Tilted Photography

None of the equations given above is valid for oblique photographs with non-vertical optical axes, because the scale varies with the magnitude and angular orientation of the tilt (Fig. 3-3). The magnitude of the tilt is expressed by the nadir angle v, which is the angle between the optical axis and the vertical line through the perspective center (nadir line) and is the complement of depression angle. Topographic relief introduces additional scale variations and radial distortions relative to the nadir point n—much the same as for true vertical photographs (see Fig. 3-2), where n is identical with the principal point or image center o. Oblique images are useful for providing overviews of an area and they are easier to understand and interpret for most people (see Chapter 2). However, obliqueness undermines the validity of many principles and algorithms used in photogrammetry. Oblique photographs therefore usually are avoided for measurement purposes, and images are classified according to their degree of tilt from vertical (see Fig. 2-2).

• True vertical: v = 0°, often difficult in practice (especially with typical SFAP platforms).

• High oblique (usually v > 70°, horizon visible).

True Vertical Photograph

FIGURE 3-3 Low-oblique photograph taken over completely flat terrain. The vertical line through the perspective center L intersects the image plane at the photographic nadir point n and meets the ground in a right angle at the ground nadir point N. The angle between the nadir line and the optical axis is the nadir angle v. Note that the distances D between all points on the ground are the same, but the corresponding distances d on the image vary continually.

FIGURE 3-3 Low-oblique photograph taken over completely flat terrain. The vertical line through the perspective center L intersects the image plane at the photographic nadir point n and meets the ground in a right angle at the ground nadir point N. The angle between the nadir line and the optical axis is the nadir angle v. Note that the distances D between all points on the ground are the same, but the corresponding distances d on the image vary continually.

Aerial Photographs With Fiducial Mark

FIGURE 3-4 Top right corner of an aerial photograph taken with a conventional analog (film) metric camera, showing one of four fiducial marks (see enlarged insert) composed of a dot, cross and circle. The text block on the left indicates lens type, number, and calibrated focal length in mm; the mechanical counter records the sequential image number.

FIGURE 3-4 Top right corner of an aerial photograph taken with a conventional analog (film) metric camera, showing one of four fiducial marks (see enlarged insert) composed of a dot, cross and circle. The text block on the left indicates lens type, number, and calibrated focal length in mm; the mechanical counter records the sequential image number.

For many practical applications, the errors resulting in simple measurements from slightly tilted images (v < 3°) can be considered negligible, but this is not the case with oblique images.

come with calibration reports. However, they may be calibrated by dedicated companies or institutions or even by the user with test-field calibration or self-calibration methods (see also Chapter 6.6.5).

3.2.3. Interior Orientation

The geometrical principles and equations mentioned above are sufficient for simple measurements from analog or digital photographs. For the precise calculation of 3D coordinates, however, the paths of rays both within and outside the camera need to be reconstructed mathematically with high precision (see also further below, Fig. 3-12). The necessary parameters for describing the geometry of the optical paths are given by the interior and exterior orientations of the camera.

The interior orientation of an aerial camera comprises the focal length (measured at infinity), the parameters of radial lens distortion, and the position of the so-called principal point in the image coordinate system. The principal point (o) is defined as the intersection of the optical axis with the image plane and falls quite close to the origin of the image coordinate system at the image center. For measurements within the image, this coordinate system has to be permanently established and rigid with respect to the optical axis. For metric analog cameras this is realized with built-in fiducial marks that protrude from the image frame and are exposed onto each photograph (Fig. 3-4). For 35-mm film cameras, fiducials do not normally exist unless the camera has been specially fitted with them (Fig. 3-5). Digital cameras do not need fiducials because a Cartesian image coordinate system is already given by the pixel cell array of the image sensor.

Various camera calibration methods exist for the determination of interior orientation values (Fraser, 1997; Wolf and Dewitt, 2000). While metric cameras are usually calibrated with laboratory methods by the manufacturer, off-the-shelf small-format cameras as used in SFAP do not

3.2.4. Exterior Orientation

The exterior orientation includes the position X, Y, Z of the camera in the ground coordinate system and the three rotations of the camera u, f, k relative to this system. The elements of exterior orientation can be determined theoretically with modern high-tech GPS/INS systems simultaneous to image acquisition, but this is hardly an option for SFAP owing to the associated costs, weights, and insufficient precisions. The commonly used method of determining exterior orientation is the post-survey reconstruction using ground control points (GCPs) with known X, Y, and Z coordinates. A theoretical minimum of three GCPs is

Photomodeler
FIGURE 3-5 35-mm transparency taken with an analog Pentax SLR camera fitted with additional fiducial marks (PhotoModeler plastic film plane inserts). Archaeological excavations at Tell Chuera settlement mound, northeastern Syria. Kite aerial photograph taken by IM and J. Wunderlich, September 2003.

required for the orientation of a single photograph—in practice, multiple photographs are usually oriented together using least-squares adjustment algorithms (see section on bundle adjustment below) which allows the use of less than three points per image.

The precision and abundance of GCPs are crucial for the precision of the exterior orientation. Standard GPS measurements or control points collected from maps are useful enough for working with small-scale traditional airphotos and satellite images, but SFAP imagery with centimeter resolution and quite large scale requires accordingly precise ground control (Chandler, 1999). Usually this has to be accomplished by pre-marking control points in the coverage area and determining their coordinates using a total station survey (see Chapter 9).

3.3. GEOMETRY OF STEREOPHOTOGRAPHS

3.3.1. Principle of Stereoscopic Viewing

Distorting effects of the central perspective are usually undesirable for the analysis of single photographs, but they also have their virtues. Because the magnitude of radial distortion is directly dependent on the terrain's elevation differences, the latter can be determined if the former can be measured. We make use of this fact in daily life with our own two eyes and our capability of stereoscopic viewing. People with normal sight have binocular vision, that is, they perceive two images simultaneously, but from slightly different positions which are separated by the eyes' distance (the eye base B, Fig. 3-6).

When the eyes focus on an object, their optical axes converge on that point at an angle (the parallactic angle g). Objects at different distances appear under different paral-lactic angles. Because the eye's central perspective causes radial distortion for objects at different distances, quite similar to the effects of mountainous terrain in airphotos, the two images on the retinae are distorted. The amount of displacement parallel to our eye base, however, is not equal in the two images because of the different positions of the eyes relative to the object. This difference between the two displacement measures is the stereoscopic parallax p. The stereoscopic parallax and thus 3D perception increase with increasing parallactic angle g, making it easier to judge differences in distances for closer objects.

Stereoscopic vision also may be created by viewing not the objects themselves but images of the objects, provided they appear under different angles in the images (Fig. 3-7). By viewing the image taken from the left with the left eye and the image taken from the right with the right eye, a virtual stereoscopic model of the image motif appears where the lines of sight from the eyes to the images intersect in the space behind. Although it is possible to

Stereoscopic Parallax

parallax p

FIGURE 3-6 Stereoscopic parallax for points at different distances in binocular vision. The differences of the angles of convergence g result in different distances of A and C projected onto each retina. Their disparity, the differential or stereoscopic parallax, is used by the brain for depth perception. After Albertz (2007, fig. 111, adapted).

parallax p

FIGURE 3-6 Stereoscopic parallax for points at different distances in binocular vision. The differences of the angles of convergence g result in different distances of A and C projected onto each retina. Their disparity, the differential or stereoscopic parallax, is used by the brain for depth perception. After Albertz (2007, fig. 111, adapted).

Karin Albertz

Left eye

FIGURE 3-7 Stereoscopic viewing of overlapping images showing the same object under different angles. A three-dimensional impression of the object—a stereomodel—appearing in the space behind the images is perceived by the brain. After Albertz (2007, fig. 111, adapted).

Left eye

FIGURE 3-7 Stereoscopic viewing of overlapping images showing the same object under different angles. A three-dimensional impression of the object—a stereomodel—appearing in the space behind the images is perceived by the brain. After Albertz (2007, fig. 111, adapted).

achieve this without the aid of optical devices, just by forcing each eye to perceive only one of the images and adjusting the lines of sight accordingly, it is difficult especially for larger photographs and may cause eye strain. Devices like lens or mirror stereoscopes (for analog images), anaglyph lenses (for both analog and digital anaglyphs, i.e. red/blue-images), or electronic shutter lenses (for stereographic cards and computer screens) make stereoviewing much easier and also provide facilities for zooming in and moving within the stereoview (see Chapter 11.5.1).

For any stereoscopic analysis, the images need to be orientated so they reflect their relative position at the moment of exposure. The direction of spacing between the images needs to be parallel to our eye base, because only the x-component of the radial distortion vector is different in the two images, effectuating stereoscopic (or x-) parallax. The amount of distortion in y-direction is the same in both images and needs to be aligned perpendicular to our eye base. This alignment procedure can be as simple as wiggling two photo positives under a lens stereoscope until they merge into a stereomodel (for using SFAP images under a stereoscope see Chapter 11.5.1). Or it may be as laborious as identifying hundreds of tie points in a series of digital images in order to compute the exact relative orientation of a large number of neighboring stereopairs prior to establishing their precise position in space as a prerequisite for the automatic extraction of digital terrain models (see following sections).

Champion Flash Photography

Champion Flash Photography

Here Is How You Can Use Flash Wisely! A Hands-on Guide On Flash Photography For Camera Friendly People!. Learn Flash Photography Essentials By Following Simple Tips.

Get My Free Ebook


Post a comment