Surface Comparison and Validation Metric Christine Xu University of North Carolina at Chapel Hill 2/11/11MIDAG tutorial - MeshValmet, Christine Xu1

Motivation Segmentation comparison Shape Statistics: compare two group means 2/11/11MIDAG tutorial - MeshValmet, Christine Xu2

Volume Overlap Dice coefficient – For segmentation X and Y, the coefficient may be defined as shared information (intersection) over the average of the X and Y volumes: What is the range of Dice coefficient? 2/11/11MIDAG tutorial - MeshValmet, Christine Xu3

Volume Overlap Measurement Pros straightforward, easy to understand and compute Cons – Value depends on the amount of boundary exposed – Missing important local shape information 2/11/11MIDAG tutorial - MeshValmet, Christine Xu 4 Scenario 1Scenario 2

Boundary Distance Measurement Between what? – Ideally, corresponding boundary points – Normally, closest points Interpoint distances for two sets, S and – Thus union over both sets: d(S, ) and d(, S) 2/11/11MIDAG tutorial - MeshValmet, Christine Xu5

Boundary Distance Measurement Pros: – detailed, capture all local shape information Cons: – Too much information: a very long distance vector 2/11/11MIDAG tutorial - MeshValmet, Christine Xu6

Reportable Values Histogram – The distribution of surface-to-surface distances Mean Standard deviation Quantiles – Divide ordered data into q essentially equal-sized subsets, the kth q-quantile is the value x such that: – The 10-quantiles are called deciles – The 100-quantiles are called percentiles The nth percentile is the smallest number that is greater than n% of the whole dataset 2/11/11MIDAG tutorial - MeshValmet, Christine Xu7

Reportable Quantiles 2/11/11MIDAG tutorial - MeshValmet, Christine Xu8 Hausdorff distance: 100% quantile – Con: reflects really weird points 95 th percentile – More or less what we wanted Hausdorff to tell us Quartiles – 75 th percentile is conservative – 50 th percentile: the median Often more representative central value than the mean More robust than the mean

MeshValmet 2/11/11MIDAG tutorial - MeshValmet, Christine Xu9

MeshValmet A tool that measures surface-to-surface distance between two triangle meshes using user-specified uniform sampling – Finer sampling: more accuracy – Sparser sampling: faster, rough feeling of error distribution Can be run in GUI mode or batch mode Provide histogram and statistical information 3D visualization of surface distances Based on the code and paper of: MESH: Measuring Errors between Surfaces using the Hausdorff distance (ICME 2002) by Nicolas Aspert. 2/11/11MIDAG tutorial - MeshValmet, Christine Xu10

MeshValmet Documentation (pdf): – Google ‘MeshValmet’ or: – Windows and Linux executables: – Windows: Windows.zip Windows.zip – Linux: 3.0-Linux.tar.gzhttp:// 3.0-Linux.tar.gz Any questions or bugs, please report to me at: 2/11/11MIDAG tutorial - MeshValmet, Christine Xu11

Usage of MeshValmet Step 1. Load in two triangle meshes. Key ‘t’ and ‘j’ to switch between the ‘trackerball’ and ‘joystick’ mode in two display windows. Step 2. Specify sampling step and minimum sampling frequency used for sub-sampling. Step 3. Choose A->B or B-> or both. This is due to the asymmetric property of Hausdorff distance. Step 4. Choose the number of bins of the resulting histogram. Step 5. Choose either signed distance error or absolute distance error. Positive: outward distance; negative: inward distance Step 6. Click button ‘Compute Error’ Step 7. (optional) Change settings in the ‘Colormap Control’ panel Step 8. (optional) Change settings in the ‘Histogram Control’ panel Step 9. View the statistical results of the comparison. 2/11/11MIDAG tutorial - MeshValmet, Christine Xu12

Statistics in MeshValmet Sample Err Mean: Sample Err STD: Face Err Mean: Face Err RMS: Hausdorff: MSD: MAD: 2/11/11MIDAG tutorial - MeshValmet, Christine Xu13

Alternative: CompareBYU Pros: – Provides volume overlap of two surfaces – Reads BYU-formatted input files - triangles or quads Cons: – Runs only on the command line and has no GUI – Do not provide user-specified uniform sampling Only computes error on original vertices in the ‘BYU’ files (if the triangle tiles in the mesh are not all the same size, the measures reported are not accurate enough) 2/11/11MIDAG tutorial - MeshValmet, Christine Xu14