QuadLoco - A fast, high precision, quadrant target center locator

This package provides a single algorithm focused on the accurate location of the precise center of a quadrant target. The input image chip is assumed to contain a prominent quad target (e.g. "detection" or "extraction" of the quad target area is assumed done).

Purpose

Quadrant targets are high contrast signal targets that are useful for performing very precise location measurements in the context of photogrammetry and computer vision applications.

The quad target pattern has characteristics that are conducive to high accuracy center point location with high precision - often to within a small fraction of a pixel.

The classic quadrant target is pattern of alternating light and dark colored quadrants of a square. These and similar patterns are often visible in industrial settings, on spacecraft launch vehicles and in precision metrology environments.

QuadLoco is a C++ open source software library that provides fast, reliable and accurate location of the center point in digital image regaions that are assumed to contain a quad target image.

In general practical applications, there are multiple phases:

• Detection (finding what features in an image are likely quadrant targets)
• Localization (finding center with subpixel precision and accuracy)
• Verification (using "find" solution to verify raster sample is a quad target)

This library focuses on localization.

Build

CC=/usr/bin/clang CXX=/usr/bin/clang++\
 \
 cmake\
 -DCMAKE_BUILD_TYPE=Release\
 -DCMAKE_PREFIX_PATH=/tmpLocal/\
 -DCMAKE_INSTALL_PREFIX=/tmpLocal/\
 ~/repos/QuadLoco\
 &&\
 cmake --build . --target all -j `nproc`\
 &&\
 ctest
 &&\
 cpack

Project Concepts

Quad Targets

• Quadrant target design

  • alternating quadrants of homogeous dark and light areas (e.g quadrants 1 and 3 are dark while 2 and 4 are light or vice versa.

Terminology

Features

• Line - infinitely long and undirected

• Segment (of line) - finite section of a line that is assigned a direction.

  • Defined by a two points: a begin and an end
  • Segment Direction (SegDir): defined as unit vector from begin toward end
  • Edge Direction (EdgDir): righthand perpendicular to SegDir

• Quadrant

  • Invariant: -- Four individual Quadrant areas that form the target signal
  • Object Space: -- Each of four areas has same geometry -- Half-turn rotation symmetry -- Quarter turn radiometric antisymmetry -- right angle radial edge segments -- Point reflection symmetry of areas
  • Image Space: -- Half-turn rotation symmetry in perspective images -- Point reflection symmetry of areas

• Radiometric Convention

  • Foregraound - bright color (like continuation of surround)

  • Surround - foreground color (bright)

  • Background - dark color (treat like holes in the surround)

  • Signal - the two background quadrants. Defined by edges including

    -- edge: radial segments (with one end at center)

    -- edge: outer segments (perpendicular to the radial edges)

    -- area: background squares delimited by four edges each

• Border

  • Corners - two: defined by intersection of adjacent outer edge segments

    -- Outside Signal Corners

    -- Inside Signal Corners (end points of radial edges)

• Edge Relationships

  • The four radial edges point toward the vicinity of the center (they do not point exactly at the center because of radiometric effects such as blooming which displace radial edges transversly)

  • Each radial edge points toward a midside corner.

  • Adjacent edges (two radial edges that share a quadrant area in common.

  • Opposite edges are the the two radial edges that are approximately colinear with each other (albeit oppositely directed).

  • Opposite edges generally exhibit approximately equal and opposite transverse displacements as a function of radiometric effects. Therefore, the midline halfway between opposite radial edges very nearly passes through the center.

• Center - theoretical point

  • For work here, the center is assumed to be part of the (pixel) data sample (e.g. center is visible in tentative selection window)

  • For practial purposes the image center can be defined as the point which simultaneously (e.g. in least squares sense) is closest to being colinear with all four radial edges.

Target Image Properties

• A perspective image of the target has theoretically useful properties that include:

  • approximately homogenous areas remain relatively homogenous -- variation due to illumination change -- radiometric noise from various sources

  • under true perspective projection, straight lines map into straight lines. For systems that have significant optical distortion either: -- algorithms should use corrected pixel coordinate locations -- detection/localization can be performed on a resampled image -- TODO/TBD - how/where to do this in design

  • there is a reasonable Signal/Noise ratio - specifically the variance of the foreground pixels and the variance of the background pixels is small compared with the distinction between background and foreground expected pixel values.

General Approach

• Obtain a raster data sample from original image. E.g. by cropping pixels from an image, or perhaps by performing a resampling operation to correct for lens distortion.

  • Assume raster sample provides intensity values. Lowest values are associated with the (darker) background signal, and higher values are associated with the (lighter) foreground signal.

• Determine candidate center points

  • An annular filter is utilized to compute a pseudo-probability that the radiometric content of the annular area has half-turn symmetry.

  • Local maxima in the annular filter response are associated with candidate peak locations (with resolution of integer pixel location)

• Compute precise center

  • The strongest peaks are utilized as nominal locations about which to run an area based half-turn symmetry filter. This area filter is run on a small neighborhood around each candidate peak location.

  • The area filter response is used to compute a subpixel location for the filter response maximum.

Software Components

Project namespace headers

Namespace Summary

The project top level namespace is "quadloco". All declarations can be accessed by including the top level file

• QuadLoco (or QuadLoco.hpp) - Project top level header - includes all others e.g.

   #include <QuadLoco>
  

The top level "quadloco" namespace includes a number of sub-namespaces:

• app:: Application level utilities (a primary resource for consuming code)

• ang:: Angle data (e.g. Ring, ...)

• cast:: Casting functions

• img:: Image space - 2D data types (e.g. Spot, Grad, Area, ...

• io:: Input/Output basic capabilities

• mat:: Matrix operations support (very minimal)

• mea:: Measurements (values plus uncertainty information)

• obj:: Object space - 3D data type (e.g. QuadTarget, ...)

• ops:: Operations and processing (GridFilter, PeakFinder, ...)

• pix:: Picture element/radiometry (e.g.Noise, ...)

• prb:: Probability theory (e.g. Gauss1D, Stats, ...)

• ras:: Raster data (e.g. Grid, RowCol, SizeHW, ...)

• sim:: Simulation capabilities (e.g. Config, QuadTarget, grid, ...)

• sys:: System utilities (e.g. timing)

• val:: Value types (scalar data)

• xfm:: Transformations (e.g. MapSizeArea, ...)

Namespace Detail

Each project namespace has its own namespace header file that includes all components of that namespace.

For details refer to the 'namespace' tab in project documenation created by Doxygen during project build.