Lecture 12 Content Stereoscopic parallax 4/23/2017 GEM 3366

Nadir and Isocenter on a photo Nadir: point vertically beneath the camera lens at the time of exposure (where a plumb line extended from the camera lens to the ground intersects the photo image) Isocenter: point on the photo that falls on a line approximately halfway between the principal point and nadir Principal Point Nadir Isocenter 4/23/2017 GEM 3366

K-Factor The ratio of the air base length to the altitude at which a pair of aerial photographs were taken (i.e. B:H) B O1 O2 H Terrain 4/23/2017 GEM 3366

Stereoscopic parallax Parallax is the distance between images of the same object on the two photographs forming a stereopair A1 A2 A2 px z py y A1 x 4/23/2017 GEM 3366

Using one eye, a person’s perception of depth is hampered Stereoscopy refers to the ability to perceive the object space in three dimension using your two eyes Using one eye, a person’s perception of depth is hampered Using one eye  monocular viewing Using two eyes  binocular viewing Binocular viewing allows the viewing from two different locations due to the separation between the eyes (eye base) 4/23/2017 GEM 3366

Convergence angle b L R H1 Φ1 H2 P1 h Φ2 P2 Because angle Φ1 is larger than Φ2 the observer will perceive point P1 as closer than point P2 difference in distance from observer, (H2-H1=h) is a function of the difference in convergence angle, Φ1- Φ2 4/23/2017 GEM 3366

Comparing binocular and stereoscopic viewing Φ1 Φ2 b L R P1 H1 H2 h b Φ1 Φ2 L R h Convergence Angle Stereoscopic Viewing 4/23/2017 GEM 3366

Angle Φ is called the parallactic angle and its linear equivalent is called parallax Assuming no tilts, both photos are taken at the same altitude, and any rotation of the camera from one photo is accommodated by replacing the fiducial system of axis by another, then the x parallax (or simply parallax) is defined by: P =x-x´ Where x and x´ are the coordinates on the left and right photographs 4/23/2017 GEM 3366

Stereoscopic parallax enables perception of height differences This is defined by the x-parallax Y-parallax once removed, defines the straight line between two consecutive photos 4/23/2017 GEM 3366

Height difference using parallax Datum p a x f x´ (H-h) Air Base = B c1 c2 E E´ A h a´ 4/23/2017 GEM 3366

Photos are H above the datum Point A is h above the same datum Coordinates x and x´ are defined by the location of a and a´ on image using the principal point on each photo as the origin That is C1a´ is equal to x´ Parallax (p) is given by x - x´ and is the line segment a´a 4/23/2017 GEM 3366

∆ aa´E and ∆ EE´A are similar: Datum p a x f x´ (H-h) Air Base = B c1 c2 E E´ A h a´ ∆ aa´E and ∆ EE´A are similar: To determine elevation of point A requires: Flying height Value of air base Camera focal length 4/23/2017 GEM 3366

Ground Coordinates formulae: Determining the ground coordinates of a point with respect to an arbitrary coordinate system whose origin is vertically below the left exposure station and with a positive X in the direction of flight Flight direction E Air Base = B E´ f f c1 x c2 a´ p x´ a´ a (H-h) XA O A h Datum 4/23/2017 GEM 3366

Triangles EOA & EC1a are similar Coordinate for A is (XA,YA) using the arbitrary coordinate system: (x is the distance on the photo for point “a”) Datum p a a’ x f x´ (H-h) Air Base = B c1 c2 E E´ A h a´ O XA Flight direction Substituting for h (derived before), we get: 4/23/2017 GEM 3366

Recall scale (S) at a point of elevation is given by: Substituting for h which is defined by the parallax height equation into the scale equation gives: This is the map scale defined as a function of the parallax and air base 4/23/2017 GEM 3366

Parallax Measurement (Manual method) Two photographs are fastened to a base aligned along the flight line The flight line is derived by locating the principal points of the two photographs. Each photo with have two points (one for its principal point and the other principal point for the neighboring photo). Connecting these four points a straight line will be formed which is indicative of the flight line Parallax can then be measure from a single measurement using a parallax bar (Such a bar measures the linear distances at a very high accuracy) The distances measured are used in the equations derived previously Once the photographs are properly secured and is in line with the flight line, the distance between the two principal points between the two photographs is measured and noted Parallax is then measured off by selecting identifiable common points on the two photographs 4/23/2017 GEM 3366

Negative ‘x’ distance from the principal point Positive ‘x’ distance from the principal point 4/23/2017 GEM 3366

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