Scale, Relief Displacement and Parallax - Concept Map
Photogrammetric Height Determination from Aerial Photos
Related concepts
Photographic Scale
Sub concepts
- Representative Fraction (RF)
- Principal Scale (at datum level)
- Scale variation with terrain elevation
- Scale calculations from flying height and focal length
Relationship to central
Foundation for understanding how image dimensions relate to ground reality; essential for interpreting displacement and parallax measurements
Relief Displacement
Sub concepts
- Radial displacement direction
- Displacement formula: d = rh/H
- Principal point as displacement origin
- Height extraction: h = dH/r
- Maximum displacement at photo edges
- Zero displacement at principal point
Relationship to central
Primary method for determining object heights from single vertical photos; caused by vertical separation from datum
Stereoscopic Parallax
Sub concepts
- Absolute parallax (P)
- Parallax difference (Δp)
- Flight line measurement direction
- Height formula: h = HΔp/(P+Δp)
- Parallax bar measurements
- Stereo model orientation
Relationship to central
Alternative height determination method using two overlapping photos; basis for stereoplotters and digital photogrammetry
Geometric Relationships
Sub concepts
- Similar triangles principle
- Radial line geometry
- Central projection perspective
- Photo coordinate systems
- Flying height above datum
Relationship to central
Mathematical foundation explaining why displacement and parallax occur; connects image geometry to 3D space
Practical Applications in Philippine Surveying
Sub concepts
- Digital elevation model (DEM) generation
- Orthophoto production
- Land classification (CA 141)
- Building height verification
- Terrain profile determination
Relationship to central
Real-world implementation in PRS92 datum and PPCS mapping; regulatory compliance under RA 4374 and RA 8560
Measurement Techniques
Sub concepts
- Radial distance measurement (r)
- Displacement measurement (d)
- Parallax bar usage
- Micrometer measurement
- Digital coordinate extraction
- Image correlation methods
Relationship to central
Practical methods for extracting numerical values from photos and stereo pairs
Error Sources and Limitations
Sub concepts
- Flying height uncertainties
- Measurement precision limits
- Tilt and swing effects
- Atmospheric refraction
- Image resolution constraints
Relationship to central
Critical understanding for quality assurance and interpretation of photogrammetric height data
Concept connections
- Relief DisplacementPhotographic ScaleRelief displacement magnitude depends on object height relative to scale; scale variation with elevation affects interpretation
- Relief DisplacementGeometric PrinciplesRelief displacement is direct result of central projection geometry; similar triangles explain the mathematical relationship
- Stereoscopic ParallaxPhotographic ScaleParallax measurement scale depends on flying height and focal length; affects precision of height calculations
- Stereoscopic ParallaxGeometric PrinciplesParallax arises from baseline difference between two camera positions; 3D similar triangles explain height formula
- Relief DisplacementMeasurement TechniquesAccurate measurement of radial distance and displacement critical for height accuracy; requires careful photo analysis
- Stereoscopic ParallaxMeasurement TechniquesParallax bar and digital correlation methods are primary tools; measurement precision directly affects height precision
- Relief DisplacementError Sources and LimitationsFlying height uncertainty, focal length error, and tilt distortion directly propagate to height error via formula
- Stereoscopic ParallaxError Sources and LimitationsAbsolute parallax measurement error and atmospheric refraction affect stereo height accuracy; baseline uncertainty critical
- Relief DisplacementPhilippine ApplicationsUsed for rapid building height verification and DEM generation for CA 141 land classification under PRS92 datum
- Stereoscopic ParallaxPhilippine ApplicationsPrimary method for generating digital elevation models and orthophotos referenced to PRS92; basis for modern mapping under RA 4374
- Photographic ScaleGeometric PrinciplesScale is inverse of flying height in perspective geometry; both scale and geometry relate image distance to ground distance
- Geometric PrinciplesMeasurement TechniquesUnderstanding perspective geometry guides proper measurement methodology and explains why certain techniques work
Diagrams
Complete Concept Map: Scale, Relief Displacement and Parallax
Comprehensive mind map showing the hierarchical organization of all key concepts in the Scale, Relief Displacement and Parallax chapter. The central concept (Photogrammetric Height Determination) branches into seven major domains: Relief Displacement, Stereoscopic Parallax, Photographic Scale, Geometric Principles, Philippine Applications, Measurement Techniques, and Error Analysis. Each domain contains specific sub-concepts and technical parameters relevant to PRC licensure examination preparation.
Relief Displacement Height Determination Workflow
Step-by-step workflow for determining object heights using relief displacement from a single vertical photo. Begins with photo preparation and principal point location, proceeds through distance and displacement measurements, incorporates flying height verification, and concludes with height calculation and datum reference. Includes decision points for quality verification and error checking.
Stereoscopic Parallax Height Determination Workflow
Complete workflow for determining heights using stereoscopic parallax from overlapping photo pairs. Includes stereo model setup, absolute parallax measurement at reference points, parallax difference measurement for target objects, height calculation using the parallax formula, and final datum referencing. Essential for DEM generation and modern digital photogrammetry applications.
Formula Selection and Problem-Solving Logic
Decision tree for selecting the appropriate formula and method based on available measurements and problem requirements. Guides students through distinguishing between relief displacement and parallax problems, identifying which variable needs to be solved for, and understanding key conditions for each formula application.
Physical Geometry: Why Relief Displacement Occurs
Conceptual explanation of the geometric principles underlying relief displacement. Shows why displacement occurs (perspective geometry of vertical photography), why it is zero at the principal point, why it increases radially outward, and how the similar triangles principle leads to the mathematical formula. Essential for understanding rather than memorizing.
Physical Geometry: Why Stereoscopic Parallax Occurs
Conceptual explanation of stereoscopic parallax geometry. Shows how the same ground point appears at different image coordinates on left and right photos due to the camera's position shift (baseline), why closer objects show larger parallax differences, and how the similar triangles relationship in 3D leads to the height calculation formula. Builds intuition for parallax-based height determination.