Chapter-4 Aerotriangulation.pptx

IOE Pashchimaanchal campus Chapter 4. Aerotriangulation Aerotriangul Content Introduction to Aero triangulation Single image Stereo-pair (two overlapping images) Single flight lines (Strip triangulation) Image blocks: Block Adjustment of Indepen...

IOE Pashchimaanchal campus Chapter 4. Aerotriangulation Aerotriangul Content Introduction to Aero triangulation Single image Stereo-pair (two overlapping images) Single flight lines (Strip triangulation) Image blocks: Block Adjustment of Independent Models (BAIM) Bundle Block Adjustment Block Adjustment with added parameters (Self-Calibration) 4.5. Advantages and disadvantages IOE Pashchimanchal campus Introduction  Aerotriangulation is the term most frequently applied to the process of determining the 𝑋, 𝑌, and 𝑍 ground coordinates of individual points based on photo coordinate measurements  Phototriangulation is perhaps a more general term, however, because the procedure can be applied to terrestrial photos as well as aerial photos  With improved photogrammetric equipment and techniques, accuracies to which ground coordinates can be determined by these procedures have become very high  One of the principal applications lies in extending or densifying ground control through strips and/or blocks of photos for use in subsequent photogrammetric operations  When used for this purpose, it is often called bridging, because in essence a "bridge" of intermediate control points is developed between field-surveyed control that exists in only a limited number of photos in a strip or block Aerotriangul IOE Pashchimaanchal campus Introduction  In this application, the practical minimum number of control points necessary in each stereomodel is three horizontal and four vertical points  For large mapping projects, therefore, the number of control points needed is extensive, and the cost of establishing them can be extremely high if it is done exclusively by field survey methods  Much of this needed control is now routinely being established by aerotriangulation from only a sparse network of field-surveyed ground control and at a substantial cost savings.  A more recent innovation involves the use of kinematic GPS and INS in the aircraft to provide coordinates and angular attitude of the camera at the instant each photograph is exposed.  In theory, this method can eliminate the need for ground control entirely, although in practice a small amount of ground control is still used to strengthen the solution Aerotriangul IOE Pashchimaanchal campus Introduction  Besides having an economic advantage over field surveying, aerotriangulation has other benefits: (1) most of the work is done under laboratory conditions, thus minimizing delays and hardships due to adverse weather conditions (2) access to much of the property within a project area is not required (3) field surveying in diffi cult areas, such as marshes, extreme slopes, and hazardous rock formations, can be minimized (4) the accuracy of the field-surveyed control necessary for bridging is verified during the aerotriangulation process, and as a consequence, chances of finding erroneous control values after initiation of compilation are minimized and usually eliminated Aerotriangul IOE Pashchimaanchal campus Introduction  Methods of performing aerotriangulation may be classified into one of three categories: analog, semianalytical, and analytical.  Early analog procedures involved manual interior, relative, and absolute orientation of the successive models of long strips of photos using stereoscopic plotting instruments having several projectors ⇨ This created long strip models from which coordinates of pass points could be read directly  Later, universal stereoplotting instruments were developed which enabled this process to be accomplished with only two projectors  Semianalytical aerotriangulation involves manual interior and relative orientation of stereomodels within a stereoplotter, followed by measurement of model coordinates  Absolute orientation is performed numerically—hence the term semianalytical aerotriangulation  Analytical methods consist of photo coordinate measurement followed by numerical interior, relative, and absolute orientation from which ground coordinates are computed Aerotriangul IOE Pashchimaanchal campus 17-2. Pass Points for Aerotriangulation  Pass points for aerotriangulation are normally selected in the general photographic locations shown in Fig. 17-1a  Historically, points were artificially generated using stereoscopic point marking devices  These devices involved drilling a hole in the photograph, destroying the emulsion on that point Figure 1 7 - 1. (a) Idealized pass point locations for aerotriangulation. (b) Locations of pass points in two adjacent stereomodels.  Nowadays, in automatic aerotriangulation, pass points are usually found using automated procedures on digital and scanned-film photography  Control points can be located manually with sub-pixel accuracy in software  There is no destruction of the photograph using digital methods, so points can easily be Aerotriangul IOE Pashchimaanchal campus 17-2. Pass Points for Aerotriangulation  A typical procedure for measuring a pass point begins by first manually digitizing the point in one photograph ⇨The pixels around this point serve as the template array  Next, the user defines a search area in other photographs for automatic image matching ⇨There are also automatic methods for defining a search area by predicting the coordinates of the point in the subsequent photographs  Finally, the pixel patch in the search area corresponding to the template array is automatically located ⇨Normalized cross-correlation followed by least squares matching is a common method for this step Aerotriangul IOE Pashchimaanchal campus 17-2. Pass Points for Aerotriangulation  To avoid poor matches and blunders, well- defined unique objects with good contrast and directionality should be selected as image- matching templates  Image-matching software usually provides a measure of how well the point was matched, such as the correlation coefficient in normalized cross-correlation Figure 1 7 - 1. (a) Idealized pass point locations for aerotriangulation. (b) ⇨This number should serve as a guide for the Locations of pass points in two adjacent stereomodels. user to decide whether or not to accept the  It is not uncommon for incorrectly matched points to have high correlation matching results coefficients  The process is repeated for each pass point keeping in mind the optimal distribution illustrated in Fig. 17-1  Due to increased redundancy, the most effective points are those that appear in the so- called tri-lap area, which is the area included on three consecutive images along a strip  Once many pass points are located, more can be added in a fully automated Aerotriangul IOE Pashchimaanchal campus Fundamentals of Semianalytical Aerotriangulation  Semianalytical aerotriangulation, often referred to as independent model aerotriangulation, is a partly analytical procedure that emerged with the development of computers.  It involves relative orientation of each stereomodel of a strip or block of photos  After the models have been formed, they are numerically adjusted to the ground system by either a sequential or a simultaneous method  In the sequential approach, contiguous models are joined analytically, one by one, to form a continuous strip model, and then absolute orientation is performed numerically to adjust the strip model to ground control  In the simultaneous approach, all models in a strip or block are joined and adjusted to ground control in a single step, much like the simultaneous transformation technique. Aerotriangul IOE Pashchimaanchal campus Fundamentals of Semianalytical Aerotriangulation An advantage of using semianalytical aerotriangulation is that independent stereo models are more convenient for operators in production processes Regardless of whether the sequential or simultaneous method is employed, the process yields coordinates of the pass points in the ground system Additionally, coordinates of the exposure stations can be determined in either process ⇨Thus, semianalytical solutions can provide initial approximations for a subsequent bundle adjustment Aerotriangul IOE Pashchimaanchal campus Sequential Construction of a Strip Model from Independent Models  In the sequential approach to semianalytical aerotriangulation, each stereopair of a strip is relatively oriented in a stereoplotter, the coordinate system of each model being independent of the others.  When relative orientation is completed, model coordinates of all control points and pass points are read and recorded.  This is done for each stereomodel in the strip. Figures 1 a and b illustrate the first three relatively oriented stereomodels of a strip and show plan views of their respective independent Figure 1 : - Independent model or semianalytical aerotriangulation. (a) Three adjacent relatively coordinate systems oriented stereomodels. (b) Individual arbitrary coordinate systems of three adjacent stereomodels. (c) Continuous strip of stereomodels formed by numerically joining the individual arbitrary coordinate systems into one system. Aerotriangul IOE Pashchimaanchal campus Sequential Construction of a Strip Model from Independent Models  A three-dimensional conformal coordinate transformation, using pass points common to adjacent models, ties each successive model to the previous one.  To make transformations geometric strength stronger, we measure the positions of the camera centers in each model and use these points for alignment.  The right exposure station of model 1-2, 𝑂2, for example, is the same point as the left exposure station of model 2-3.  To transform model 2-3 to model 1-2, therefore, coordinates of common points 𝑑, 𝑒, 𝑓, and 𝑂2 of Figure 2. Independent model or semianalytical aerotriangulation. (a) Three adjacent relatively model 2-3 are made to coincide with their oriented (b) Individual arbitrary coordinate systems stereomodels. of three adjacent stereomodels. (c) Continuous strip of stereomodels corresponding model 1-2 coordinates. formed by numerically joining the individual arbitrary coordinate systems into one system. Aerotriangul IOE Pashchimaanchal campus Sequential Construction of a Strip Model from Independent Models  Once the parameters for this transformation have been computed, they are applied to the coordinates of points 𝑔, h, 𝑖, and 𝑂3 in the system of model 2-3 to obtain their coordinates in the model 1-2 system  These points in turn become control for a transformation of the points of model 3-4  By applying successive coordinate transformations, a continuous strip of stereomodels may be formed, as illustrated in Fig. 2c  The entire strip model so constructed is in the Figure 1 7 -2. Independent model or semianalytical coordinate system defined by model 1-2 aerotriangulation. (a) Three adjacent relatively oriented stereomodels. (b) Individual arbitrary coordinate systems of three adjacent stereomodels. (c) Continuous strip of stereomodels formed by numerically joining the individual arbitrary coordinate systems into one system. Aerotriangul IOE Pashchimaanchal campus Adjustment of a Strip Model to Ground  After a strip model has been formed, it is numerically adjusted to the ground coordinate system using all available control points.  If the strip is short, i.e., up to about four models, this adjustment may be done using a three- dimensional conformal coordinate transformation  This requires that a minimum of two horizontal control points and three vertical control points be present in the strip  More control than the minimum is desirable, however, as it adds stability and redundancy to the solution (least square adjustment is used)  If the strip is long, a polynomial adjustment is preferred to transform model coordinates to the ground coordinate system Aerotriangul IOE Pashchimaanchal campus Adjustment of a Strip Model to Ground Due to the nature of sequential strip formation, random errors will accumulate along the strip  Often, this accumulated error will manifest itself in a systematic manner with the errors increasing in a nonlinear fashion.  This effect, illustrated in Fig. 3, can be significant, particularly in long strips  Figure 3 a shows a strip model comprised of seven contiguous stereomodels from a single flight line Figure 3. (a) Plan view of control extension of a seven-model strip. (b) Smooth curves indication accumulation of errors in X, Y, and Z coordinates during control extension of a strip. Aerotriangul IOE Pashchimaanchal campus Adjustment of a Strip Model to Ground  The remaining control points (in models 4-5 and 7-8) can then be used as checkpoints to reveal accumulated errors along the strip  Figure 3b shows a plot of the discrepancies between model and ground coordinates for the checkpoints as a function of 𝑋 coordinates along the strip  Except for the ground control in the first model, which was used to absolutely orient the strip, discrepancies exist between model positions of horizontal and vertical control points and their corresponding field-surveyed positions Figure 3 (a) Plan view of control extension of a  Smooth curves are fi t to the discrepancies as shown in seven-model strip. (b) Smooth curves indication accumulation of the figure errors in X, Y, and Z coordinates during control extension of a strip. Aerotriangul IOE Pashchimaanchal campus Adjustment of a Strip Model to Ground  If sufficient control is distributed along the length of the strip, a three-dimensional polynomial transformation can be used instead of a conformal transformation to perform absolute orientation and thus obtain corrected coordinates for all pass points  This polynomial transformation yields higher accuracy through modeling of systematic errors along the strip.  Most of the polynomials in use for adjusting strips formed by aerotriangulation are variations of the following third-order equations: (1)  Where 𝑋, 𝑌 and 𝑍 are the transformed ground coordinates; 𝑋 and 𝑌 are strip model coordinates; and the 𝑎′𝑠, 𝑏′𝑠, and 𝑐′𝑠 are coefficients which define the shape of the polynomial error curves.  The equations contain 30 unknown coefficients (𝑎′𝑠, 𝑏′𝑠, and 𝑐′𝑠)  Each 3D control point enables the above three polynomial equations to be written, and thus 10 three-dimensional control points are required in the strip for an exact solution. Aerotriangul IOE Pashchimaanchal campus 17-5. Adjustment of a Strip Model to Ground  When dealing with transformations involving polynomials, however, it is imperative to use redundant control which is well distributed throughout the strip  It is important that the control points occur at the periphery as well, since extrapolation from polynomials can result in excessive corrections  As illustrated by Fig. 17-4b, errors in 𝑋, 𝑌, and 𝑍 are principally functions of the linear distance (𝑋 coordinate) of the point along the  However, the nature of error strip propagation along strips formed by aerotriangulation is such that discrepancies in 𝑋, 𝑌, and Figure 1 7 - 4. (a) Plan view of control extension of a seven-model strip. (b) Smooth curves indication 𝑍 coordinates are also each accumulation of errors in X, Y, and Z coordinates during control extension of a strip. somewhat related to the 𝑌 positions of the points in the strip Aerotriangul IOE Pashchimaanchal campus Adjustment of a Strip Model to Ground (1)  Depending on the complexity of the distortion, certain terms may be eliminated from Eqs. (1) if they are found not to be significant  This serves to increase redundancy in transformation which generally results in more accurate results Aerotriangul IOE Pashchimaanchal campus Simultaneous Bundle Adjustment  The most elementary approaches to analytical aerotriangulation consist of the same basic steps as those of analog and semianalytical methods and include (1) relative orientation of each stereomodel (2) connection of adjacent models to form continuous strips and/or blocks (3) simultaneous adjustment of the photos from the strips and/or blocks to field- surveyed ground control  What is different about analytical methods is that the basic input consists of precisely measured photo coordinates of control points and pass points  Relative orientation is then performed analytically based upon the measured coordinates and known camera constants  Finally, the entire block of photographs is adjusted simultaneously to the ground coordinate system Aerotriangul IOE Pashchimaanchal campus Simultaneous Bundle Adjustment  Analytical aerotriangulation tends to be more accurate than analog or semianalytical methods, largely because analytical techniques can more effectively eliminate systematic errors such as film shrinkage, atmospheric refraction distortions, and camera lens distortions  In fact, 𝑋 and 𝑌 coordinates of pass points can quite routinely be located analytically to an accuracy of within about 1/15,000 of the flying height, and 𝑍 coordinates can be located to an accuracy of about 1/10,000 of the flying height  With specialized equipment and procedures, planimetric accuracy of 1/350,000 of the flying height and vertical accuracy of 1/180,000 have been achieved  Another advantage of analytical methods is the freedom from the mechanical or optical limitations imposed by stereoplotters  Photography of any focal length, tilt, and flying height can be handled with the same efficiency  The calculations involved are rather complex ⇨however, a number of suitable computer programs are available to Aerotriangul IOE Pashchimaanchal campus Simultaneous Bundle Adjustment  All different variations in analytical aerotriangulation techniques consist of writing condition equations that express the unknown elements of exterior orientation of each photo in terms of camera constants, measured photo coordinates, and ground coordinates  The equations are solved to determine the unknown orientation parameters, and either simultaneously or subsequently, coordinates of pass points are calculated  Analytical procedures have been developed which can simultaneously enforce collinearity conditions onto units which consist of hundreds of photographs  The ultimate extension of the principles is to adjust all photogrammetric measurements to ground control values in a single solution known as a bundle adjustment  The bundles from all photos are adjusted simultaneously so that corresponding light rays intersect at positions of the pass points and control points on the ground  The process is an extension of the principles of analytical photogrammetry, applied to an unlimited number of overlapping photographs Aerotriangul IOE Pashchimaanchal campus Aerotriangul IOE Pashchimaanchal campus Aerotriangul IOE Pashchimaanchal campus Aerotriangul IOE Pashchimaanchal campus Aerotriangul IOE Pashchimaanchal campus Aerotriangul IOE Pashchimaanchal campus Aerotriangul IOE Pashchimaanchal campus Aerotriangul IOE Pashchimaanchal campus Aerotriangul IOE Pashchimaanchal campus Aerotriangul IOE Pashchimaanchal campus Aerotriangul IOE Pashchimaanchal campus Aerotriangul IOE Pashchimaanchal campus Aerotriangul IOE Pashchimaanchal campus Aerotriangul IOE Pashchimaanchal campus Block Adjustment with Added Parameters (Self-calibration) Camera calibration was formerly performed as a separate procedure Interior orientation parameters of the camera were determined and held constant during the triangulation procedure Image coordinate measurements were assumed to be corrected for systematic effects before adjustment, e.g. lens distortion, atmospheric refraction Assumption: Image measurements are uncorrelated Presence of random errors only, NO systematic errors Aerotriangul IOE Pashchimaanchal campus Block Adjustment with Added Parameters (Self-calibration)  Systematic errors also exist under operational conditions as part of the solution  Such errors exist due to change in environmental conditions between the calibration laboratory and operational environment  Not always feasible to calibrate the camera in a laboratory;  e.g. non-metric camera used in close range photogrammetry and UAV applications  Navigational sensor like INS have systematic drifts that increases with time  Though overall characteristics are known, exact amount of drift can not be determined in advance and must be part of the solution Aerotriangul IOE Pashchimaanchal campus Block Adjustment with Added Parameters (Self-calibration)  Principal point coordinates and focal length used in Collinearity equation can be treated as additional unknowns  Refined image coordinates could be replaced by unrefined image coordinates  The problem with naively solving for interior orientation parameters:  NOT enough geometric information to separate the effects of parameters  Parameters are correlated: choosing a value for one parameter fixes the value of other. E.g. infinite # of combinations for ‘f’ and ‘H’  Same applies to aerial triangulation with added parameters Aerotriangul IOE Pashchimaanchal campus Block Adjustment with Added Parameters (Self-calibration)  Parameters must be carefully chosen in self calibration  Image acquisition geometry must be designed to minimize correlation  Several formulations of self calibration parameters have been proposed  They are based on first modeling known systematic errors, such as lens distortion, principal distance error, or principal point offset  Additional terms are added to cover general deformations Aerotriangul IOE Pashchimaanchal campus Block Adjustment with Added Parameters (Self-calibration) A set of added parameters proposed by Brown (1976): x and y are image coordinates c = principal distance a1-21 = added parameters ∆x and ∆y are the corrections Aerotriangul IOE Pashchimaanchal campus Block Adjustment with Added Parameters (Self-calibration) Self calibration parameters may apply to Individual images Flight lines Sub-blocks Entire block This may be done if more than one camera was used, flights were made on different days or under different conditions Proper design with highly redundant photo coverage is crucial for successful use of self calibration For aerial Photography: 60% side overlap Uses unified Least Square method, a priori weights can be applied to the added parameters to control and stabilize the solution Aerotriangul IOE Pashchimaanchal campus Evaluation of Block Adjustment Statistical Evaluation Used to evaluate block adjustment output Evaluation in 3 different accepts- Precision, accuracy and reliability. Each evaluated with appropriate statistical techniques- assure id the solution is valid. 1. Precision: - The precision of the solution by examining the covariances of the parameters. variance of a parameter - specifying the spread of its value A perfectly known parameter would have a zero variance, while a completely unknown parameter would have infinite variance. Aerotriangul IOE Pashchimaanchal campus Evaluation of Block Adjustment we usually prefer to speak in terms of the standard deviation, which is the square root of the variance and has the same units as the parameter. One of the products of a least squares adjustment is the covariance matrix of the parameters. The diagonal elements of the covariance matrix are the parameter variances. and the off-diagonal elements are the covariances between the parameters. For example, a covariance matrix for a point's X, Y, and Z ground coordinates might be Aerotriangul IOE Pashchimaanchal campus Evaluation of Block Adjustment 2. Accuracy A fundamental requirement for a block adjustment is that it be accurate, so that the results from the block adjustment reflect the actual state of the world. Accuracy cannot be determined by examining the solution, since a solution can be very consistent within itself (very precise, as discussed in the previous section), but still not be accurate An external comparison is required to determine accuracy. Block adjustment accuracy is evaluated using check points whose world coordinates are known but which were not used as control in the solution. The root mean square of the differences between the computed coordinates and the known values provides a measure of the solution accuracy. If only a few check points are available, it may be possible to repeat the adjustment using some control points as check points and some check points as control points Aerotriangul IOE Pashchimaanchal campus Evaluation of Block Adjustment 3. Reliability Important consideration-Statistical Evaluation Resistance to gross errors, blunders in input Bad inputs- solution is compromised or completely invalidation Bad data – checked with redundant observations Blunders- detected by examining the residuals for each observations Robust estimation with least square method- valuable editing large datasets having blunders. Block adjustment-multiple image rays-complicated geometry Detection of weak configurations difficult Inspection of individuals residuals- also complicated Statistical measure- quantify the susceptibility of each residual to measurement error- Establish criteria for individuals measurement based on residuals Aerotriangul