Mapping and Analysis System for Precision Farming Applications

1. Technical Field

This invention relates to farming and, more particularly, to apparatus and methods for producing georeferenced agricultural maps of farming fields and for analyzing the maps to match farm inputs, such as chemicals and water, to current soil and vegetation characteristics to optimize productivity of the farming field.

2. Discussion

Productivity of agricultural lands has a major impact on the world economy and, as world population increases, this impact will increase substantially. Over the last four decades, productivity has doubled while labor has been reduced by a factor of three. Most of the improved productivity and reduced labor can be attributed to advances in irrigation and harvesting machinery and in improved fertilizing and insecticide chemicals.

Specific soil characteristics can vary significantly within a farming field. Particular regions of the farming field can receive too much or too little fertilizer, water and/or insecticide. Environmental damage can occur due to excess inputs and sub-optimal crop yield can occur in farming regions receiving insufficient farming inputs.

Precision farming has been proposed to provide farming inputs which are varied to match specific soil characteristics of each region of a farming field to prevent environmental damage and to allow crop yield optimization. Conventional chemical spreading machinery can currently spread chemicals at variable rates based upon an input soil map. Similarly, conventional irrigation systems allow chemicals and water to be controlled and varied over time and location based upon an input soil map. However, conventional prescription farming approaches are limited with respect to the type and/or extent of data provided. In other words, current approaches do not generate sufficiently competent data for incorporation into the input soil maps which control the chemical spreading machinery and the irrigation systems.

One approach generates soil maps from aerial photographs. While the photographs provides some indication of soil conditions, little or no information relating to crop development and/or yield is provided. Spectral image data provided is limited and difficult to correlate to quantifiable conditions.

A second approach generates soil maps from manual measurements made using soil probes. The second approach also provide some indication of soil conditions but does not provide information relating to crop development and/or yield. The second approach is labor intensive and provides limited or discrete data samples which do not adequately represent soil and vegetation characteristics.

A third approach, related to the second approach, generates soil maps from "on-the-move" soil probes. While the third approach is more comprehensive than the second approach, similar disadvantages are present. The third approach provides some indication of soil conditions but does not provide information relating to crop development and/or yield. The third approach is similarly labor intensive and provides limited or discrete data samples which, as above, do not adequately represent soil and vegetation characteristics.

A fourth approach generates spectral images or maps from airborne or spaceborne multispectral sensors which generate spectral signals related to soil type and crop stress. Vegetation indices are calculated from the spectral signals generated from a limited number of spectral bands, typically less than four spectral bands.

Data generated using the fourth approach has not been used for generating input soil maps for chemical spreading machinery and/or irrigation systems because the spectral images are not georeferenced and therefore do not provide sufficient precision. The vegetation indices calculated from the spectral signals are not calibrated with nutrient contents of the soil and/or vegetation. Calibrating spectral imagery generated by the fourth approach from day to day has been difficult since the magnitude of spectral reflectance is related to light intensity and atmospheric conditions. As a result, databases which summarize soil and vegetation characteristics and other related data for the farming field have been either unobtainable or imprecise.

Therefore, a precision farming system addressing the above problems is desired.

A mapping and analysis system according to the invention generates agricultural maps and analyzes the agricultural maps to match farm inputs of a farming field to current soil and vegetation characteristics to optimize the productivity of the farming field. The mapping and analysis system includes an air-based device for generating spectral image data related to at least one of vegetation stress and soil characteristics for a portion of the farming field. A position device generates position data related to the position of said air-based device with respect to said portion of the farming field. A georeferencing device synchronizes said position data with said spectral image data to generate georeferenced spectral image data.

According to one feature of the invention, a database is generated using the georeferenced data to monitor and analyze the farming field for a growing season and over multiple growing seasons to improve productivity thereof.

According to another feature of the invention, ground-based measurements are correlated with georeferenced spectral image data in said database. Over time, data contained in said database allows crop and soil status categories to be determined from said collected and georeferenced spectral image data.

In still another feature of the invention, visualization, image processing, mathematical techniques, and/or adaptive signal processing are used to classify collected georeferenced spectral image data in said crop and soil status categories.

Other objects, features and advantages will be readily apparent.

The various advantages of the present invention will become apparent to those skilled in the art after studying the following specification and by reference to the drawings in which:

FIG. 1 illustrates a mapping and analysis system including an air-based station and a ground station according to the invention in use over a farming field;

FIG. 2 is a functional block diagram of portions of said air-based station;

FIG. 3 is a functional block diagram of portions of said ground station;

FIG. 4 is a detailed functional block diagram of both the air-based station and the ground station;

FIG. 5 illustrates data acquisition hardware interfaces which can be incorporated in the air-based station;

FIG. 6 is a block diagram illustrating footprint generation and image rectification;

FIG. 7 illustrates world and image coordinate systems; and

FIG. 8 illustrates non-planar terrain calculations.

In FIG. 1, a mapping and analysis system 10 for precision farming applications is illustrated and produces agricultural maps for precision farming from a combination of high resolution airborne and ground-based sensors. Mapping and analysis system 10 utilizes databases which include information relating to current as well as prior aerial-based imaging, ground-based imaging, other ground-based sampling, etc. and generates electronic maps or hardcopy reports for use in optimizing productivity, by chemical (for example fertilizer, insecticide, etc.) and/or water distribution control systems, etc.

While mapping and analysis system 10 is described in conjunction with mapping and analyzing productivity of farming fields, one can appreciate that mapping and analysis system 10 has other applications such as monitoring and analyzing wetlands, exploring, evaluating lands containing hazardous materials, land mapping forests and ranges, etc. Other applications will be readily apparent.

Mapping and analysis system 10 includes an air-based station 14 (further illustrated in FIG. 2) carried by an aircraft 16 and a ground-based station 18. While aircraft 16 is shown as an airplane, other aircraft, satellites, etc. are contemplated. Air-based station 14 includes image sensing devices 22 for measuring spatial and spectral resolution data of a farming field 24 under study.

Sensing devices 22 can include an image spectrometer 26 which collects spectral image data across a wide spectrum and a camera 30 for providing visual images of farming field 24 under study. Preferably camera 30 is a high resolution color and/or thermal imaging camera. For purposes of flexibility, the camera 30 can be attached to aircraft 14 using a steerable mount 32. Spectrometer 26 can also include a steerable mount. Air-based station 14 can communicate with ground-based station 18 using a transmit/receive antenna 34.

Many techniques for remote characterization of crops and soil have been developed, for example "Remote Sensing of Vegetation Characteristics for Farm Management", Volume 475, Society of Photo-Optical Instrumentation Engineers, pp. 81-96 (1984), hereby incorporated by reference. Apparatus for spreading fertilizer based upon digitized maps have been developed and described in U.S. Pat. No. 4,630,773 to Ortlip.

Referring to FIG. 2, air-based station 14 includes an airborne computer 40 with a microprocessor 42, memory 44 which can include external and internal RAM, ROM, etc., input/output (I/O) interface 46, an input device 47 and display device 48, such as a keyboard and a cathode ray tube (CRT), respectively. Air-based station 14 includes an airborne navigation/position system 50 which provides signals indicative of aircraft position (longitude, latitude, and altitude), heading, pitch, roll, and yaw in real-time to aircraft computer 40 via I/O interface 46. A datalink device 54 connected to antenna 34 receives and transmits data to ground station 18, as will be described further below. Aircraft computer 40 can include an elevation database including digital data related to the elevation of farming field 24 under study. The elevation data can be generated under control of and in synchronization with the aircraft position signals provided by airborne navigation/position system 50.

Airborne computer 40 records collected spectral and visual image data generated by image spectrometer 26 and camera 30 in memory 44. Airborne computer 40 georeferences image data generated by image spectrometer 26 and camera 30 in real time using the real-time navigation/position signals generated by aircraft navigation/position system 50, pointing signals generated by steerable mount 32, and the elevation database.

Automated control of actuation and scanning field size for image spectrometer 26 is controlled by airborne computer 40 in accordance with operator input and/or preprogrammed flight plans. Airborne computer 40 automates control of pointing, zooming (image enlargement and reduction), and actuation of camera 30 according to operator input and/or the preprogrammed flight plan.

Airborne computer 40 cues steerable camera mount 32 by analyzing spectral image data generated by image spectrometer 26 and by generating a camera pointing signal. Airborne computer 40 can automatically capture and associate image data with geographical coordinates generated by navigation/position system 50. Airborne computer 40 outputs in real-time spectral image data generated by image spectrometer 26 and camera 30 to display device 48 for review by an optional operator. Airborne computer 40 can output in real time georeferenced image data to display device 48 for data collection management by the operator. An output device 52 such as a disk drive, a printer, a video cassette recorder, digital tape, etc. may also be provided.

Airborne computer 40 provides automatic and/or operator assisted (via input device 47) mosaicking and overlapping of georeferenced images to create digital maps for large farming fields 24. The digital maps can be stored in memory 44 for later retrieval or transmitted via data link device 54 to ground station 18 for further analysis and/or output to farming machinery, etc. Airborne computer 40 can also overlay georeferenced image data onto registered vector and raster map backgrounds.

Airborne computer 40 also allows annotation of the digital maps with additional text and graphics with imagery/map products, for example "tick marking" of an exact georeferenced position of an object within georeference oblique or nadir imagery and storage of the additional text and graphics.

Referring to FIG. 3, ground-based station 18 can include a ground-based computer 70 with a microprocessor 72, memory 74 which can include external and internal RAM, ROM, etc., input/output (I/O) interface 76, an input device 78 and display device 82, such as a keyboard (and/or diskdrive, etc.) and a cathode ray tube (CRT), respectively. Ground-based station 18 communicates with airborne computer 40 via datalink device 88. Ground-based computer 70 also can include an output device 98 such as a modem, digital tape, or CD-ROM drive, a map/image scanner 92, and a computer network interface 94.

A playback/recording device 89 allows video or digital input from tapes generated by air-based station 14. A ground-based spectrometer 90 collects detailed spectral image data at ground-level for vegetation and soil regions of interest. The spectral image data collected by ground-based spectrometer 90 is collected over several hundred channels over the same spectrum as the air-borne spectrometer 26. A spectrometer positioning system 94 guides and positions ground-based spectrometer 90 for recording the spectral image data for specific regions of interest.

Ground-based computer 70 and/or airborne computer 40 can perform data analysis, historical database development, and playback of airborne-collected data. Ground-based computer 70 and/or airborne computer 40 can store, retrieve, and associate airborne collected spectral image data with ground-collected spectral image data according to geographical location and date/time. Ground-based computer 70 and/or airborne computer 40 can store, retrieve, and associate ground-based soil and vegetation measurements according to geographical location and date/time.

Ground-based computer 70 and/or airborne computer 40 can correlate measurable crop characteristics, such as greenness, leaf area index and productivity with collected spectral image, nutrient, and moisture data for a growing season. Ground-based computer 70 and/or airborne computer 40 can classify collected spectral data from the camera 30 and the spectrometer 26 into crop and soil status categories using visualization (by an operator or automated), image processing, mathematical techniques, and/or an adaptive signal processing using device 99 (such as a neural network using historical spectral, vegetation and soil data). Adaptive signal processing device 99 can be executed using firmware or software and can be executed by a separate microprocessor or microprocessor 72. Ground-based computer 70 and/or airborne computer 40 can generate digital maps in hard copy and/or electronic formats for transmission via network, modem or storage on magnetic tape, disk, or CD-ROM.

Datalink devices 54 and 88 allow quick dissemination of the digital maps directly to precision farming equipment, and/or to ground station 18 which can output the digital maps or appropriate control signals to output devices 98 such as precision farming equipment, printers, and/or electronic interfaces. The digital maps can be transmitted in a variety of formats including raw images, images overlaid on raster maps, image annotation, or images with overlaid annotation. Datalink devices 54 and 88 can use image compression to achieve acceptable transfer time and digital map quality. For example, Joint Photographic Experts Group (JPEG) image compression has been found to have acceptable performance.

Referring to FIG. 4, aircraft computer 40 of FIG. 2 can include an airborne computer 100 connected to a monitor 102, a keyboard 106, a mouse 110, and a printer 114. Airborne computer 100 can include memory 116, for example internal RAM and ROM (not shown) and external memory such as CD ROM 118, tape 120, and/or a hard drive 122. Other types of internal and external memory are contemplated.

Camera 30 of FIG. 2 can be a high resolution color and/or thermal camera 130 connected to a steerable camera mount 32 which can be actuated using manual camera controller 134 and/or automated camera control signals can be provided by the airborne computer 100 via data bus 136 and digital interface 138. Camera 130 generates and outputs image data to a video recorder 142 which records a video signal. The video signal is transmitted by video bus 144 to a video digitizer 148 which digitizes the video signal for storage in memory 44. The camera 130 may provide direct digital output. Alternately, the camera 130 may provide analog film output that is digitized by the map/image scanner 92 at the ground station 18.

The airborne computer 100 modifies the digitized video signal by adding georeferencing, mosaicking, etc., for storage to memory, disk 122, or tape 120. The airborne computer 100 outputs position, attitude, and sensor/mount status on data bus 136 to video encoder 150 which generates an analog video signal. The analog video signal can be recorded by video recorder 142. Upon returning to the ground, the videotape can be transferred to a video playback device 160 associated with ground-based station 18, as will be described further below. Video bus 144 can also be connected to a LCD monitor 162 and a cockpit display 163 if desired.

The data link device 54 of FIG. 2 can include an antenna 172, an ultra high frequency radio (UHF) radio 174, and data radio modem 178 which are connected to data bus 136 by digital interface 180. Aircraft station 14 can also be in audio contact with ground station 18 using an antenna 184, a very high frequency (VHF) radio 186, headset 188 and speaker 190.

Airborne computer 100 can include a database in internal or external memory. The database can include elevation data, past vegetation and soil characteristics, etc. for the farming field under study. Alternatively, an on-line database accessed via a computer network can be used, for example via Ethernet.RTM.. The database can also be associated with a ground-based computer 230, described below.

The aircraft navigation/position system 50 of FIG. 2 can include a flux gate sensor 194 connected to an attitude heading reference system 196 which is connected by a digital interface 200 to data bus 136 of airborne computer 100. The aircraft navigation/positioning system 50 further includes a global positioning satellite (GPS) unit 204 and an antenna 206 for receiving a first positioning signal from a GPS. The first positioning signal provides longitude, latitude and altitude data for the aircraft 16. A long-range navigation (LORAN) interface 210 and antenna 212 generates a second positioning signal which provides longitude, latitude and altitude data. GPS unit (or position/attitude unit) 204 and LORAN interface 210 are connected by digital interface 220 to the data bus 136.

A linescanner 224 generates and collects spectral data across a wide spectrum and is connected by a digital interface 228 to the data bus 136 and computer 100. The linescanner generates and outputs spectral image data to a digital interface 228. The digital data is stored in memory 44 and/or on magnetic tape 120.

Airborne computer 100 modifies the digital data by adding georeferencing, mosaicking, etc., for storage to memory, disk 122, or tape 120. The airborne computer 100 outputs position, attitude, and sensor/mount status for storage along with the digital linescanner data to memory, disk 122, or tape 120. Upon returning to the ground, the digital tape can be transferred to playback/recording device 89 associated with ground-based station 18, as will be described further below. The digital input stream can be displayed directly on to the monitor 162 from memory. Monitor 168 can be a liquid crystal diode (LCD) monitor.

Ground-based station 18 includes a ground-based computer 230 connected to a monitor 232, a keyboard 236, a mouse 240, and a printer 244. Ground-based computer 100 can include memory 246, for example internal RAM and ROM (not shown) and external memory such as CD ROM 248, tape 250, a hard disk drive 252, and/or floppy disk drive 256. Other types of internal and external memory are contemplated.

The data link device 98 of FIG. 3 can include an antenna 272, an ultra high frequency radio (UHF) radio 274, and data radio modem 278 which can include digital interfacing for direct connection to computer 230. Ground-based station 18 can also be in audio contact with air-based station 14 using an antenna 284, a very high frequency (VHF) radio 286, headset 288 and speaker 290.

Ground-based station 18 can include a database in internal or external memory. The database can include elevation data, past vegetation and soil characteristics, etc. for the farming field under study. Alternatively, an on-line database accessed via a computer network can be used, for example via Ethernet.RTM.. Ground-based station 18 can interface with air-based station 14 via the computer network if desired.

In use, airborne station 18 collects high resolution spectral image data over farming fields located using a preprogrammed flight plan or interactively selected by an operator. Airborne station 18 georeferences the collected spectral image data. Unusual soil surface characteristics and regions of vegetative stress are identified using vegetative stress, temperature and color indicators. Camera 30 provides zoom color image data for areas of interest by cueing based upon automated imagery analysis cues, a programmed plan, and/or operator direction.

Zoom color and/or thermal images are collected for areas of interest by cueing based on automated imagery analysis, a programmed plan, and/or operator direction. Large areas are mapped by automatic or operator-assisted mosaicking of adjacent captured images. The locations of unusual characteristics are used to direct ground-based spectral measurements and nutrition/moisture measurements. The location of the ground measurement points and other processed data can be transmitted to the ground within a few minutes of collection through datalink devices 54 and 88. Ground measurements can also be made at "normal" areas in the field.

This process is repeated on a periodic basis (daily, weekly, monthly) through the course of the growing season, with the data being stored and correlated based upon geographic location at ground-based computer 230 and/or airborne computer 100. Known conditions and/or problems are characterized and stored with the data. Crop growth trends are charted with the measured data and models are updated. Field maps showing crop and soil status are developed using manual and/or automated visualization, image processing, and mathematical techniques. The maps are output in paper or electronic form for dissemination via modem, tape, or CD-ROM.

Known conditions and nutrient/moisture status are correlated to the ground-based spectral measurements using visualization, image processing, mathematical, and/or adaptive signal processing techniques. Each ground-based spectral signature is characterized by the positions of minimum (absorption) and maximum (reflection) values (2nd derivative) and rates of change (1st derivative) between selected minima and maxima. These characteristics are generally invariant of light intensity and atmospheric factors and therefore can be correlated over time. Collected spectral image data, known conditions, and collected plant and soil data for multiple fields (and for different times) are used to build up a large sample set to develop the spectral characteristics for various stages of crop development.

Over time, and a large enough sample set, the prescription farming system 10 learns the spectral signature trends associated with normal crop growth, nutrient/moisture status, and specific crop problems on a crop-by-crop, region-by-region, and field-by-field basis.

As the ground-based spectral database is developed, algorithms for more precise detection of soil and vegetation characteristics are developed and are incorporated in airborne computer 100 along with the classification techniques for crop conditions and nutrient status. These are used to generate real-time status maps of the field directly by airborne computer 100 which can be datalinked to precision farming equipment or ground-based computers using the optional datalink. Maps can also be produced at the ground-station for hardcopy or electronic dissemination. Automated collection plans for future airborne missions are created at the ground computer and downloaded to the airborne computer system.

Referring to FIGS. 5 and 6, the following sections illustrate a data acquisition interface 400 for mapping and analysis system 10 according to the inventor.

A scanner hardware interface (HWIF) 402 reads input data from image spectrometer 26 (e.g. linescanner 224) such as scan lines of imagery pixels and roll values. Scanner HWIF 402 can be a parallel interface. Input data is read in as scan line-size blocks and placed into a shared memory 406.

A position/attitude HWIF 410 reads data from an input port (which can be serial) connected to position/attitude unit 204. Position/attitude unit 204 can be a Trimble Navigation GPS unit which generates data in ASCII format. A state table can be constructed and, based on the input data, a branch can be taken to read a specific token. The Latitude, Longitude, Altitude, Attitude, and Track (used for heading) are linked with appropriate scan lines in shared memory 406.

A ball HWIF 414 (for example associated with steerable sensor mount 32) points a ball with a sensor mounted inside to a target specified either by the user or automatically computed by the system. The ball can be used with the camera or the image spectrometer. Directional parameters (e.g. azimuth and elevation) of the ball (and consequently the sensor mounted therein) are output to shared memory 406. The ball HWIF 414 must continuously send commands to the hardware to keep the ball pointed in the proper location.

All the navigation, attitude, and camera angle measurements from video sensor 423 are input to an encoder HWIF 424 which encodes the data on an input video signal. Decoder HWIF 420 decodes the navigation, attitude and camera angle measurements as previously described.

A decoder HWIF 420 decodes all navigation, attitude, and camera angle measurements from the video signal and stores the data in shared memory 406.

A tape HWIF 428 is used during collection and playback modes. When collecting, the tape 124 stores all data written to shared memory 406 by GPS HWIF 410 and scanner HWIF 402. During playback, tape HWIF 428 restores the contents of shared memory 406 to the same state as during collection. The GPS and scanner HWIF 410 and 402 are not running during playback.

A video capture display 432 captures a video signal from the real-time video display and saves the frame (or multiframe) along with navigation, attitude, and camera angle parameters to a snap shot. This data is output to a map display 436 for image rectification.

A real-time waterfall display 440 reads imagery data from shared memory 406 and displays the imagery data to the user in a window where the scan lines are scrolled from the top of the display to the bottom. When the user saves a snapshot, the snapshot data is sent to the map display 436 along with its navigation data used for image rectification.

The mapping and analysis system 10 has the ability to display, in real-time, a footprint (FIGS. 6 and 7) that is an indication of a sensor's field of view on the ground. The real-time nature of the sensor footprint is extremely useful when producing a mosaic of imagery by providing the operator with the ability to optimize ground coverage.

Furthermore, the sensor image data may be projected within the footprint onto a map to provide image geo-referencing. Two suitable map projections are Mercator and Universal Transverse Mercator (UTM), representing planar or elevation mapping.

Additionally, the mapping and analysis system 10 operates with three different sensor types: framing camera, scanning camera and single line scanner. Each of these sensors is parameterized so that a database may be created to support sensors of varying specifications.

In the mapping and analysis system 10, the sensor footprint is calculated using the sensor type, the sensor's orientation relative to the aircraft, and the aircraft's orientation relative to the ground. The sensor footprint is initially calculated relative to a point directly below the aircraft. The aircraft's position along with the map projection determines where the footprint points are rendered on the map display. Image rectification parameters are determined from the sensor footprint calculation and are then used to project the image onto the map.

A. Footprint And Rectification Transformations

A transformation that describes the relationship between points in the image and points on the ground must be defined to calculate the sensor footprint and perform image rectification. Sensor footprint calculation and image rectification are inverse functions. For the sensor footprint calculation, the location of the boundary points (four corners) of the image on the ground are located. Conversely, the projection of the sensor image onto the ground requires the transformation of each point within the footprint to the image point (or pixel) that projects to that point.

B. Reference Coordinate Systems

To define the transformation, a world coordinate system is chosen with the origin at sea level directly below the aircraft navigation/position system 50 (or GPS unit 204) of the aircraft. Referring to FIG. 7, the axes of the world coordinate system are defined as follows:

Assuming the image coordinate system is aligned with GPS unit 204, the axes of the image coordinate system are defined as follows:

The reference position of the aircraft, (i.e. roll=pitch=heading=0), is defined as the nose pointing along the positive Y axis with the wings in the X-Y plane.

C. Transform Calculation

The following data is provided dynamically from the aircraft navigation/position system 50 and the sensor (or sensor mounting system, e.g., steerable camera mount 32):

The following are defined:

Equations defining the transformation between world and image coordinates are given by the following:

Note that equations (1) and (2) are parametric equations of a line in world coordinates originating at the sensor location.

The rotation matrix R is a composite of the aircraft and sensor rotations defined as follows:

To express the transform in terms of available measurements, part of equation (1) can be expanded as follows: ##EQU1## Note that the measurement V is defined as the offset of the sensor from the GPS unit 204 with respect to the aircraft coordinate system. This may be expressed as:

We can now solve for E as:

Equations (1) and (2) form the basis for the rectification and footprint algorithms respectively.

To complete the transformation algorithms we need a relationship between image coordinates, I, and pixel coordinates P. This portion of the transformation is dependent on the type of sensor used and is described more fully below.

Note that for each sensor pixel coordinate system we consider the pixels to be indexed by sample and line with indices increasing from upper left to bottom right.

D. Frame Camera Model

For the frame camera model, the following parameters are

The following parameters are defined:

The relationship between image coordinates and pixel coordinates is then given by: ##EQU2## To incorporate this relationship into equations (1) and (2) we can further define the matrices J and K as: ##EQU3## such that

to incorporate J and K into M and R, let

now, substituting (13) and (14) into equations (1) and (2) gives

E. Scanning Camera Model

For the scanning camera model, the following parameters are given:

The following parameters are defined:

The relationship between image coordinates and pixel coordinates is given by: ##EQU4## with

such that ##EQU5## Substituting (20) into equation (1) and solving for S and L gives: ##EQU6##

Substituting (20) into equation (2) gives: ##EQU7## F. Single Line Scanner Model

The line scanner 224 model is essentially a one dimensional version of the scanning camera (N.sub.L =1). For the line scanner model, the following parameters are given:

The following are defined:

The relationship between image coordinates and pixel coordinates is given by: ##EQU8## with

so that ##EQU9## Substituting (25) into equation (1) and solving for S gives: ##EQU10## Substituting (25) into equation (2) gives: ##EQU11##

In general, footprint calculation consists of projecting the four corner points of the image onto the ground. These calculations are based on equation (2) and are recomputed for each navigational update, sensor movement, or image snapshot. To illustrate the footprint calculation process we will consider the frame camera model. The equations for the remaining sensor types are analogous to those of the frame camera.

In all cases, we initially compute R and E from the sensor and navigation data. When an image snapshot is taken (i.e. current sensor image is geo-referenced), the matrix M is additionally computed and saved along with E for this image.

A. Planar Terrain

For planar terrain, we make the assumption that a ray from the sensor intersects the ground at a point where W.sub.z =Z.sub.T, where Z.sub.T is a known constant.

For the frame camera, equation (2) may be rewritten as:

We can solve for .lambda. in equation (31) as ##EQU12## Solving for W.sub.x and W.sub.y gives: ##EQU13## Equations (32) and (33) may now be evaluated at each of the four corner points of the image as follows: ##EQU14## to determine the world coordinates of the footprint. These coordinates are the offsets in the meters of the corners of the footprint from the point on the ground directly below the aircraft position sensor (GPS). Now, based on the aircraft position, (in latitude and longitude), and the map projection, the footprint is plotted in the map coordinate system.

B. Non-Planar Terrain

In the planar case, we made the assumption that ray from the sensor intersects the ground at Z.sub.T which allowed easy computation of .lambda.. However, for non-planar terrain, we can not make this assumption as the point of intersection is dependent of the terrain elevation. Additionally, .lambda. must be determined for each corner of the footprint. The value of .lambda., (and subsequently W), may be calculated iteratively. FIG. 8 is a graphical illustration of the iteration scheme. Once the world coordinates of the footprint have been determined, the footprint may be projected onto the map as in the planar case. Note that this is only an approximation of the footprint since we have only considered the corner points of the image. To be more precise, each point along the footprint boundary must be calculated in a manner similar to the corner calculations.

In general, image rectification involves selecting an area on the ground, and then determining which image pixels (if any) project to the points in that area. The image rectification calculations are based on equation (1) and are computed for each image snapshot. At the point the image rectification is performed, the values of M and E are known from the footprint calculation. Additionally, the bounding rectangle of the footprint is used to limit the ground area of the image projection.

A. Planar Terrain

For the planar terrain case we make the same assumptions as for the footprint calculation (W.sub.z =Z.sub.T). Equation (1) may be rewritten as: ##EQU15## Solving for S and L gives: ##EQU16## To perform the rectification, (S.sub.i, L.sub.i) are calculated for each point (W.sub.x, W.sub.y) in the bounding rectangle. The choice of sampling of the bounding rectangle is based on the sampling in the map display. If a given (S.sub.i, L.sub.i) is within the image area, [O, NS] and [O, N.sub.L ], then (W.sub.x, W.sub.y) is set to a value proportional to the image pixel value at (S.sub.i, L.sub.i). Note that the above calculation does not result in discrete values for S.sub.i and L.sub.i therefore bi-cubic interpolation of the pixel values is performed in the neighborhood of (S.sub.i, L.sub.i) to determine the value.

B. Non-Planar Terrain

In the non-planar case, the terrain elevation is given for each point within the bounding area. This may be expressed as:

Equations (35) and (36) now become: ##EQU17## At this point, the rectification procedure is the same as the planar case.

The following pseudo-code illustrates the implementation of the footprint calculation and image rectification algorithms for the frame camera model on planar terrain.

The following values are common to all functions.

Image.sub.-- Footprint () calculates the four corner ground points of the image footprint based on the aircraft and sensor position and orientation.

Image.sub.-- To.sub.-- World.sub.-- XY() is a function called by Image.sub.-- Footprint() to convert an image pixel coordinate to a point on the ground.

Image.sub.-- Rectify() is used to rectify a src array of pixels onto the dst array based on the rectification parameters computed in Image.sub.-- Footprint().

The image spectrometer 26 (also linescanner 224) preferably has a spectrum which includes wavelengths between 400 nanometers (nm) and 12,000 nm. A minimum of 32-35 bands should be used for accurate spectral representation of the farming field under study. In contrast, spectrometer 90 should use significantly higher number of bands, preferably several hundred bands. In other words, the spectrometer 26 collects spectral image data over a wide spatial area on relatively few bands while spectrometer 90 collects spectral image data over a narrow spatial area for a relatively high number of bands. Additional bands can be utilized for higher spectral resolution.

The various advantages of the present invention will become apparent to those skilled in the art after a study of the foregoing specification and following claims.