different information (and perhaps useful information) available from the two bands concerning the same pixel (or ground area). Second, note the various peaks of the histograms. Each peak separated from neighbouring peaks by valleys is called a mode of the histogram. Often it is found that a mode corresponds to a particular feature on the ground. The presence of several of these modes (a multi-modal histogram) leads to the conclusion that several (different) environmental features have been imaged. Next, consider the band B histogram. There are two major modes in this histogram, separated by the valley at intensity level 2. Since band B is a reflective infrared band, knowledge of the infrared reflection characteristics of land and water can help identify these two modes. Water strongly absorbs infrared, resulting in low reflectivity. The typically vegetation-covered land surfaces will have high reflection during the summer months. Thus, the assumption is made that the left peak or mode designates water while the large mode on the right is of the land surfaces. By counting the number of pixels in each mode, we already have an idea of the relative size of areas of land and water in the image, even though we haven t seen the image as yet!

4 Geography 309 Lab 3 Answer Page 4 Two-Dimensional Histograms The spectral signature of any one pixel is the combination of its intensity levels across all the bands in an image. For a two-band image, this characteristic may be plotted in a two-dimensional (2-D) histogram. In a 2-D histogram, the two axes depict the intensity levels for the two bands. What is to be plotted is the frequency of occurrence of any one combination of band A and band B intensities. Stated in another manner, a 2-D histogram indicates the number of pixels that have a particular combination of intensities in the two bands. As an example, refer to pixel number 6 of line 2 (using Figure 1b). In band A it has an intensity value of 4, and in band B a value of 6. Thus in Figure 4 it would be plotted at the coordinates 4,6 for the band A and band B axes respectively. What the completed histogram will show, is the data distribution of both bands simultaneously. Question 4: Using the digital maps of Figure 1b, tabulate the intensity coordinates for each pixel on Figure 4a by placing a tick mark in the appropriate square. These tick marks will be summed later to find the total in any one square. Only the pixels in the first three lines of Figure 1b should be plotted, since the last four lines are already assembled for you in Figure 4a. Transfer the data of Figure 4a into Figure 4b by summing the tick marks in each square and placing the numerical value in the corresponding square of Figure 4b. Each square, or location, in the completed 2-D histogram is called a cell or sometimes a vector. The number in any one cell of Figure 4b depicts the frequency of occurrence of that particular set of intensity coordinates to be found in the original 7 x 7 image. This 2-D histogram plot is also the spectral signature domain. Cells which are close to each other in this plot have near-similar spectral characteristics and likely represent the same feature in the image. This is just like one of the ways our own human visual system works: we associate pixels which appear to have the same colour to us (i.e., have "near-similar spectral characteristics") with the same feature in the image. In the example you just completed, you created a 2-D histogram from two bands of image data. In reality, however, most remotely sensed images have more than two bands. Although it is impossible for us to visualize 4- or 7- or even 100-dimensional histograms, computers can generate them in memory quite easily. Thus, one of the key tasks we ask of most image analysis software is to construct multi-dimensional histograms of image data and group cells with similar spectral characteristics into the same category. This process is called image classification and will be the subject of a future lab. Question 5: What is the name used by Geomatica for 2-D Histograms?

5 Geography 309 Lab 3 Answer Page 5 B. Acquiring Remote Sensing Imagery Background The reception of imagery from polar-orbiting remote sensing satellites, such as Landsat and SPOT, requires complex satellite dishes capable of tracking the spacecraft as it moves across the sky. Such satellite data receiving stations are expensive to build and maintain hence are of little interest to private citizens. Further, since the sensors are owned or operated by private commercial enterprises or foreign governments their images are not available for free. Most remote sensing data are subject to copyright laws and cannot be distributed without paying some sort of acquisition fee or royalty. Many governments around the world have entered into licensing agreements with the satellite owners in which, for a set fee, they are allowed to receive and disseminate remote sensing imagery of their own country or region to inhabitants of their country or region. The Government of Canada, through the Canada Centre for Remote Sensing (CCRS), has agreements with many of the remote sensing satellite operators around the world to collect Canadian imagery at its satellite receiving stations near Prince Albert, Saskatchewan and Gatineau, Québec. In this lab you will assume the role of a remote sensing consultant. You have been asked by your client to determine what imagery is available for a specific area. You will search some on-line image catalogs to see what is available. Problem Statement The City of Saskatoon has been experiencing rapid growth recently. The City s planning department is having a tough time getting a handle on how all the various developments are affecting urban sprawl. In order to see the whole picture they have contracted you to acquire imagery for the City and its immediate surroundings (approx. 10 km radius). They would like you to advise them on the availability of Landsat Thematic Mapper (TM) or Enhanced Thematic Mapper (ETM) data for the summers of 1990 and 2010, two decades apart. Specifically, they are interested in images acquired at the height of the growing season (near August 1) since much of the urban growth is occurring at the expense of prime agricultural land. 1. Register at the USGS The U.S. Geological Survey (USGS) maintains the largest archive of Landsat imagery for the world. The USGS image search system is called EarthExplorer. Open the EarthExplorer home page - Important: Turn your web browser's popup blocker off for this site. The first thing you need to do is to register at the USGS site so that the system can send you s to update you on the status of your imagery orders. 1. Click on Register on the dark grey toolbar that runs along the top of the EarthExplorer window. 2. Enter your name and address, as requested. Do not worry if the system asks you for a billing address the data you will be downloading are free.

6 Geography 309 Lab 3 Answer Page 6 3. After you have successfully registered, click on the <- Go Back button to return to the EarthExplorer home page. 2. Search for 1990 Imagery The EarthExplorer search window is divided into frames where you enter the information for your image search. Each box has a numbered title 1. Select your dataset(s), 2. Enter your search criteria, and 3. Search >>>. In the Lab instructions below, I start each step with the title of the frame I am referring to. 1. Select your dataset(s) Expand the list under the Landsat Archive heading. Check the Landsat 4-5 TM item. Question 6: (2 marks) a) What is it about the Landsats 4 and 5 TM sensors that allows us to search for their data at the same time? b) Why is it pointless to include Landsat 6 ETM or Landsat 7 ETM+ imagery in this search? 2. Enter your search criteria Leave the Address/Place name search box empty. Enter the time period you want your imagery to come from in the From and To boxes. Using the small calendar tools next to each box, or just typing the dates in directly, enter: o From 07/01/1990 o To 08/31/1990 Specify where you want your imagery to be located. Zoom up on Saskatoon in the Google Earth image. You should zoom in close enough so that the city fills most of the window. Click Add Map to Selection and you will notice that Latitudes and Longitudes of your window will be automatically added to the Area Selected box beneath the image. Change the Number of Results to 100 (there won't be 100 images in the archive, but I like to set this to a very large number just to make sure I don't miss any images). 3. Search >>> Scroll down to the bottom of the page and click Search. Recall that the planners in Saskatoon are interested in images acquired near August 1. Since the temporal resolution of the Landsat satellites is 16 days, there is only a slim chance that there was an image acquired on that day. Although you should still try to find an image as close to August 1 as possible, you can increase your chances of finding a good, cloud-free scene by expanding your search window by 1 month before and after this date (i.e., from July 1 to August 31). 4. While the system is searching the archive, the Results Summary page will be updated on your screen every 10 seconds. Wait until the Status indicates that the search is Complete. Click on the Results button. 5. You are now presented with a list of images which match your search criteria.

7 Geography 309 Lab 3 Answer Page 7 Notes: You can evaluate each dataset by examining its Preview Image and Acquisition Date. The objective is to find an image that clearly shows your region of interest that was acquired on a day as close to August 1 as possible. For each image in the list, click on the miniature thumbnail image to open a new window to show you what the image looks like. It doesn't matter if there are lots of clouds in your image, as long as the area you are looking for (the City of Saskatoon and its immediate surroundings) is clear. It doesn't matter if your region of interest is in the middle or at the side of an image, as long as the entire area you are interested in is included in the scene. Preview images sometimes appear as different colour composites; such colour changes can be ignored. 6. Select the image that best matches your criteria and get more information ("metadata") about your it by clicking in its Show all Fields button. Tip: print this page for your records. 7. Check the text in the Download column for your selected image: If there is a Download link: Click on Download Click Start Downlad from the Data Download window. When asked if you want to Open or Save the file, click Save File. If you are downloading the file on a University computer, save it to your memory stick or to the D:\ drive of the computer you are working on. DO NOT save the file to your My Documents folder or to your I:\ drive there is not enough room in these locations. If the Download column says that this image is Available by ordering: Place a in this scene's Order box. Click Add Selected Items to Shopping Basket.at the bottom of the window. 8. Leave the EarthExplorer Results window open for the next step. 2. Search for 2010 Imagery 1. Click on Redefine Criteria at the bottom of the Results window. This will take you back to the Search Criteria page. 2. Select your dataset(s) Leave the Landsat 4-5 TM item checked. These files can be Mb in size. Be sure that you have enough free disk space before you start to download them.

8 Geography 309 Lab 3 Answer Page 8 Question 7: (2 marks) a) Why isn't there an option to include Landsat 6 ETM imagery in the search? b) For what technical reason about the ETM+ sensor didn't I ask you to include Landsat 7 ETM+ imagery in the search? 3. Enter your search criteria Leave everything as it was before but change the time period you want your imagery to come from in the From and To boxes. Using the small calendar tools next to each box, or just typing the dates in directly, enter: o From 07/01/2010 o To 08/31/ Search >>> Scroll down to the bottom of the page and click Search. 5. While the system is searching the archive, the Results Summary page will be updated on your screen every 10 seconds. Wait until the Status indicates that the search from both data sets is Complete. Click on the Results button. 6. You are now presented with a list of images which match your search criteria. You evaluate each dataset by examining its Preview Image and Acquisition Date. The objective is to find an image that: a) clearly shows your region of interest; b) was acquired as close as possible to the date of the 1990 image; c) was acquired as close as possible to August 1. In order to get a good image match, you may need to: revise your 1990 image selection based on the available data from 2010; and/or choose a different year(s) for one (or both) of your images - it is usually better to extend the time difference between the images by 1 year than to reduce it by 1 year (if possible). 7. Select the image that best matches your criteria and get more information ("metadata") about your it by clicking in its Show all Fields button. Tip: print this page for your records. 8. For your selected image, either click on Download or Add Selected Items to Shopping Basket. 9. If you were able to download both your images directly: Close all EarthExplorer windows, you are finished with this website. Proceed to Step If you needed to add one of your images to the shopping basket: For the purposes of this Lab, you only need to download 1 of your 2 images. It doesn't matter which image you use. It is simpler and faster if you can directly download a scene, rather than ordering it through the shopping basket. So if you were able to download your 1990 image, you do not need to do anything more than find a suitable 2010 image and record its metadata. If you needed to add your 1990 image to the shopping basket and the 2010 image is available as a direct download, use the 2010 image. If you have added an image to the shopping basket but are not going to order it, it is good internet etiquette to empty your basket before leaving this site.

9 Geography 309 Lab 3 Answer Page 9 click View Shopping Basket at the bottom of the Results window. click Checkout -> on the USGS Shopping Basket window. Review your USGS Shopping Basket again. Click Continue ->. Make sure your address is correct on the Summary page and then click Submit Order -> Close all EarthExplorer windows, you are finished with this website. Check your account that you specified when you created your USGS account. You should receive a USGS On-line Order Confirmation message within 5 10 minutes. After some time 1 hour or 1 day or 1 week you will receive an with the subject USGS Landsat scene request order number ### available for download. Click on the link included in the Click on Download Click Start Downlad from the Data Download window. When asked if you want to Open or Save the file, click Save File. If you are downloading the file on a University computer, save it to your memory stick or to the D:\ drive of the computer you are working on. DO NOT save the file to your My Documents folder or to your I:\ drive there is not enough room in these locations. 11. Once your image has been downloaded to your computer, you need to decompress it. In order to save disk space in the USGS archive and to speed up download times, the data in these images have been doubly compressed, first with a UNIX tar command and secondly with a gzip utility. The standard unzip function built into Windows will not decompress these files, instead you need to use a program like PowerArchiver 2 to decode the imagery. Run PowerArchiver to decompress your imagery. Run the decompression until a folder is created on your system that contains 7 or more TIF files. These files can be Mb in size. Be sure that you have enough free disk space before you start to download them. The decompressed imagery can be Mb in size. Be sure that you have enough free disk space before you start to decompress them. Each TIF file contains one band of TM/ETM imagery, as denoted by the _B#0.TIF at the end of the filename. For example, the file ending in _B50.TIF contains Landsat TM/ETM band 5 data. The _GCP.txt, _MTL.txt, and README.GTF are all text files that you can open in Word. You should review the useful and interesting information they contain. 2 PowerArchiver is available on the computers in the Map Library. If you are working on your home computer, you can download a free version of PowerArchiver 6.1 from the bottom of the course homepage.

10 Geography 309 Lab 3 Answer Page 10 Question 8: Provide the following details for your selected 1990 and 2010 images: (a) Satellite Number (b) Sensor (c) Image Date (d) Entire Scene Cloud Cover (%) as reported in the scene metadata (e) Entire Scene Cloud Cover (%) your own approximation (2 marks) 12. In order for you to work with this image in Geomatica, you need to combine all of the individual bands into a single.pix file. a) Open all 7 of your.tiff images in Focus. b) In the Focus window, select Tools Data Merge c) Data Merge Wizard-Step 1 window: All 7 of your images will be listed there. Place a check beside each file to select it. Click Next >. d) Data Merge Wizard-Step 2 window: 1. Output File: Browse to your memory stick or your D:\ drive folder and give your new file a name. Tip: Although you can name your file anything you want I like to include the image date in my file names. 2. Output format: PIX:PCIDSK 3. Projection: From File 1. Select any one of your images from the pull-down list beside the Browse button. 4. Extents: Intersection of Input Data. 1. If you get a message indicating that The provided pixel size, and georeferencing bounds imply a non-integral database size click on Change Lower Right. 5. Resolution: From File 1. Select one of your images from the pull-down list beside the Browse button. 6. Resampling: Nearest 7. Transform Order: Exact 8. Sampling Interval: 1 9. Next > e) Data Merge Wizard-Step 3 window: 1. All 7 of your images will be listed here, but they may not be in the correct order. You can click on a file name in this list and drag it up or down to change its position. Arrange all of the images so that they are in sequence from B01 at the top to B07 at the bottom.

11 Geography 309 Lab 3 Answer Page Unfortunately, the 7 bands don't have very meaningful names ("Contents Not Specified "). Now is a good time to do some housekeeping with the channel names. Right-click on the first channel listed and select Rename. Type in a more meaningful name. I recommend something like TM 1. Repeat the above 2 steps for each of the 7 files. Now all your channels have understandable labels. Finish f) When the Data Merge is complete (this could take a few minutes), load your new file into the Focus window. Load some of the different bands into the view to get a feel for the data. Question 9: (3 marks) Why, when comparing images from different years, it is important to try and have the images: (a) coincide on the day and month of acquisition as closely as possible (give 2 reasons)? (b) come from the same sensor (give 1 reason)?

12 Geography 309 Lab 3 Answer Page 12 C. Geometric Correction Background Due to a variety of reasons, there are geometric distortions inherent in most sensing images. These distortions affect the data only in the sense that you cannot accurately locate a point in the scene based on its geographic coordinates. If a remote sensing project requires this capability or if you wish to integrate your remote sensing image with other geospatial data (as you might in a GIS), then you will need to geometrically correct the scene. Geometric correction is also known as georeferencing and image rectification. A geometric correction process follows 2 steps: 1. Establish ground control. In this step you set up the transformation that is required to convert your data from image coordinates (i.e., lines and pixels) to geographic coordinates (i.e., latitude and longitude or UTM, etc.). The procedure is quite simple: You select pairs of points one from the image and the other from a map for the same location. These points are known as Ground Control Points (GCPs). This is repeated for several locations across your scene. The analysis system will use these GCPs to establish the "best-fit" transformation (commonly a polynomial equation) that can be used to convert from image coordinates to geographic coordinates. 2. Resample the image. Once you have established a reliable transformation you are ready to create a new, geometrically corrected image. Since the position of the pixels in the geometrically corrected image will differ from those in your source image, the software follows a predefined sampling strategy to determine which source pixels should be used to define each georeferenced pixel. Assignment Geometrically correct the Saskatoon.pix image. Before you begin You will need to copy the Saskatoon.pix image from the course disk (T:\ drive) to your local disk. If you examine the properties of the image that you downloaded in Part B of this lab, you will note that it already has a map projection associated with it. In other words, it has already been geometrically corrected. In Geomatica, you will refer to this scene as the Geocoded Image and you will adjust the projection of the Saskatoon.pix image to match it.

13 Geography 309 Lab 3 Answer Page Load your Geocoded Image into Focus so that you can retrieve its projection information. a) Click on the Files tab at the top of the control panel. b) Right-click on the panchromatic image and select Properties. In the File Properties window click on the Projection tab. c) Make a note the projection, UTM zone, and datum code of these data. 2. The Geomatica procedure for geometric correction is called OrthoEngine. You can find instructions for using this program in the Geomatica Visual Guide accessible from the course web page. 3. Register Saskatoon.pix to the same UTM projection and datum of your geocoded image / GIS database / topographic base map. 4. Select an appropriate output pixel size according to the table included in the Geomatica Visual Guide. 5. When collecting GCPs, select Geocoded image as the Ground control source. 6. Collect between 10 and 15 GCPs. When evaluating the accuracy of the proposed polynomial transformation, try to achieve an overall RMS error of less than 1 pixel. If you choose to temporarily or permanently delete GCPs from the transformation, be sure that still have at least 10 active points. 7. You need only create a corrected image with the image bands necessary to display a colour composite image. 8. Follow the instructions outlined under Simple Mapping in the Geomatica Visual Guide to produce your image map.

14 Geography 309 Lab 3 Answer Page 14 Question 8: (3 marks) Submit a map of your geometrically corrected image (black and white is acceptable). Use the Map View Mode in Focus to add an appropriate map surround including a neatline, border, title, and grid. Change the Title to something more appropriate. Include your name as the subtitle. Change the Grid surround to have a Spacing with a Column Width and Row Height of 2500 metres. Question 9: Submit a Residual Report (from the Reports Processing Step in OrthoEngine). Question 10: (2 marks) Name and describe 3 sources of geometric distortion inherent in spaceborne remote sensing imagery?

15 Geography 309 Lab 3 Answer Page 15 NAME: MARK Lab 3: Image Acquisition and Geometric Correction Answer Sheets Due Date: October 22 Question 1: Beginning at START in Figure 1a, mark off every seven numbers from left to right, and label the first seven for band A, the second seven for band B, the third seven for band A, and so on. Now, insert the numbers from the data stream into their appropriate geometric position thus: The first seven numbers of band A from Figure 1a are positioned as pixels 1-7 of line No. 1 of the band A matrix in Figure 1b. The next seven numbers from the data stream are for pixels 1-7 of line No. 1 of band B in Figure 1b. Continue in this manner until the two matrices of Figure 1b are filled. START END Figure 1a: A digitized image, 2 bands, 7 x 7 area, line interleaved. PIXELS PIXELS L 1 L 1 I 2 I 2 N 3 N 3 E 4 E 4 S 5 S BAND A BAND B

16 Geography 309 Lab 3 Answer Page 16 Figure 1b: Digital images arranged in proper geometry. Question 2: For each of the band A and B digital images (Figure 1b), transform the numerical values of each pixel into a shade of grey according to the following convention: Numerical Value Grey Level and sketch these transformed pixels into Figure 2. Note that the smallest intensities are represented as the darkest.. PIXELS PIXELS L 1 L 1 I 2 I 2 N 3 N 3 E 4 E 4 S 5 S BAND A BAND B Figure 2: Grey maps.

17 Geography 309 Lab 3 Answer Page 17 Question 3: Using band A from the digital image in Figure 1b, count the number of pixels which have an intensity of zero. Enter this number in the space provided for band 'A' of Figure 3a. Now count the number of times that the intensity level 1 occurs and similarly record it on Figure 3a. Continue for all levels. Check that the sum of these values is 49 (= 7 x 7). Now plot these values as bar charts on the graphs in Figure 3b and join the plotted points with vertical bars, progressing from left to right. Similarly construct the histogram for band B. BAND A BAND B INTENSITY LEVEL INTENSITY LEVEL Sum = Sum = Figure 3a: Frequency counts. 10 BAND A 10 BAND B # 9 # O 7 Of 7 f P 45 P 45 I 34 I 34 X 23 X 23 E 12 E 12 L 01 L 01 S 0 S INTENSITY LEVEL INTENSITY LEVEL Figure 3b: One-dimensional histograms.

18 Geography 309 Lab 3 Answer Page 18 Question 4: Using the digital maps of Figure 1b, tabulate the intensity coordinates for each pixel on Figure 4a by placing a tick mark in the appropriate square. These tick marks will be summed later to find the total in any one square. Only the pixels in the first three lines of Figure 1b should be plotted, since the last four lines are already assembled for you in Figure 4a. Transfer the data of Figure 4a into Figure 4b by summing the tick marks in each square and placing the numerical value in the corresponding square of Figure 4b. I n t e n s i t i e s 9 8 //// / B 7 //// a 6 // n 5 /// d 4 / / 3 / / / 'B' 2 1 / / 0 / // /// Band A Figure 4a: Two-dimensional frequency counts.

19 Geography 309 Lab 3 Answer Page B 7 a 6 n 5 d 4 3 'B' I n t e n s i t i e s Band A Figure 4b: Two-dimensional histogram. Question 5: What is the name used by Geomatica for 2-D Histograms?