GELE Photogrammetry & Cartography — Stereoscopy, DEM and OrthophotoStudy Notes

Stereoscopy is the process of viewing two overlapping photographs taken from slightly different positions (successive camera exposures) to perceive a three-dimensional model of the terrain. The human visual system fuses these two images into a single three-dimensional percept—a process called stereoscopic fusion. In aerial photogrammetry, the two photographs are aligned so that corresponding features on the left and right images can be identified and measured. The key principle is **parallax**: the apparent shift of objects between the two images due to the change in viewpoint. Objects at different heights show different parallax values; this parallax difference is directly proportional to the object's elevation and is the basis for height determination in photogrammetry. For stereoscopic viewing to work effectively, the two photographs must have substantial overlap. In aerial survey practice, **forward overlap** (overlap along the flight line) is typically 60%, meaning that 60% of each photograph overlaps with its adjacent photograph. This 60% overlap is a standard established through decades of practice because it provides adequate stereoscopic base while maintaining efficient survey coverage. Additionally, **sidelap** (overlap between adjacent flight lines) is usually 20–30% to ensure seamless coverage of the survey area. The geometry of the stereo pair is characterized by the **air-base B** (the distance between two successive camera positions in the air) and the **flying height H** (the height of the aircraft above the terrain). These two quantities define the **base-height ratio B/H**, which is a critical parameter controlling the geometric strength of the stereoscopic model.

The **base-height ratio (B/H)** is the ratio of the air-base B to the flying height H above terrain. This ratio is the single most important parameter controlling the **vertical exaggeration** (or stereoscopic exaggeration) and **height-measurement precision** of a stereo model. Mathematically: $$\frac{B}{H} = \frac{\text{air-base (m)}}{\text{flying height above terrain (m)}}$$ A larger B/H ratio means the stereo base is longer relative to the height, producing a stronger geometric configuration for height measurement. Conversely, a small B/H ratio (e.g., 0.2) means the base is short, and the stereo geometry is weak—small errors in parallax measurement cause large errors in height. **Vertical Exaggeration**: When B/H is large (e.g., 0.6), the terrain in the stereoscopic model appears vertically exaggerated—hills look steeper and valleys deeper than their true proportions. This exaggeration is sometimes desirable for identifying subtle topography; however, it can also lead to errors if the interpreter does not account for it. The vertical exaggeration factor is approximately equal to (H/B), so a B/H of 0.5 produces roughly 2× vertical exaggeration. For typical aerial survey: - B/H ≈ 0.6 is common for manned aircraft surveys (60% overlap, moderate flying heights). - B/H ≈ 0.3–0.4 is typical for small unmanned aerial vehicles (UAVs/drones) operating at lower altitudes with shorter baselines. - B/H ≈ 0.1–0.2 for satellite stereoscopy (e.g., ASTER, Pleiades) where the base is small relative to orbital height. Height precision improves as B/H increases, but there is a practical limit: if the base is too long, the overlap may be insufficient, or terrain relief may cause image matching problems.

A **Digital Elevation Model (DEM)** is a digital representation of terrain elevation, typically stored as a regular grid (raster) of height values, or alternatively as a Triangulated Irregular Network (TIN). The DEM is a foundational dataset in modern geodetic and cartographic work, used for contour generation, volume calculations, hydrological and viewshed analysis, and orthorectification. **Data Sources for DEM Production**: 1. **Photogrammetry (Image Matching)**: Automated or manual measurement of parallax in stereo pairs yields heights at discrete points (cloud) or dense grid. Photogrammetric DEMs rely on the stereoscopic measurement process described earlier. Modern **Structure-from-Motion (SfM)** techniques using overlapping UAV or terrestrial images can also generate DEMs. Photogrammetric DEMs capture terrain detail where imagery resolution is high; they may have resolution from 1 m to 0.1 m GSD (ground sample distance) depending on camera and flying height. 2. **LiDAR (Light Detection and Ranging)**: An active sensor that emits laser pulses and measures return time to derive 3-D point coordinates. LiDAR is independent of sunlight and can penetrate thin vegetation to measure bare-earth elevation. LiDAR-derived DEMs are often denser and more accurate than photogrammetry, especially in forested terrain. Typical LiDAR DEM resolution: 1–5 m, sometimes 0.5 m in high-spec surveys. 3. **Radar (InSAR, Interferometric Synthetic Aperture Radar)**: SAR satellites (e.g., SRTM—Shuttle Radar Topography Mission) measure phase differences between radar pulses to estimate elevation. InSAR DEMs cover large areas efficiently but may have coarser resolution (~30 m, though newer SAR is finer) and can be affected by layover in steep mountains. SRTM global DEM (~30 m) is freely available and widely used for regional Philippine mapping. 4. **Contour Digitization**: Older DEMs were created by digitizing contours from existing topographic maps, interpolating height between contours. This method is labor-intensive and produces artifacts at contour lines but can be acceptable for low-precision applications. **DEM vs DSM vs DTM**: - **DEM (Digital Elevation Model)**: Bare-earth elevation, excluding buildings and vegetation (the "terrain"). - **DSM (Digital Surface Model)**: Elevation of the surface as encountered by the sensor, including buildings, trees, bridges (the "surface"). - **DTM (Digital Terrain Model)**: Sometimes used synonymously with DEM; represents the bare-earth terrain. Photogrammetry often produces a DSM initially (tops of trees and buildings); filtering algorithms are applied to remove non-terrain features and create a DEM. LiDAR can directly measure both DSM and DEM (the last return gives ground, first return gives canopy top). **DEM Grid Properties**: - **Spatial resolution (pixel size)**: e.g., 1 m × 1 m, 5 m × 5 m, 30 m × 30 m. Finer grids (smaller cells) capture more terrain detail but require more storage and processing. - **Vertical accuracy**: Depends on method and terrain. Photogrammetric: ±0.5–2 m typical. LiDAR: ±0.1–0.5 m typical. Coarse InSAR: ±10–30 m typical. - **Coverage**: Global DEMs (SRTM, ASTER GDEM) at ~30 m resolution; national/regional DEMs at 1–10 m resolution; project-specific DEMs at <1 m. - **Datum and projection**: DEMs should be clearly referenced to a standard datum (WGS84, PRS92 for Philippines) and projection (UTM zone, PCS). **Common DEM Applications in the Philippines**: - Contour line generation for topographic maps (under RA 4374 survey practice). - Volume calculations for excavation, landfill, and quarry projects (CA 141—Cadastral Act requires accurate surveys). - Hydrological analysis: watershed delineation, stream network extraction, flow direction and accumulation. - Viewshed analysis: visibility from communication towers, line-of-sight for microwave links. - Flood modeling: terrain slope and aspect for inundation modeling. - Orthorectification: essential for creating accurate orthophotos (see Section 4).

An **orthophoto** (orthophotograph) is a photograph that has been geometrically corrected (rectified) so that every point on the image is in its correct planimetric (horizontal) position at a uniform scale, removing the effects of relief displacement and camera tilt. Unlike a raw aerial photograph, an orthophoto can be used for direct measurement and mapping, much like a conventional topographic map, while retaining the detail and clarity of a photograph. **Why Raw Photographs Cannot Be Measured Directly**: A raw aerial photograph has variable scale across the image due to two effects: 1. **Relief Displacement**: Terrain elevation variations cause the image scale to change. A point at a higher elevation (e.g., a mountain peak) appears larger and is displaced outward from the principal point compared to a point at lower elevation. The displacement is radial from the principal point and proportional to elevation. This was discussed in detail in earlier chapters on perspective geometry. 2. **Tilt Displacement**: If the camera axis is not perfectly vertical (e.g., due to aircraft attitude), points in the image are displaced according to the tilt. This adds another scale variation across the image. Result: A raw photograph's scale is not uniform—distances measured on the photo are incorrect unless the elevation and tilt are accounted for. The error is typically a few percent for low relief and vertical photography, but can exceed 10–20% in mountainous terrain or with significant tilt. **Orthophoto Production Process**: The orthophoto is created by **resampling** the raw photograph using the DEM (or DTM) and camera orientation parameters: 1. **Establish DEM and Ground Control**: A DEM (from photogrammetry, LiDAR, or other source) covers the area. The raw photograph is georeferenced using ground control points (GCPs) or by direct georeferencing (if camera position and orientation are known from an IMU/GNSS system). 2. **Determine Camera Parameters**: The interior orientation (focal length, principal point offset, lens distortion) and exterior orientation (camera position X₀, Y₀, Z₀ and angles ω, φ, κ) are determined from camera calibration and/or tie points to the DEM. 3. **Back-Projection Onto DEM**: For each output pixel in the orthophoto grid (at a specified coordinate and elevation from the DEM), the algorithm performs **back-projection**: it traces a ray from the camera position through the pixel's ground position and queries the DEM for elevation. The elevation from the DEM is used to reconstruct the ray in the raw image, which determines which pixel from the raw photograph to sample. 4. **Resampling and Interpolation**: The gray level (or color) of the output pixel is obtained by interpolating from the surrounding pixels in the raw image (using nearest-neighbor, bilinear, or cubic convolution). This is done for every output pixel. 5. **Mosaic Assembly**: If multiple photographs cover the area, the individual orthophotos are edge-matched and seamed into an **orthomosaic**—a seamless, consistent base map. **Key Advantages of Orthophotos**: - **Uniform scale**: Can be measured like a map; areas and distances are correct. - **Photographic detail**: Preserves the clarity and recognizability of features compared to a line-drawn map. - **Direct overlay**: Can be overlaid with vector layers (roads, boundaries, utilities) and draped over 3-D models. - **Rapid updating**: Aerial or drone photos can be acquired frequently, so orthomosaics are easy to update. - **Cost-effective**: Faster to produce than traditional line-drawn maps; less labor in feature interpretation if only a backdrop is needed. **Applications in the Philippines**: - **Cadastral surveys** (CA 141): Orthomosaics serve as base maps for property boundary verification and record updating. - **Land-use mapping** (RA 7160, Local Government Code): Urban planners use orthomosaics to identify unauthorized structures, land-use changes. - **Infrastructure planning** (RA 7942, Mining Act; RA 9275, Clean Water Act): Orthomosaics are used to plan roads, pipelines, environmental monitoring sites. - **Disaster response** (RA 10121, Disaster Risk Reduction Act): Post-flood or post-earthquake orthomosaics help assess damage and plan recovery. - **Coastal zone management** (RA 9147, Wildlife Act): Orthomosaics monitor beach erosion, mangrove encroachment, coral reef condition. **Orthophoto Specifications**: Philippine orthophoto standards (under PD 1529 and RA 4374 survey guidelines) typically specify: - **Spatial resolution (pixel size)**: 0.5 m (high-resolution), 1 m (standard), 5 m (regional). - **Horizontal accuracy**: ±(0.5 to 2 × pixel size) depending on purpose; ±0.5 m for cadastral-grade, ±2 m for regional. - **Datum and projection**: WGS84 geodetic; UTM zone or Philippine Coast & Geodetic Survey (PCGS) PCS. - **Radiometric quality**: True-color RGB, or multispectral if available. - **Metadata**: Acquisition date, source sensor, GCP accuracy, DEM source and resolution. **Common Pitfalls in Orthophoto Generation**: 1. **Poor DEM quality**: If the DEM has large errors (especially in the vertical direction), the orthophoto will have corresponding geometric errors. A DEM error of ±1 m can cause planimetric errors of a few meters in steep terrain. 2. **Insufficient ground control**: If the raw photograph is not accurately georeferenced, the resampling will be biased, and the orthophoto will not align correctly with other datasets. 3. **Disregarding edge effects**: At image edges, where the ground is far from the photograph's nadir point, relief displacement is largest, and resampling quality may degrade. It is good practice to discard or blend image edges in an orthomosaic. 4. **Mismatched image seams**: In an orthomosaic, brightness and color differences between adjacent orthophotos can create visible seams; sophisticated seaming algorithms (e.g., feathering, histogram matching) are needed for a professional product. 5. **Confusing orthophoto with map**: Although an orthophoto can be measured, it is not a cartographic map—it does not have generalized feature representation, standardized symbols, or curated metadata. An orthophoto should be labeled as "orthophoto" not "map."

Understanding stereoscopy, DEM production, and orthophoto generation as an integrated process is essential for geodetic engineering practice. This section synthesizes the workflow. **Step-by-Step Workflow**: **1. Flight Planning & Aerial Photography**: - Design flight lines with 60% forward overlap, 20–30% sidelap. - Choose flying height H to achieve desired ground resolution. For a camera with 150 mm focal length to achieve 0.5 m GSD: H = (0.5 m × 0.150 m) ÷ (sensor pixel size) ≈ 1000–1500 m (depending on sensor). - Establish ground control points (GCPs) with known coordinates (WGS84 geodetic, then converted to PCS/UTM). Typically, ≥4 GCPs per orthophoto, more for large areas. - Acquire stereo photographs with high overlap. Use GPS/IMU system to record camera position and orientation (direct georeferencing) if available, to reduce GCP dependence. **2. Image Orientation & Tie-Point Matching**: - Measure interior orientation (focal length, principal point, lens distortion) from camera calibration report. - Identify and measure **tie points**: feature coordinates that are visible in multiple overlapping images. - Perform bundle adjustment: simultaneously solve for camera exterior orientation (position and angles) and 3-D tie-point coordinates, constrained by GCPs. This yields the refined camera parameters and relative positions of consecutive exposures, enabling stereo matching. **3. Stereo Image Matching & Dense Point Cloud**: - Use automated image-matching algorithms (cross-correlation, Semi-Global Matching) to find corresponding points in the left (reference) and right (search) images of each stereo pair. - Measure parallax for thousands or millions of matching points, converting parallax to elevation using the stereo baseline and camera parameters. - The result is a dense **point cloud** (often called an XYZ cloud or disparity map) covering the entire stereo overlap area, with coordinates in the project datum. **4. DEM Generation**: - Grid the point cloud into a regular raster DEM. Cell size chosen based on survey requirements: 0.5–1 m for high-detail work, 5–10 m for regional mapping. - Apply filtering to remove outliers (blunders from image matching) and to convert DSM (digital surface model, including vegetation/buildings) to DEM (bare-earth) if needed. - Validate DEM against check points: compare DEM elevations with independently surveyed elevation control. Typical vertical RMS error for photogrammetric DEM: ±0.5–2 m depending on terrain and image quality. **5. Orthophoto Production**: - For each raw photograph, use the exterior orientation parameters (from bundle adjustment) and the DEM to perform back-projection and resampling, yielding an individual orthophoto. - Specify orthophoto pixel size (typically equal to DEM cell size or finer): 0.5–1 m for detail, 5 m for regional. - Apply radiometric corrections (brightness/contrast normalization) to prepare for mosaicking. **6. Orthophoto Mosaicking**: - Register adjacent orthophotos using tie points and feathering algorithms to create seamless seams. - Perform color/tone balancing to ensure consistent appearance across the mosaic. - Trim excess edges to remove low-quality pixels at photograph margins. - The final product is an **orthomosaic**: a seamless, georeferenced, measurable image covering the entire project area. **7. Validation & Quality Control**: - Check horizontal accuracy: compare orthophoto feature positions with independently surveyed GCPs or high-accuracy reference data (e.g., differential GPS or high-order traverse). Acceptance criterion: RMS error ≤ 0.5–2 m depending on specification. - Check vertical accuracy of DEM: compare check-point elevations with DEM. Acceptance: RMS ≤ 0.5–2 m. - Verify coverage: ensure no data gaps or anomalies; check for image-matching failures in difficult terrain (shadows, water, uniform slopes). - Validate metadata: confirm datum (WGS84 with conversion to PRS92 for Philippines), projection (UTM zone, PCS), acquisition date, sensor specifications, and DEM source. **Data Products Delivered**: - **Raw photographs** (archived) - **Point cloud** (LAS format, often; useful for 3-D visualization and detail surveys) - **DEM** (GeoTIFF, ArcGRID, or HDF5 format; single-band, float32, with proper georeferencing) - **Orthophoto/orthomosaic** (GeoTIFF, 3-band RGB or single-band grayscale; typically UTM/PCS projection) - **Metadata & calibration reports** (camera calibration, bundle adjustment residuals, GCP coordinates, accuracy assessment) **Quality Metrics**: Philippine standard (PD 1529, RA 4374): - **Horizontal accuracy** (orthophoto): ±(0.5 to 2 × pixel size); ±0.5 m for cadastral, ±2 m for regional. - **Vertical accuracy** (DEM): ±(0.3 to 2 m); ±0.3 m for detailed design, ±2 m for regional planning. - **Spatial resolution**: 0.5–1 m high-detail, 5–10 m regional. - **Temporal freshness**: Preferred acquisition within 2–3 years for administrative mapping, recent as possible for disaster response. The workflow is **iterative and quality-driven**: errors detected in DEM validation may require re-processing of image matching or acquisition of additional GCPs and photographs.