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Camera Model

We use the pinhole camera model (Wikipedia) without any distortion. We implement two projection plane reference frames: :centered and :offset, which are defined as illustrated here:

For offset, u point right and v points down. and the origin is in the top left. For centered, u points left and v points up, and the origin is at the image center.

We also support defining the camera model either through CameraConfig or through CameraMatrix.

:offset vs :centered

using RunwayLib, Unitful.DefaultSymbols, Rotations
cam_pos = WorldPoint(-10m, 0m, 0m)
cam_rot = RotZYX(zeros(3)...)
world_pt = WorldPoint(0m, 0m, 0m)

focal_length = 25mm
pixel_size = 5μm/px
camconf_centered = CameraConfig{:centered}(focal_length, pixel_size, 4096.0px, 2048.0px)
project(cam_pos, cam_rot, world_pt, camconf_centered)
2-element WorldPoint{Float64{pixel}} with indices SOneTo(2):
 0.0 pixel
 0.0 pixel

With an offset camera model:

camconf_offset = CameraConfig{:offset}(focal_length, pixel_size, 4096.0px, 2048.0px)
project(cam_pos, cam_rot, world_pt, camconf_offset)
2-element WorldPoint{Float64{pixel}} with indices SOneTo(2):
 2048.0 pixel
 1024.0 pixel

And for a non-centered point:

world_pt2 = WorldPoint(0m, 1m, 1m)
project(cam_pos, cam_rot, world_pt2, camconf_centered)
2-element WorldPoint{Float64{pixel}} with indices SOneTo(2):
 500.0 pixel
 500.0 pixel
project(cam_pos, cam_rot, world_pt2, camconf_offset)
2-element WorldPoint{Float64{pixel}} with indices SOneTo(2):
 1548.0 pixel
 524.0 pixel

Line Projections

For :offset camera models, we also currently support line features. Lines are specified with respect to a reference point chosen to be the "offset origin" and parameterized by their Hough transform, i.e., the angle and radius.

Reference

RunwayLib.project — Function
function project(
    cam_pos::WorldPoint{T}, cam_rot::RotZYX, world_pt::WorldPoint{T′},
    camconfig::CameraConfig{S}=CAMERA_CONFIG_OFFSET
) where {T,T′,S}

Project 3D world point to 2D image coordinates using pinhole camera model. See Camera Model for more information.

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function project(
    cam_pos::WorldPoint{T}, cam_rot::RotZYX, world_pt::WorldPoint{T′},
    camconfig::CameraMatrix{S,U}
) where {T,T′,S,U}

Version dispatching on CameraMatrix.

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RunwayLib.CameraConfig — Type
struct CameraConfig{S} <: RunwayLib.AbstractCameraConfig{S}

Camera configuration with reference frame S being either :offset or :centered. Check Camera Model for further explanation.

Fields

  • focal_length_px::Unitful.Quantity{Float64, NoDims, Unitful.FreeUnits{(pixel,), NoDims, nothing}}

  • image_width::Unitful.Quantity{Float64, NoDims, Unitful.FreeUnits{(pixel,), NoDims, nothing}}

  • image_height::Unitful.Quantity{Float64, NoDims, Unitful.FreeUnits{(pixel,), NoDims, nothing}}

Examples

using RunwayLib, Unitful.DefaultSymbols, Rotations
cam_pos = WorldPoint(-10m, 0m, 0m)
cam_rot = RotZYX(zeros(3)...)
world_pt = WorldPoint(0m, 0m, 0m)

focal_length = 25mm
pixel_size = 5μm/px
camconf_centered = CameraConfig{:centered}(focal_length, pixel_size, 4096.0px, 2048.0px)
project(cam_pos, cam_rot, world_pt, camconf_centered); nothing
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RunwayLib.CameraMatrix — Type
struct CameraMatrix{S,T<:WithDims(px)} <: AbstractCameraConfig{S}

Camera model using 3x3 projection matrix with uniform pixel units. The reference frame S can either be :offset or :centered. See Camera Model for more explanation.

Note

Notably it is the user's responsibility to construct the matrix such that the axes are aligned correctly, i.e., for S=:offset the first two offdiagonal elements must be negative.

Warning

At this time, only S = :offset is implemented.

Examples

using StaticArrays, RunwayLib
f_px = 5e6px  # focal length in pixels
cx, cy = 2048px, 1024px
matrix = SA[
    -f_px   0px  cx
    0px   -f_px  cy
    0px   0px   1px
]
CameraMatrix{:offset}(matrix, 2cx, 2cy); nothing

Related Functions

See also project.

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