MARKLESS REGISTRATION FOR SCANS OF FREE-FORM OBJECTS

Laboratory of photogrammetry of NTUA Artemis Valanis, PhD Student Charalambos Ioannidis, Professor

Target: to initialize the ICP algorithmin order to register partial scans of uniform or free-form objects

Difficulty: no targets present no characteristic points identifiable in the area of overlap

Problem identification

Motivation

Front view Side view

Initial state

Front view Side view

MotivationResult of ICP - no prior processing

Various approaches for automatic ICP initialization:

Bae & Lichti, 2004 Geometric primitives Gelfand, 2005 Feature points Hansen, 2006 Plane-matching Makadia, 2006 Extended Gaussian

Images Biswas, 2006 Isosurfaces

Related Literature

Bae & Lichti, 2004 Geometric primitives Gelfand, 2005 Feature points Hansen, 2006 Plane-matching Makadia, 2006 Extended Gaussian Images Biswas, 2006 Isosurfaces

Example Objects

Constrained acquisition process Properly adjusted methods that:◦Recover the relative transformation between two or more

partial scans◦Approximately align the point clouds◦Enable the initialization of ICP ◦Achieve the optimal alignment of partial scans without the

use of targets or the identification of conjugate points

Proposed approach

Worked cases

Worked cases

HDS2500FOV 40ox40o spot size = 6mm position accuracy = ±6mm (50m range)

Equipment used

Key Idea

Y

XZ

Y

X Z

Y

X

Zω

Acquisition scenario

Key Idea

Y

X Z

Y

X Z

Y

X

Zω

Y

X

Zω

Acquisition scenario Acquired dataProposed approach

Front view Side view

Initial state

Front view

Result of ICP combined with the proposed method

Front view Side view

Data imported:2 scans acquired either by rotating the scan head vertically (ω angle) or horizontally (φ angle)

Process:The space of the unknown parameter (ω or φ angle) is sequentially sampled in order to obtain an approximation of the unknown angle. If the value of the evaluated measure is minimized then an approximate value is derived

Proposed algorithm

If the unknown rotation is ω

◦The ω is given an initial value 0 that is increased by 5g in every loop

◦For every ω value, a rotation matrix is calculated and applied to the point-cloud that needs to be registered

◦After the transformation, the area of overlap between the reference and the moving scan is calculated and a rectangular grid is defined

Sampling process 1/2

◦The evaluated function i.e. the median of the distances of the two point clouds at the nodes of the grid along the Z direction, is derived based on 2D tesselations created for each point-cloud

◦Once the comparison measure reaches a minimum, the process is repeated at the respective interval with a step of 1g

◦When another minimum is detected, the final value is derived by a simple interpolation

Sampling process 2/2

2 scans acquired by different ω angle 5 targets used to evaluate the results Algorithm implemented in Matlab Calculation of the unknown transform in Cyclone and

in Matlab

Method Validation

Initial State

Target distances as calculated for the original scans

T (X,Y,Z) 0.0000 0.0000 0.0000 (m)

R (ω,φ,κ) 0.0000 0.0000 0.0000 (grad)

TargetID X-error (m)

Y-error (m)

Z-error (m)

Total error (m)

4 -0.0202 1.9803 -0.5524 2.0560

7 -0.0251 2.4629 -0.4710 2.5077

3 -0.0254 2.5420 -0.4685 2.5849

1 -0.0322 3.3798 -0.8934 3.4960

13 -0.0321 3.1860 -0.8455 3.2964

Results of the sampling process

Coarse sampling Fine sampling

ωι sign(mzi) |mzi| ωι sign(mzi) |mzi|

0 (-) 1.2349m 10 (-) 0.084m

5 (-) 0.6235m 11 (+) 0.0221m

10 (-) 0.084m Approximate value

15 (+) 0.4264m ωο =10.7920g

Results after the approximate alignment

Results after the approximate alignment

T (X,Y,Z): 0.0000 0.0000 0.0000 (m)

R (ω,φ,κ): 10.7920 0.0000 0.0000 (grad)

TargetID X-error (m)

Y-error (m)

Z-error (m)

Total error (m)

4 -0.0202 0.0070 0.0109 0.0240

7 -0.0251 0.0113 0.0090 0.0289

3 -0.0254 0.0106 0.0048 0.0279

1 -0.0322 0.0198 -0.0067 0.0384

13 -0.0321 0.0159 -0.0016 0.0359

Result of ICP after the application of the proposed algorithm

T(X,Y,Z): -0.0007 -0.0074 0.0122 (m)

R(ω,φ,κ): 10.8685 0.1134 0.0156 (grad)

TargetID X-error (m)

Y-error (m)

Z-error (m)

Total error (m)

4 0.0004 -0.0003 -0.0008 0.0010

7 0.0001 -0.0010 0.0012 0.0016

3 -0.0004 0.0013 0.0022 0.0026

1 -0.0013 0.0012 0.0015 0.0023

13 0.0005 0.0025 0.0007 0.0027

Results of ICP after the application of the proposed algorithm

Application of the method for the monument of Zalongon

9 set-ups

14 scans in total

4 scans with no tagets

Back

3 set-ups

4 scans (2 single and a scan-pair)

Front

6 set-ups

10 scans (3 single, 2 scan-pairs and a scan-

triplet)

Accuracy evaluation for 2 scan-pairs

Scan couple of set-up 5 (top to base)

ICP initialization for ωο =25.0327g

TargetID X-error (m) Y-error (m)

Z-error (m)

Total error (m)

11 -0.0003 -0.0020 0.0016 0.0026

10 -0.0003 -0.0038 0.0012 0.0040

Scan couple of set-up 6 (top to base)

ICP initialization for ωο =35.6083g

TargetID X-error (m) Y-error (m)

Z-error (m)

Total error (m)

16 -0.0016 -0.0071 0.0013 0.0074

Scan triplet of set-up 7 (top to middle)

ICP initialization for ωο =18.1991g

Average alignment error = 0.0070m

Scan triplet of set-up 7 (top & middle to base)

ICP initialization for ωο =18.1828g

Average alignment error = 0.0067m

TargetIDX-error

(m) Y-error (m) Z-error (m)Total error

(m)

15 0.0005 -0.0027 0.0009 0.0029

6 0.0022 -0.0009 0.0009 0.0026

Accuracy evaluation for a scan-triplet

Registration results

3D surface model

With minor modifications, it is as easily applied for horizontal rotations

Applicable also for sequences of scans acquired under the described conditions

Provides a solution in cases of serious space limitations

A non-elaborate and effective solution for all of those who have invested on similar equipment

Merits of the proposed approach

Thank you for your attention!