Remote sensing computation with Panoramic imagery
Panoramic imagery is a type of the close-ranging photogrammetric techniques adopted in the close-ranging and mobile mapping system, it combines two or more fish-eye lens to capture a very-wide field of view images. The distortion and depth estimation will be a complex problem, but still it produce accuracy bearing from the post-processed (stitched) image.
Line-line intersection
In terms of the mathematics, by the line-line intersection can estimate and compute the target point with two camera point and it corresponding geodetic azimuth (the azimuth is the horizontal circle angle from the north to the point), the formula is as follows:
x = (m1 lon1 — m2 lon2 — lat1 + lat2) / (m1 — m2)
y = m1 (x — lon1) + lat1
For m1 = tan(azimuth1) and m2 = tan(azimuth2)
Remember need to convert the result from radians to degrees
Explanations of the Line-line intersection
Since we have lat, long and azimuth angle
The slope of the point 1 = m1 = tan(azimuth 1) and the slope of the point 2 = m2 = tan(azimuth 2).
Equation of point 1,
y = m1(x-long1)+lat1
y — lat1 = m1(x-long1) -> y-lat1 = m1(x-m1)long1
Equation of point 2,
y = m2(x-long2)+lat2
y = m2(x-m2)long2+lat2
Combine the equation:
m1 x — m1 long1 = m2 x — m2 long2 + lat2 — lat1 ->
(m1-m2)x = m2 long2 — m1 long1 + lat 2 — lat 1
For x = (m2 long 2 — m1 long 1 + lat2 — lat1)/ (m1-m2)
For y = m1(x — long1)+lat1
Vector based method
Direction vector for the line 1 = v1 = cos(azimuth1),sin(azimuth1)
Direction vector for the line 2 = v2 = cos(azimuth2),sin(azimuth2)
Line 1 = (x1,y1) + t1 v1 and
Line 2 = (x2,y2) + t2 v2
Since finding the intersection point, so Line 1 = Line 2
(x1,y1) + t1 v1 = (x2,y2) +t2 v2
(x1,y1) — (x2,y2) = v2 — t1 v1
(v1, -v2) (t1 t2) = (x1,y1) — (x2,y2)
Let A be the coefficient matrix, A = (v1, -v2)
Vector on the right hand side, b = (x1,y1) — (x2,y2)
Do the least square fitting to computed scaler for the intersection point,
t1 and t2 are the key to determine the intersection,
intersection point lat = (x2-x1) + t1 v1
intersection point long = (y2-y1) + t2 v2
Height estimation by Trigonometric
Height estimation from the tilting angles, for example:
θ = 141.98–111.21 = 30.77
Δ lat = | target lat — original lat | and
Δ long = | target long- original long |
by Haversine formula (we accounted for the earth curvature in the height estimation),
a = sin(Δ lat/2)² + cos(original lat) math.cos(target lat) sin(Δ long/2)²
c = 2 arctan (√(a) √(1-a))²
d = earth radius x c -> 6371000 c
Estimated height = d tan(θ)
Sample result:
0.9285912410222996 meters
Pros and Cons of the pano images
Simple decoding of the pano image from the Google Street view URL
Data fusion from pano to mapping and GIS
In the field of the urban forestry or urban informatics, the close-ranging pano images can help to derive the complex features which cannot be extract from Airborne or aerial photogrammetry, such as the tree species identification, road defects detection and road inventories.
Here are some sample of the tree identification map by pano images from Google Street view.
Reference list:
Tsai, Victor & Chang, Chun-Ting. (2013). Three-dimensional positioning from Google street view panoramas. Image Processing, IET. 7. 229–239. 10.1049/iet-ipr.2012.0323.
