Basics of Photogrammetry Note#6

Transcription

1 Basics of Photogrammetry Note#6 Photogrammetry Art and science of making accurate measurements by means of aerial photography Analog: visual and manual analysis of aerial photographs in hard-copy format such as photographic prints (9x9in) or positive transparency, with the aid of mechanical and/or optical instruments. Analytical or digital: computer aided analysis of digitized aerial photographs Measurements from Single Vertical Photograph Scale of photograph Object height Object length Area of an object Perimeter of an object Color/tone of an object Measurements from Stereoscopic Photographs Precise planimetric (x, y) position of an object Precise height Orthophotographs with planimetrically accurate position Contours DEMs Flight procedures for stereo coverage Aerial camera exposures are controlled by an intervalometer; Each vertical aerial photograph overlaps the next photograph in the flightline by approximately 60% forward overlap. This is referred to as stereoscopic overlap A 20-30% sidelap for adjacent flightlines. Multiple flights lines with sidelap are commonly referred to as a block of aerial photography. Number of flight lines W NL + 2 D S g where W is width of study area, D is lateral ground distance of single photo, Sg is sidelap gained by each successive flight line. 2 is the number of extra flight lines added to the sides of the study area to assure total coverage. Number of photos per flight line L NP + 4 D O g where L is length of study area, D is lateral ground distance of single photo, Og is overlap gained by each successive photo. 4 is the number of photo added to assure total coverage. 1

2 Basic concepts of Vertical Photographs Fiducial marks There are 4 or 8 fiducial marks on the aerial photograph margin in order to locate the principal point Principal point Geometric center of photograph. It is the intersection point between lines that link the opposite fiducial marks; It is the nadir of the optical axis of the camera during the instant of exposure. Conjugate Principal point The corresponding location of a principal point on each of two adjacent aerial photographs. The actual flight line can be determined by drawing a line through the principal points and conjugate principal points. Photo base Distance between principal point and conjugate principal point measured on a single photograph. Ground (air) base Ground (air) distance between principal points of overlapping photographs. Geometry of Vertical Aerial Photography Positive prints, transparency or digitized image are used in the analysis The photographic coordinate x radiates from the principal point and run along the flight line, and the y axis is radiates from principal point and perpendicular to the flight line. Determination of Airphoto Scale Scale can be represented by Representative Fraction (RF), graphic bar, or verbal statement. Based on focal length and flight altitude: f scale (1) H Based on photo distance and ground distance d photo scale (2) d ground Ground distance can be measured by using GPS, topographic map Variation of photo scale The scale depends on the average height above the ground. In rugged terrain, photo scale varies because of large height differences within the photograph. Likewise oblique or non-vertical photos also display scale variation. Because of the single-point perspective nature of photography, objects toward the edge of a photograph suffer relief displacement. Tall objects appear to lean away from the photo center; low objects are displaced toward the center. Relief displacement is minimal near the photo center and becomes extreme at the photo edge. This allows for a "side view" of tall objects near the edge of the photo. f scalemin H h min 2

3 f scalemax H hmax f scaleavg H havg Ground Coverage of Aerial Photograph W photo W ground S photo W ground : width of ground coverage, W photo : width of aerial photo S photo : Scale of aerial photo Monocular Depth Perception There are clues to the depth of field of objects that can be perceived/appreciated monocularily. Monocular or one eye depth perception deals with in-born cues that humans instinctively employ when viewing objects. There are limits, however, to monocular depth perception. Object Height Measurement From Single Aerial Photographs 1) Relief Displacement Method Relief displacement Any objects that are higher or lower than the principal point are displaced from its true planimetric (x,y) location on a vertical aerial photograph. This displacement is referred to as relief displacement or terrain distortion. The relief displacement is outward from the principal point for objects whose elevations are above the local datum, and toward the principal point for objects whose elevation are below the local datum. The direction of relief displacement is radial from the principal point. Height from Relief Displacement d h r Where h is height of the object referenced to the local datum; H is the altitude above the local datum; d is object length from base to top on the image, namely, relief displacement; r is radial distance from the photo nadir (principal point) to the top of the object. Conditions for Relief Displacement Method Aerial photographs must be vertical or near vertical (<3 of tilt). Namely, the principle point is the photo nadir; The top and the bottom of the object are visible The object is on level base and vertical. H 2) Shadow Height Method: Simple trigonometry where θ is the sun elevation angle, L is the shadow length, h L tanθ 3

4 Sun elevation angle The sun angle above local horizon can be derived using a solar ephemeris table, given the latitude and longitude of the site and the photograph acquisition date and time. Conditions The shadow on which the ground falls is level The object is vertical. 3-D Photography Stereo viewing: vertical exaggeration Stereoscopes: a stereo pair of photographs taken from slightly different viewpoints can be viewed through a stereoscope to perceive 3-D view. Stereo coverage: 60% overlapping area of the adjacent photographs Stereoscopy Stereoscopy is the science and art that deals with the use of binocular vision for the observation of overlapping photographs or other perspective views and the method by which such views are produced. Essentially most of us have the ability to see and appreciate depth of field through the perception of parallax. Binocular Vision With binocular vision each eye sees a different picture and the brain fuses the two images into one. Depth Perception The normal interpupillary distance (eye base) in humans is 2.5 to 2.6 inches (63-69mm). If we could increase this distance we would increase our perception of depth. Stereo pairs greatly stretch this normal eye base (interpupillary distance) and generate the exaggerated 3-D photographic effect we perceive when viewing the stereo pairs. Stereoscopic Viewing method 1) Keeping the lines of sight parallel with the aid of a stereoscope 2) Keeping the lines of sight parallel with the aid of a stereoscope Situates the overlapping portion of two stereo photographs adjacent to one another Position the head about 8 in from the photographs Let the eyes relax as if they were looking at infinity Gradually the mind will fuse the two stereoscopic images into athird image in the middle of the two stereo images 3) Crossing the eyes and reversing the order of the stereoscopic images 4) Using anaglyphic or polarizing glasses Parallax Parallax is the apparent displacement in the position of an object when viewed or photographed from different vantage points It is the basis for 3-D stereoscopic vision as well as 3-D photogrammetry. Parallax Height Measurement from Stereo Photo Pair Absolute X-Parallax 4

5 Considering a pair of aerial photographs, the absolute parallax of a pint is the algebraic difference of the distances of this point on two images from their respective photo principal points (PPs) measured in a horizontal plane and parallel to the air base. All objects in an image at the same altitude will have the same amount of x parallax. Differential Parallax The difference in the absolute stereoscopic x-parallaxes of two points imaged on a stereo pair of photographs. This is usually employed in the determination of the differences in the elevation of objects. Almost all topographic maps are made based on the measurement of differential parallax. Height Determination from Differential Parallax This is the most used method of measuring heights on air photos. dp h H P + dp Where h is the height of the object of interest; H is the altitude of aircraft above the local datum; P is the absolute stereoscopic parallax at the base of the object dp is the differential parallax between the base and top of the object. Note: for the convenience and ease of measurement, the average photo airbase of a stereopair is commonly substitutes as the absolute stereoscopic parallax (P) in the computation. Calculation Steps 1) Determine the altitude of the aircraft above the ground level. 2) Locate the principal point (PP) on each of the photographs by drawing lines through the opposing four fiducial marks on each photograph. 3) Find the conjugate principal point (CPP) on both photos by locating the position of each photo s principal point on the other photograph. 4) Position the photographs along the flightline by aligning the PP and CPP of each photograph so that they are in a straight line. This represents the line of flight. 5) Determine the average photo air base (absolute stereoscopic parallax, P). Namely measure the distances between the PP and CPP ob each photograph and then take the average. 6) Measure the differential parallax (dp) between the base and top of the object. The parallax of the top and the parallax of the base of the object can be measured from the fiducial line using a ruler Conditions: Photo tilt is less than 3 ; The two adjacent photographs in the stereo pair must be acquired from approximately the same altitude above the ground. The principal point (PPs) of both photographs must lie at approximately the same elevation above the ground level The base of the object is at approximately the same altitude as that of the PPs. Products Derived from Vertical Stereo Aerial Photographs Contour Maps Using an optical stereoplotter, contours can be traced. 5

6 Floating marks can be placed at the top of an object and the parallax of the point can be read. If the floating marks (fused, red three-dimensional ball) were moved around the stereo model so that it maintained contact with terrain, namely, it was not allowed float above the terrain or below the terrain, then the line of the constant stereoscopic x-parallax would be derived. When drawing contours, the floating mark is located on the ground at the desired elevation. An attached pencil is lowered from the tracing table, and the operator traces a contour onto the map sheet by moving the entire tracing over the map while keeping the floating mark on the ground within the stereo model. DEMs Measure the differential parallax for a dense set of points, and then interpolate them into a regular array of elevation values Orthoretification and orthoimages Orthographic projection With the orthographic projection of a map, all features are located in their correct horizontal positions and are depicted as through they were each being viewed from directly overhead. Only the base (or top) of an object can be seen and represented by a map (with orthographic projection) Central (perspective) projection As in the vertical aerial photograph, all objects are positioned as if they were being viewed from the same point Most ground objects are shifted or displaced from their correct planimetric positions due to the relief displacement. Orthorectification Uncorrected aerial photographs are not maps. They are single-point perspective views of the Earth's surface, whereas maps are orthogonal representations of the surface. Sizes, shapes, and positions of objects are distorted in raw aerial photographs. However, aerial photographs can be used to construct maps and to accurately measure distances, heights and elevations. The effects of topographic relief displacement and distortions induced by the variation in altitude, speed, and attitude of the platform are removed in orthoimagery, resulting in a planimetrically correct (x,y) positions of image pixels. This allows to use orthoimages like maps for making direct measurements of geographic location, distances, direction (angles) and areas on images Airphoto Mosaick Mosaic Typically the aircraft flies back and forth across an area acquiring a set of photos that overlap. Often it is necessary to create a mosaic of several airphotos to cover the desired area by scanning, rectifying, and assemble individual images. An airphoto mosaic is an assemblage of two or more overlapping photographs that form a continuous representation, a composite view of the area covered by the individual photos. 6

7 To create a mosaic, individual images must be registered to the same geographic datum and map projection. Aerial photographs have a "roll off" of intensity across the photo, and also change chroma due to lens refraction. In other words, the photos often appear darker towards the edges, and have a subtle color shift from the center to the edges. In order to mosaic aerial photographs with no visible seams, these artifacts must be removed. Histogram matching and feathering techniques can be used to minimize seams in mosaics. Feathering The process of blending the data values in areas where two datasets overlap so that they gradually transition (or "feather") from one to the other. Feathering works by progressively blending, or averaging, the data values between two images in the zone where they overlap. Feathering can also be effective to hide small misalignments between features on adjacent images and to help them appear to be one continuous image. Radiometric (color) balancing Histogram matching method is often used for color balancing operation. For each color layer, the histogram of each individual aerial photograph is modified to match the specified histogram. Reading Assignment: Chapter 6 in Jensen, J.R Remote Sensing of the Environment: An Earth Resource Perspective. Upper Saddle River, NJ, Prentice Hall. 544 pp. 7