GELE Photogrammetry & Cartography — Scale, Relief Displacement and ParallaxExam Answer Templates

Marks

1

Topic

Relief Displacement

Difficulty

easy

Template Id

T1

Examiner Tip

The single most rewarded phrase is 'radially outward from the principal point.' Any answer missing this spatial direction will be penalized.

Model Answer

Relief displacement is the radially outward shift of an object's image from the principal point of a vertical aerial photograph, caused by the object's elevation above the datum. The displacement is zero at the principal point and increases toward the edges of the photo.

Question Type

very_short_answer

Answer Structure

• Line 1: State the definition — radially outward shift due to elevation above datum [1 mark]

Scoring Breakdown

Common Mark Deductions

• Writing 'displacement from the center of the photo' without specifying 'principal point'
• Omitting the direction (radially outward)
• Confusing relief displacement with tilt displacement

Key Phrases To Include

• radially outward
• principal point
• elevation above datum
• vertical photograph

Marks

2

Topic

Relief Displacement

Difficulty

easy

Template Id

T2

Examiner Tip

Examiners specifically check whether r is described as the distance to the 'top' of the object's image, not to its base. This distinction demonstrates real understanding.

Model Answer

The relief displacement formula is: d = (r · h) / H where: d = relief displacement (mm) — radial shift of the image from the principal point r = radial distance of the image (top of the object) from the principal point (mm) h = height of the object above the datum (m) H = flying height of the aircraft above the datum (m)

Question Type

very_short_answer

Answer Structure

• Line 1: Write the formula d = rh/H [1 mark]
• Line 2: Define all three variables with correct units [1 mark]

Scoring Breakdown

Common Mark Deductions

• Writing H as 'altitude' without specifying 'above datum'
• Describing r as distance from the edge or center without specifying 'principal point'
• Omitting units in variable identification

Key Phrases To Include

• d = rh/H
• radial distance from principal point
• flying height above datum
• image of the top of the object

Marks

2

Topic

Relief Displacement

Difficulty

easy

Template Id

T3

Examiner Tip

Link every conceptual statement back to the formula. Examiners reward mathematical reasoning, not just descriptive answers.

Model Answer

Relief displacement d = rh/H is directly proportional to r, the radial distance of the image from the principal point. At the principal point, r = 0, therefore d = 0 regardless of object height — an object directly below the camera lens plots at its true planimetric position. Toward the edges of the photo, r increases, so d increases proportionally. This means tall objects near the edges appear to lean strongly outward, while objects at the center appear upright.

Question Type

short_answer

Answer Structure

• Line 1: Cite the formula and note d is proportional to r [1 mark]
• Line 2: Explain zero case (r = 0 at PP) and maximum at edges (large r) with physical interpretation [1 mark]

Scoring Breakdown

Common Mark Deductions

• Stating the result without referencing the formula as the reason
• Confusing 'principal point' with 'nadir point' or 'isocenter'
• Failing to state the physical consequence (objects appear to lean)

Key Phrases To Include

• directly proportional to r
• r = 0 at the principal point
• d = 0
• increases toward the edges
• lean outward

Marks

2

Topic

Relief Displacement

Difficulty

easy

Template Id

T4

Examiner Tip

Notice that H cancels the unit of h (both in m), leaving d in the same unit as r. Always check unit consistency before computing.

Model Answer

Given: H = 1,800 m (flying height above datum) r = 95 mm (radial distance of image top from principal point) h = 60 m (tower height above datum) Formula: d = (r · h) / H Substitution: d = (95 mm × 60 m) / 1,800 m d = 5,700 / 1,800 ∴ d = 3.167 mm (radially outward from the principal point)

Question Type

numerical

Answer Structure

• Line 1–3: List all given values with units [0.5 mark]
• Line 4: Write the formula [0.5 mark]
• Line 5–6: Substitute and compute [0.5 mark]
• Line 7: State final answer with unit and direction [0.5 mark]

Scoring Breakdown

Common Mark Deductions

• Mixing units — using r in metres instead of mm (answer must be in mm if r is in mm)
• Rounding prematurely before the final answer
• Omitting the direction 'radially outward'

Key Phrases To Include

• d = rh/H
• 3.167 mm
• radially outward

Marks

3

Topic

Relief Displacement

Difficulty

easy

Template Id

T5

Examiner Tip

Rearranging and explicitly writing h = dH/r earns a dedicated mark. Never skip this step even if the arithmetic is straightforward.

Model Answer

Given: H = 2,000 m d = 3.0 mm r = 100 mm Required: h (building height in m) Formula (rearranged from d = rh/H): h = (d · H) / r Substitution: h = (3.0 mm × 2,000 m) / 100 mm h = 6,000 / 100 ∴ h = 60.0 m Interpretation: The building is 60.0 m tall above the datum reference plane.

Question Type

numerical

Answer Structure

• Line 1–3: Identify all given variables with units [1 mark]
• Line 4: State the rearranged formula h = dH/r [1 mark]
• Line 5–7: Correct substitution and arithmetic [1 mark]

Scoring Breakdown

Common Mark Deductions

• Using d = rh/H without rearranging (writing h in the wrong position)
• Forgetting to state the formula before substituting
• Omitting 'm' as the unit of the final answer

Key Phrases To Include

• h = dH/r
• 60.0 m
• above datum

Marks

2

Topic

Stereoscopic Parallax

Difficulty

easy

Template Id

T6

Examiner Tip

The direction qualifier 'parallel to the flight line' is always tested. A definition without it is considered incomplete.

Model Answer

Stereoscopic parallax is the apparent lateral displacement (measured parallel to the flight line) of a point as seen from two different exposure stations in an overlapping stereo pair. Points at higher elevations have greater parallax than points at lower elevations. The height of an object is determined from the parallax difference formula: h = (H · Δp) / (P + Δp) where H = flying height above datum, Δp = parallax difference between top and base of the object, and P = absolute parallax of the base.

Question Type

short_answer

Answer Structure

• Line 1–2: Definition of parallax with direction qualifier (parallel to flight line) [1 mark]
• Line 3–4: Correct formula with all variables defined [1 mark]

Scoring Breakdown

Common Mark Deductions

• Writing 'perpendicular to the flight line' instead of 'parallel'
• Writing the approximate formula only (HΔp/P) without acknowledging the exact form
• Failing to define Δp as the difference between top and base parallax

Key Phrases To Include

• apparent lateral displacement
• parallel to the flight line
• two exposure stations
• h = HΔp/(P + Δp)
• parallax difference

Marks

3

Topic

Stereoscopic Parallax

Difficulty

medium

Template Id

T7

Examiner Tip

Always show the Δp computation as a separate numbered step. This intermediate value earns its own mark and prevents cascading arithmetic errors.

Model Answer

Given: H = 1,500 m P (base absolute parallax) = 90 mm P_top (top absolute parallax) = 91.5 mm Step 1 — Compute parallax difference: Δp = P_top − P = 91.5 − 90.0 = 1.5 mm Step 2 — Apply the height formula: h = (H · Δp) / (P + Δp) h = (1,500 × 1.5) / (90 + 1.5) h = 2,250 / 91.5 ∴ h = 24.6 m The chimney is 24.6 m tall.

Question Type

numerical

Answer Structure

• Line 1–3: List given values [0.5 mark]
• Line 4–5: Compute Δp correctly [1 mark]
• Line 6–8: Apply h = HΔp/(P + Δp) [1 mark]
• Line 9: Correct final answer with unit [0.5 mark]

Scoring Breakdown

Common Mark Deductions

• Using the approximate formula HΔp/P and getting 25.0 m — loses ½ mark for not using exact formula
• Using P + Δp in the numerator instead of the denominator
• Failing to subtract base parallax to get Δp first

Key Phrases To Include

• Δp = P_top − P
• h = HΔp/(P + Δp)
• 24.6 m

Marks

3

Topic

Relief Displacement and Parallax

Difficulty

medium

Template Id

T8

Examiner Tip

A comparison table is perfectly acceptable and often faster: two rows (Relief Displacement, Parallax), columns (Definition, Formula, Photo requirement, Direction, Application).

Model Answer

Relief displacement is the radially outward shift of an elevated object's image on a SINGLE vertical photograph, caused by the object's height above datum; it is governed by d = rh/H. Stereoscopic parallax is the apparent lateral shift of a point measured BETWEEN TWO overlapping photographs (a stereo pair), measured parallel to the flight line; height is derived via h = HΔp/(P + Δp). Key difference: Relief displacement occurs on one photo and increases radially outward from the principal point. Parallax requires two photos and is measured along the flight direction. Applications: • Relief displacement: Used to measure building or tower heights from a single aerial photograph using h = dH/r. • Parallax: Used to generate digital elevation models (DEMs) and topographic maps from stereo aerial imagery.

Question Type

short_answer

Answer Structure

• Lines 1–2: Define relief displacement with formula and characteristic (single photo, radial) [1 mark]
• Lines 3–4: Define parallax with formula and characteristic (two photos, parallel to flight line) [1 mark]
• Lines 5–6: State one application each, correctly matched [1 mark]

Scoring Breakdown

Common Mark Deductions

• Treating both as the same phenomenon
• Stating applications that are identical for both (e.g., 'both measure heights')
• Omitting formulas when differentiating

Key Phrases To Include

• single photograph
• radially outward
• two photographs / stereo pair
• parallel to the flight line
• d = rh/H
• h = HΔp/(P + Δp)
• digital elevation model

Marks

3

Topic

Relief Displacement

Difficulty

medium

Template Id

T9

Examiner Tip

Quantitative justification (referencing the formula explicitly) always outscores a purely descriptive answer for 'justify' type questions.

Model Answer

The relief displacement formula is d = rh/H. Rearranged, the height is: h = dH/r For height measurement to be accurate, d must be large enough to be measured reliably. Since d = rh/H, a larger radial distance r from the principal point produces a larger displacement d for the same object height h and flying height H. Near the center of the photo (small r), a tall building produces only a tiny displacement d, which is difficult to measure precisely and leads to large percentage errors in the computed h. Near the edges (large r), the displacement d is proportionally larger and easier to measure accurately. The ratio d/r remains constant for a given h and H, but the absolute value of d increases, improving measurement precision. Therefore, height measurements from relief displacement are more reliable when the object image is toward the edges of the photo where r is large.

Question Type

short_answer

Answer Structure

• Lines 1–2: State and rearrange the formula [1 mark]
• Lines 3–4: Explain the effect of small r at center — small d, large relative error [1 mark]
• Lines 5–6: Explain large r at edges — large d, better precision [1 mark]

Scoring Breakdown

Common Mark Deductions

• Stating the answer without mathematical justification
• Claiming heights cannot be measured at all near the center (overclaiming)
• Confusing precision with accuracy without distinguishing the two

Key Phrases To Include

• d = rh/H
• h = dH/r
• small r near center
• large d near edges
• measurement precision
• percentage error

Marks

5

Topic

Stereoscopic Parallax

Difficulty

hard

Template Id

T10

Examiner Tip

Five-mark questions always have a multi-part structure. Allocate a clear numbered heading for each part (a), (b) so the examiner can identify and credit each component independently.

Model Answer

Given: H = 1,600 m P = 88 mm (absolute parallax at base) Δp = 2.2 mm (parallax difference, top minus base) (a) Exact height using h = HΔp/(P + Δp): h = (1,600 × 2.2) / (88 + 2.2) h = 3,520 / 90.2 h = 39.02 m ∴ Exact height h = 39.0 m (to 3 significant figures) (b) Approximate height using h_approx ≈ HΔp/P: h_approx = (1,600 × 2.2) / 88 h_approx = 3,520 / 88 h_approx = 40.0 m Percentage difference: % diff = |h_approx − h_exact| / h_exact × 100 % diff = |40.0 − 39.02| / 39.02 × 100 % diff = 0.98 / 39.02 × 100 ∴ Percentage difference ≈ 2.51% Conclusion: The approximate formula overestimates the height by approximately 2.5%, which is acceptable for preliminary surveys but the exact formula should be used for precise height determination.

Question Type

numerical

Answer Structure

• Lines 1–3: List all given data with units [0.5 mark]
• Lines 4–6: Apply exact formula h = HΔp/(P + Δp) [1.5 marks]
• Lines 7–9: Correct exact answer h = 39.0 m [0.5 mark]
• Lines 10–12: Apply approximate formula h ≈ HΔp/P [1 mark]
• Lines 13–16: Compute percentage difference correctly [1 mark]
• Line 17: Conclusion on practical significance [0.5 mark]

Scoring Breakdown

Common Mark Deductions

• Computing only the approximate formula and skipping the exact formula
• Incorrect percentage difference formula (dividing by approximate instead of exact)
• Not stating a conclusion on practical significance — loses the interpretation mark
• Carrying forward arithmetic errors from part (a) into part (b)

Key Phrases To Include

• h = HΔp/(P + Δp)
• h ≈ HΔp/P
• 39.0 m
• 40.0 m
• percentage difference
• approximate formula overestimates

Marks

2

Topic

Photo Scale

Difficulty

easy

Template Id

T11

Examiner Tip

Photo scale problems are often combined with relief displacement problems in a single multi-part question. Always compute H from the scale first, then use that H in the relief displacement formula.

Model Answer

Given: Photo scale S = 1:10,000 (i.e., scale factor = 1/10,000) Focal length f = 152 mm = 0.152 m Formula (photo scale of a vertical photo): S = f / H → H = f / S Substitution: H = 0.152 m / (1/10,000) H = 0.152 × 10,000 ∴ H = 1,520 m above datum

Question Type

numerical

Answer Structure

• Line 1–2: List given data including unit conversion for f [0.5 mark]
• Line 3: State scale formula S = f/H and rearrange to H = f/S [0.5 mark]
• Line 4–5: Correct substitution and arithmetic [0.5 mark]
• Line 6: Final answer H = 1,520 m with unit [0.5 mark]

Scoring Breakdown

Common Mark Deductions

• Failing to convert f from mm to m before computing H in metres
• Inverting the scale fraction incorrectly (using 10,000 in denominator instead of numerator)
• Not stating the unit of H

Key Phrases To Include

• S = f/H
• H = f/S
• 1,520 m
• above datum

Marks

3

Topic

Relief Displacement

Difficulty

easy

Template Id

T12

Examiner Tip

Enumeration questions reward distinct, non-overlapping points. Plan your three points before writing to avoid repetition.

Model Answer

1. Direction: Relief displacement is always radially outward from the principal point of the photograph — the tops of elevated objects appear displaced away from the PP. 2. Magnitude: Displacement is directly proportional to both the object height h and the radial distance r of the image from the PP, and inversely proportional to the flying height H: d = rh/H. 3. Zero at the principal point: At the principal point (r = 0), relief displacement is exactly zero. An object directly below the camera plots at its true planimetric position regardless of its height.

Question Type

very_short_answer

Answer Structure

• Point 1: Direction — radially outward from PP [1 mark]
• Point 2: Magnitude relationship via d = rh/H [1 mark]
• Point 3: Zero displacement at the principal point [1 mark]

Scoring Breakdown

Common Mark Deductions

• Listing three characteristics that are all variations of the same point (e.g., listing 'increases away from center' and 'largest at edges' as two separate points)
• Stating direction as 'inward' or 'perpendicular'
• Omitting the formula reference for the magnitude characteristic

Key Phrases To Include

• radially outward
• principal point
• d = rh/H
• directly proportional to h and r
• inversely proportional to H
• zero at the principal point

Marks

3

Topic

Relief Displacement

Difficulty

medium

Template Id

T13

Examiner Tip

When both base and top radial distances are given, the relief displacement d = r_top − r_base. The formula h = dH/r uses r = r_top (the image of the top of the object).

Model Answer

Given: H = 1,500 m r_top = 80 mm (radial distance of building top image from PP) r_base = 78 mm (radial distance of building base image from PP) Step 1 — Compute relief displacement d: d = r_top − r_base = 80 − 78 = 2 mm Note: The displacement d is the difference in radial distances because both the top and base images are measured along the same radial direction from the PP. Step 2 — Compute building height using h = dH/r: (Use r = r_top = 80 mm, the radial distance of the top image) h = (d × H) / r_top h = (2 × 1,500) / 80 h = 3,000 / 80 ∴ h = 37.5 m The building is 37.5 m tall.

Question Type

numerical

Answer Structure

• Lines 1–3: Identify given data [0.5 mark]
• Lines 4–5: Compute d = r_top − r_base = 2 mm [1 mark]
• Lines 6–8: Apply h = dH/r_top correctly [1 mark]
• Line 9: Final answer h = 37.5 m [0.5 mark]

Scoring Breakdown

Common Mark Deductions

• Using r_base instead of r_top in the denominator of h = dH/r
• Forgetting to compute d from the two radial distances and using r_top directly as d
• Not explaining why r_top is used (it is the radial distance of the displaced image)

Key Phrases To Include

• d = r_top − r_base
• h = dH/r
• r = r_top
• 37.5 m

Marks

5

Topic

Stereoscopic Parallax

Difficulty

hard

Template Id

T14

Examiner Tip

A 5-mark long answer must have a structured, multi-step procedure. Use numbered steps with bold headings. One step = one coherent idea = one potential mark. Examiners follow the marking scheme step by step.

Model Answer

Procedure for Height Measurement Using Stereoscopic Parallax: Step 1 — Set up the stereo pair Select two overlapping vertical aerial photographs (typically 60% forward overlap) covering the area where the tree is located. Orient both photos so the flight line runs left-right (the conventional orientation for parallax measurement). Step 2 — Identify conjugate image points Locate the image of the top of the tree (point A_top) on both the left and right photographs. Also locate the base of the tree (point A_base) on both photographs. Step 3 — Measure absolute parallaxes Measure the x-coordinates of the conjugate points on each photo along the flight-line direction (x-axis): • Parallax of top: P_top = x_L(top) − x_R(top) • Parallax of base: P = x_L(base) − x_R(base) All measurements in millimetres. Step 4 — Compute parallax difference Δp = P_top − P Step 5 — Apply the height formula h = (H · Δp) / (P + Δp) where: h = height of the tree (m) H = flying height above the datum (m) Δp = parallax difference between top and base (mm) P = absolute parallax of the base of the tree (mm) Note: The approximate formula h ≈ HΔp/P is valid when Δp << P (which holds for most objects shorter than ~5% of H). Step 6 — Interpret the result The computed h is the height of the tree above its base datum. If the base elevation is known from ground control, the tree-top elevation above mean sea level is: Elevation_top = Elevation_base + h. In digital photogrammetry (using software such as SOCET SET or Agisoft Metashape), Steps 1–4 are automated through feature matching and the height is extracted directly from the stereo model.

Question Type

long_answer

Answer Structure

• Step 1: Setup description — stereo pair, overlap [0.5 mark]
• Step 2: Identification of conjugate image points (top and base) [0.5 mark]
• Step 3: Measurement of absolute parallaxes with formula [1 mark]
• Step 4: Computation of Δp [0.5 mark]
• Step 5: Height formula with all variables defined [1 mark]
• Step 6: Interpretation and elevation conversion [0.5 mark]
• Mention of digital photogrammetry application [1 mark]

Scoring Breakdown

Common Mark Deductions

• Describing only the formula without the measurement procedure
• Omitting the requirement to measure parallax parallel to the flight line
• Not defining Δp as the difference between top and base parallax
• Failing to address how the computed h relates to absolute elevation
• Confusing x-parallax (along flight line) with y-parallax (across flight line)

Key Phrases To Include

• 60% forward overlap
• conjugate image points
• flight-line direction
• absolute parallax
• parallax difference Δp = P_top − P
• h = HΔp/(P + Δp)
• approximate formula h ≈ HΔp/P
• digital photogrammetry

Marks

5

Topic

Photo Scale and Relief Displacement with Legal Reference

Difficulty

hard

Template Id

T15

Examiner Tip

PRC board exam questions increasingly combine numerical computation with legal/professional knowledge. Memorize the key provisions of PD 1529, RA 8560, CA 141, and RA 4374/RA 8560 as they relate to geodetic surveys, land titling, and cadastral work.

Model Answer

Given: H = 1,800 m f = 152 mm = 0.152 m d = 4.5 mm r = 90 mm (a) Photo Scale: S = f / H S = 0.152 m / 1,800 m S = 1 / 11,842 ∴ Photo scale ≈ 1:11,842 (approximately 1:12,000) (b) Building Height: h = (d × H) / r h = (4.5 mm × 1,800 m) / 90 mm h = 8,100 / 90 ∴ h = 90.0 m The Makati high-rise building is 90.0 m tall. (c) Relevant Provision of PD 1529 (Property Registration Decree, 1978): Under PD 1529, the boundaries of land parcels must be accurately determined and described in the application for original registration of title (Section 14, PD 1529). Aerial photographs, when supported by ground control surveys and processed photogrammetrically to extract accurate coordinates, can be used to verify boundary locations and parcel areas prior to cadastral survey and Torrens title registration. However, PD 1529 requires that the final technical description of a land parcel be prepared and signed by a licensed Geodetic Engineer under RA 8560 (Geodetic Engineering Act of 1998), and the survey must be approved by the Land Registration Authority (LRA).

Question Type

case_study

Answer Structure

• Part (a): Photo scale formula S = f/H, substitution, S ≈ 1:11,842 [1.5 marks]
• Part (b): Formula h = dH/r, substitution, h = 90.0 m [2 marks]
• Part (c): Relevant PD 1529 provision with geodetic engineering reference [1.5 marks]

Scoring Breakdown

Common Mark Deductions

• Citing the wrong law (e.g., CA 141 instead of PD 1529 for registration of title)
• Giving a generic answer about PD 1529 without a specific relevant section
• Forgetting to convert f to metres before computing scale
• Not connecting the legal provision to the photogrammetric context of the question

Key Phrases To Include

• S = f/H
• 1:11,842
• h = dH/r
• 90.0 m
• PD 1529
• Property Registration Decree
• RA 8560
• licensed Geodetic Engineer
• Land Registration Authority