Structure from motion¶

The structure from motion primitives used by Kontiki are perhaps a bit different from what you are used to. Instead of modelling landmarks as e.g. a 3D-point in world coordinates, we instead use a combination of a reference observation and an inverse depth.

This formulation is nice because it is simple to represent landmarks at infinity, and also only require us to optimize a single scalar (the inverse depth) instead of a full 3D-point. For a more detailed description see e.g. [Lovegrove2013].

Usage¶

To setup a structure from motion problem we create View and Landmark objects, and then add Observation objects by calling View.create_observation(). Note that it is impossible to create Observation objects any other way.

Assume that we have a list of tracks that each contain a list of tuples (n, x), where n is a frame number, and y is an image point. Then creating the structure from motion objects looks like this:

landmarks = []
views = {}  # frame number -> View

for track_data in tracks:
    lm = Landmark()
    for n, y in track_data:
        view = views.get(n, View(n / frame_rate))
        view.create_observation(lm, y)

To be usable, we also need to set the reference observation for each landmark. Easiest is to use the first one:

for lm in landmarks:
    lm.reference = lm.observations[0]

Classes¶

class kontiki.sfm.View¶

create_observation(self: kontiki.sfm.View, arg0: kontiki.sfm.Landmark, arg1: numpy.ndarray[float64[2, 1]]) → kontiki.sfm.Observation¶: Create a new observation

frame_nr¶: Frame number

observations¶: List of observations

remove_observation(self: kontiki.sfm.View, arg0: kontiki.sfm.Observation) → None¶: Remove an observation

t0¶: Start of frame time

class kontiki.sfm.Landmark¶

A 3D landmark

Landmarks are represented by a reference observation, and an inverse depth.

id¶: Landmark ID

Warning

The landmark ID is only unique within a session. You can not trust an ID to be the same e.g. if loading the same problem from disk twice.

inverse_depth¶: The inverse depth, relative to the reference observation

locked¶: Lock landmark to not allow it to change during optimization. Defaults to False.

observations¶: List of all landmark observations

reference¶: Reference observation

class kontiki.sfm.Observation¶

An observation of a landmark in a view

is_reference¶: True if this is the landmark reference observation

landmark¶: The Landmark this observation belongs to

uv¶: The image measurement.

view¶: The View this observation belongs to

References

[Lovegrove2013]

Lovegrove, S.; Patron-Perez, A.; and Sibley, G. Spline Fusion: A continuous-time representation for visual-inertial fusion with application to rolling shutter cameras In Procedings of the British Machine Vision Conference 2013