Lecture 2 Flashcards
Earths orbital revolution
an _____ path around the sun
____(angle) with the _____ plane
- An elliptical path around Sun
- Earth–Sun distance varies between aphelion &
perihelion points - 23.50 with the ecliptic plane
Celestial Coordinate system
North & South celestial pole - point in sky directly
above north/south pole on earth (zenith of north/south
pole & + 90o/- 90o respectively)
• Celestial equator – circle surrounding equator on
earth
• Ecliptic – pathfollowed by the sun through the sky over the course of the year.
declination
Declination – angle from celestial equator (0o
), positive going
UP, negative going Down
celestial Prime meridian
• Celestial Prime meridian – point where sun is located at the vernal equinox (spring)
Right ascension
Right ascension (RA)
– angle (degree) from celestial “prime meridian”
(equivalent of celestial longitude) 68
RA – typically expressed as a time going east – 0 to
24 hours is 3600
georeferencing
“To establish a relationship between page
coordinates on a planar map and known realworld
coordinates”.
Or other way
…..is the act of assigning geographic locations
to features of the spatial data that do not have
any real world coordinates
Geographic transformation
Transformation involves: _____, _____, ______, and ______ a dataset to a given set of
geographic or projected coordinates
“The process of converting a digitized map, satellite
image, or aerial photograph from one coordinate system
to another by using a set of control points and a
transformation equation”.
Transformation involves: scaling, rotation,
translation, and skew a dataset to a given set of
geographic or projected coordinates
3 steps in geographic tranformation
Step 1 updates the control points to real-world coordinates. Step 2 uses the control points to run a transformation. Step 3 creates the output by applying the transformation equations to the input features. h
Transformation methods are distinguished by the _______ properties it can preserve and the changes it allows
the changes could be
change of ____ and ____
change of _____
change in _____ and ______
Many mathematical models (equations)
Each method distinguished by the geometric
properties it can preserve and the changes it allows
The changes could be
Change of position and direction
Change of scale
Changes in shape and size
4 Commonly used tranformation methods
- Equiarea Transformation allows rotation and
preserves shape and size - Similarity Transformation allows rotation and
preserves shape but not size - Affine Transformation allows angular distortion
but preserves parallelism - Projective transformation allows both angular
and length distortion. So a rectangle to be
transformed into an irregular quadrilateral
EAT SAUSAGES AT PRISON
______ transformation method is most
commonly use
Affine transformation method is most
commonly use
Resampling of pixel values
Result of geometric transformation of a image is a
new image based on a given coordinate system
New image has no pixel values. These must be
filled through resampling
Resampling refers to filling of each pixel of new
image with a value derived from original image
Various methods exist
3 common resampling of pixel methods
Three common resampling methods:
1. Nearest neighbor resampling:
fills each pixel of the new image with the nearest
pixel value from the original image.
2. Bilinear interpolation method:
uses the average of the four nearest pixel values
from three linear interpolations.
3. Cubic convolution method:
uses the average of the 16 nearest pixel values
from five cubic polynomial interpolations.
NEVER BITE COCKS
Affine Transformation
X = Ax + By + C ……….. (1) Y = Dx + Ey + F ………...(2)
.x, y are input coordinates and X, Y are output
coordinates
.Coefficient C represents translation in the x
direction, and coefficient F the translation in
the y direction
.Coefficients A, B, D, and E are related to
rotation, skew, and scaling
Allows rotation, translation, skew, differential scaling while preserving line parallelism
Affine transformation Allows rotation, translation, skew,
differential scaling while preserving _____ _____
Allows rotation, translation, skew, differential scaling while preserving line parallelism
Affine Transformation properties
the equations requires at least ____ known points to
estimate its six coefficients. Points also known as ____’s
At least ____ known points are commonly used for
reducing problems with measurement errors and to
allow for a least-squares solution
From the ___ ____ ____ (RMS) error value is the
indicator for the goodness of control points that
derives from the least-square equation
The equations requires at least Three known points to
estimate its six coefficients.
The known points are also knows as tics/ground
control points (GCPs)
At least Four known points are commonly used for
reducing problems with measurement errors and to
allow for a least-squares solution
From the Root Mean Square (RMS) error value is the
indicator for the goodness of control points that
derives from the least-square equation.
Polynomial order in transformations
Describe 3 orders of polynomial
- 1st order polynomial (affine)
requires a minimum of 3 displacement links, but should have more
even though 3 gives RMSE=0!
is a homogeneous transformation: only shifts origin, scales and
rotates
straight lines will be preserved - 2nd order polynomial
requires 6 points (displacement links) minimum
is a differential transformation so it “warps” the raster
straightlines on raster may no longer be straight - 3rd order polynomial
requires 10 points minimum
Polynomials are global transformations which strive to achieve a best fit globally or
overall. Only 1st order with exactly 3 points will exactly match control points.
- ___ order polynomial (affine)
- 1st order polynomial (affine)
Root mean square error
The root mean square (RMS) error is a common measure of
the goodness of control points.
It measures the average deviation between the actual (true)
and estimated (digitized or selected) locations of control
points.
The RMS error is derived from the equation:
T OR F
Low acceptable RMS error does not always ensure the data accuracy
T
_____ ______ method is the most commonly used as
resampling techniques that fills each pixel of the new
image with the nearest pixel value from the original image.
Nearest neighbor method is the most commonly used as
resampling techniques that fills each pixel of the new
image with the nearest pixel value from the original image.
Reprojection
Reprojection:
.using data from different projection systems to bring into one system under same
point registration
Registration: bringing to points together that are on different projections/maps but represent the same location
When a map is scanned, an image is divided into individual pixels which are assigned a value based on ________
When a map is scanned, an image is divided into individual pixels which are assigned a value based on grayscale (gray colour level- 0 is black, higher #’s are lighter)