6. Detecting Failure, Assessing Success

Chap 6 Notes

6.  Detecting Failure, Assessing Success

6.1.  Introduction

§  Registration is useful only if embedded in a complete system

·  Registration provides only an aligning transformation

·  Rest of embedding system makes transformation useful

§  Quality of registration is determined by its degree of alignment

6.2.  Measures of Success

§  Maintz gives 8 measures of success, including accuracy

§  We measure success of registration in terms only of accuracy

§  Accuracy is measured in terms of

·  Visual inspection

·  Comparison with a “gold standard”

·  Self consistency

§  Two categories of success:

·  For a class of images

·  For a given patient

6.2.1.  Alignment Errors

6.2.1.1.  Target Registration Error (TRE)

§  TRE = Displacement between two corresponding points after registration

§  “Target” means subject of some intervention or diagnosis

§  Has intrinsic meaning to the diagnostician or surgeon

§  TRE = T(p) – q

§  Varies from point to point

§  Typically only the magnitude |TRE| of the displacement is reported

6.2.1.2.  Fiducial Registration Error (FRE)

§  Fiducials are features chosen because they are easy to localize.

·  Attached “fiducial markers”

·  Anatomic points (rarely accurate)

§  FRE = Displacement between localized fiducial points after registration

§  Has intrinsic meaning neither to the diagnostician nor the surgeon

§  FRE is typically reported as an RMS of magnitudes:

§  FRE2 = Sum over i of |T(pi) – qi|2.

§  Fiducial Localization Error (FLE)

·  Displacement between true fiducial point and estimated fiducial point

·  Nonzero FLE causes both nonzero TRE and nonzero FRE

·  Misregistration happens because the transformation is chosen to align points that, because |FLE| > 0, do not correspond

§  FRE is often used as a measure of system accuracy

·  A poor measure

·  Typically underestimates or overestimates TRE

·  Used because FRE is readily available and TRE is not

§  Relationship between FRE, and FLE is known for rigid registration with uncorrelated FLEs:

·  RMS(FRE) = (1 – 2/N)1/2 RMS(FLE)

·  Makes it possible to determine accuracy (FLE) from self-consistency (FRE), which sets point-based systems apart from all others.

6.2.1.3.  Other Error Measures

§  Distances between lines or between surfaces

·  Tends to miss errors parallel to the feature

§  Angular displacements for rigid transformations

·  Independent of choice of origin

·  A global measure only

·  TRE increases with distance from rotation axis

§  Translational displacements for rigid transformations

·  Depends on choice of origin if rotation nonzero

6.2.2.  Statistics

§  Mean, standard deviation, root-mean-square, median are all reasonable measures of observed error

§  Error statistics have meaning only within a given pair of modalities, given anatomy, and given pathology

§  TRE varies with position, so TRE statistics also have meaning only for a given position

§  FRE as a measure of success

·  Cannot be used to estimate TRE for a given patient

·  Can be used to estimate whether system is working properly for a given patient

6.3.  Methods for Estimating Error

6.3.1.  Gold Standards

6.3.1.1.  Computer Simulations

6.3.1.2.  Target Features

6.3.1.3.  Fiducial Marker Systems

6.3.1.4.  Other Standards

6.3.2.  Registration Circuits

6.4.  Accounting for Error in the Standard

§  Target feature

·  Target Localization Error (TLE)

·  Leads to exaggeration of TRE by TREm

·  Eq. (6.4)

§  Comparison to gold standard

·  Target Regist. Error of gold standard (TREg)

·  Leads to exaggeration of TRE by TREm

·  Eq. (6.5)