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Photogrammetry & Remote Sensing formula solvers

Categories — 58 of them, 1453 solvers in all
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Air Base from Endlap

B=Wg (1−pend)B = W_g \, (1 - p_{end})

Photogrammetry & Remote SensingHow far the aircraft travels between one exposure and the next: the along-track ground width of the frame, less the fraction of it that must overlap the previous frame. Endlap is the overlap between CONSECUTIVE frames on one line — not between lines, which is sidelap and a different number.

Camera Trigger Interval

t=BVgt = \frac{B}{V_g}

Photogrammetry & Remote SensingHow often the shutter must fire: the air base divided by the ground speed. The bridge between a geometric flight plan and the two settings the aircraft actually flies with — an interval and a speed. If the camera cannot cycle this fast, the plan is not flyable and the speed has to come down.

Flight Line Spacing from Sidelap

S=Wc (1−pside)S = W_c \, (1 - p_{side})

Photogrammetry & Remote SensingHow far apart the flight lines go: the across-track ground width of the frame, less the fraction that must overlap the neighbouring line. Sidelap is the overlap between ADJACENT LINES — not between consecutive frames, which is endlap and a different number on a different sensor edge.

Ground Sample Distance (GSD)

GSD=H pf\mathrm{GSD} = \frac{H \, p}{f}

Photogrammetry & Remote SensingHow much ground one pixel covers: flying height times pixel pitch, divided by focal length. It is the number every drone mapping flight is planned around, and it is the number most often misquoted as an accuracy. GSD is the spacing of pixel centres on the ground — not the smallest feature you can resolve, and not the accuracy of your survey.

Height from Stereo Parallax

h=H Δppa+Δph = \frac{H \, \Delta p}{p_a + \Delta p}

Photogrammetry & Remote SensingThe height of an object read off a stereo pair: the difference in parallax between its top and its base, against the absolute parallax at the base. The relation behind every height ever measured on a stereoscope, and the same geometry a modern dense matcher is solving a hundred million times over.

Image Count for a Block

n=(⌊LB⌋+1)(⌊WS⌋+1)n = \left( \left\lfloor \frac{L}{B} \right\rfloor + 1 \right) \left( \left\lfloor \frac{W}{S} \right\rfloor + 1 \right)

Photogrammetry & Remote SensingHow many frames a rectangular block costs: the frames along one line, times the number of lines. Each count is a division that rounds down plus one, because the first exposure sits at the start of the line and the first line sits at the edge of the block. This is the number that decides battery swaps, card space and processing time.

Image Ground Footprint

A=GSD2 nx nyA = \mathrm{GSD}^{2} \, n_x \, n_y

Photogrammetry & Remote SensingWhat one frame covers on the ground: the ground sample distance multiplied by the pixel count, in each direction. The area follows as the product of the two edges. This is the number that turns a GSD into a flight plan — it sets the air base, the line spacing and, through those, the whole image count.

Motion Blur Speed Limit

Vmax=k  GSDtexpV_{max} = \frac{k \; \mathrm{GSD}}{t_{exp}}

Photogrammetry & Remote SensingThe fastest ground speed that keeps the smear from forward motion inside a stated fraction of a pixel. The image moves across the sensor while the shutter is open, and that smear is a hard limit on real resolution that no amount of fine GSD can rescue.

NDVI — Normalized Difference Vegetation Index

NDVI=ρNIR−ρredρNIR+ρred\mathrm{NDVI} = \frac{\rho_{NIR} - \rho_{red}}{\rho_{NIR} + \rho_{red}}

Photogrammetry & Remote SensingThe oldest and most-used vegetation index: near-infrared reflectance minus red, over their sum. Healthy leaves absorb red for photosynthesis and scatter near-infrared strongly, so the difference tracks green canopy. Defined by Rouse, Haas, Schell and Deering in NASA SP-351 (1974) page 309, from ERTS-1 imagery of the Great Plains.

Photo Scale

S=fH−hS = \frac{f}{H - h}

Photogrammetry & Remote SensingThe scale of a vertical photograph: focal length divided by the height of the camera above the ground being imaged. Written as a fraction — 1:20 000 means one on the photo is twenty thousand on the ground. The classical form of the same similar triangles that give the ground sample distance, and the one every photogrammetry course starts with.

SAVI — Soil-Adjusted Vegetation Index

SAVI=(ρNIR−ρred)(1+L)ρNIR+ρred+L\mathrm{SAVI} = \frac{(\rho_{NIR} - \rho_{red})(1 + L)}{\rho_{NIR} + \rho_{red} + L}

Photogrammetry & Remote SensingNDVI with a soil correction: a constant L in the denominator, and a matching (1 + L) on top to keep the range. Huete introduced it in Remote Sensing of Environment 25 (1988) 295 after showing that NDVI over partial canopy moves with soil brightness rather than with the plants. It exists because NDVI fails on sparse cover, which is exactly when an agronomist most wants a reading.

Vertical Precision from Base-to-Height Ratio

σZ=HB⋅Hf⋅σp\sigma_Z = \frac{H}{B} \cdot \frac{H}{f} \cdot \sigma_p

Photogrammetry & Remote SensingThe height precision a stereo geometry can deliver: the parallax measuring precision, magnified by the image scale and again by the inverse of the base-to-height ratio. This is the number that should be quoted as a survey's vertical accuracy, and it is several times larger than the ground sample distance everyone quotes instead.