Progress Report

July 19th, 2005

Overview

• Bending energy
• Number of modes and syntheses in evaluation
• Euclidean distance variant
• Segmentation propagation and joint registration
• Set of experiments for a future ISBI 2006 submission

Bending Energy and Knot-points

• We select a knot-points set whenever applying CPS warps to an image
• We also consider a different number of knot-points when perturbing images
• Plotted is the mean bending energy, calculated over 10 random instantiations for a different number of knot-points (indicated by the numbers in the legend)
• Warp magnitude is overly high, hence not easily comparable across different numbers of knot-points
• Note: Y scale is logarithmic

Bending Energy and Knot-points Visually

The curves show a 'mis-behaved' increase in values since scale of deformations is ill-chosen

Synthetic Images in Evaluation

• Investigate the number of synthetic images which are necessary for evaluation
• Number of modes and number of instantiations not fully understood
• Shown in the next slide is an exploration of the model evaluation method
• The model being evaluated was constructed from a set of 38 non-rigidly registered images

Synthetic Images in Evaluation - Ctd.

• Figures show Specificity and Generalisation as a function of the number of model syntheses being generated for evaluation
• 3 curves are plotted to account for yet another parameter, namely the number of modes
• Important: This set is properly (though not perfectly) registered
• Yet to be compared against similar plots generated for a different model
• Later, a model will be constructed from images which are badly registered (otherwise said to be perturbed)

Synthesis and Number of Modes

Generalisability for the different number of modes and an increasing synthetic set size. The model was built from a registered set

Synthesis and Number of Modes

Specificity for the different number of modes and an increasing synthetic set size. The model was built from a registered set

Synthetic Images and a Perturbed Set

• Perturbed image set can be investigated to see if similar results are obtained regardless of the quality of registration
• Figures are drawn in the same way as previously done
• They also appear to behave similarly
• Further experiments can validate this test using different data

Synthesis and Number of Modes - Perturbed Set

Generalisability for the different number of modes and an increasing synthetic set size. The model was built from a perturbed set

Synthesis and Number of Modes - Perturbed Set

Specificity for the different number of modes and an increasing synthetic set size. The model was built from a perturbed set

IMage Euclidean Distance (IMED)

• Towards implementation if necessary and suitable
• Needs to be implemented in C++ (VXL)
• This consistent implementation is necessary for comparability
• Explanation of the principles
• a great deal of basic geometry is involved
• use of a spatial coefficient to be robust to deformation

IMage Euclidean Distance (IMED) - Ctd.

• Computing the distance and angle between pixels (or angles between voxels)
• Nearby pixels will be treated as related (distance dependence)
• Similar to the shuffle distance in practical terms
• Related closely to image smoothing
• Implies that smoothing noiseless image assists computation of image distance
• Offered as an improvement over simple Euclidean distance

IMage Euclidean Distance (IMED) - Ctd.

• The method sounds plausible, but not convincing as work which is said to offer improvements
• Performance probably does not equate to that of the Hausdorff distance
• A pro is said to be the easy embedment in algorithms
• A limited number of examples of embedment are demonstrated with quantitative results
• Future work will make use of tengential distance as well

IMage Euclidean Distance (IMED) - Ctd.

• The group has not considered the shuffle distance yet
• Shuffle distance is expected to outperform this method
• Overall, not entirely convincing

Model Evaluation/Registration Assessment

• VXL code for 2-D registration appears to be unready
• Document on milestones - ISBI 2006 submission plan (PDF)
• Needs to be discussed or at least confirmed to be a reasonable plan
• Primary issue is feasibility because scale is currently a misfit

Segmentation, Registartion and Models

• Experiments which demonstrate the application of our methods to segmentation
• Approach involves the following stages:
  • take a group of images
  • build a model from this group of images
  • warp (register) the images to improve their model
  • segment one image in the image set
  • use the model to propagate this segmentation to all other images in the set

Segmentation, Registartion and Models - Results

• It is possible to convince ourselves that this approach works
• Based on several results that have been accumulated (c/f experiments archive)
• There are several pitfalls (yet to be listed)
• The next slide contains an example experiment where propagation of small labels is estimated

Label Propagation Example

The automatic propagation of labels after only 10 iterations of registration (10-20 seconds in duration)

Weaknesses of the Approach

• MSD-based objective function works brutally on the data
• Yet, MSD-based OF does not identify the true correspondences
• Better performance achieved when a model-base objective function gets used
• If the experiments are run for too long, flat regions (background) get deformed
• Fitting to noise in data rather than improving the structures within

Weaknesses of the Approach - Ctd.

• Results are often far from satisfactory
• Their success if based on that of model-based registration (determinant minimisation)
• Registration is slow and unsuccessful in the MATLAB implementation
• It does roughly the right thing
• Capable of producing moderate appearance models

Summary/Conclusions

• Bending energy
  • appears to increase quadratically as a function of warp magnitude
  • warps must be made small for comparable experiments
• In model/registration evaluation:
  • the number of modes accounted for does not matter much
  • this may vary depending on the data and the size of the dataset

Summary/Conclusions - Ctd.

• Euclidean distance
  • needs extra work on VXL code
  • will not lead to much-desired results
• Segmentation propagation:
  • feasibility "proof of concept"
  • lacks accuracy and suffers from lack of constraints
• Agreement on scale of experiments towards a ISBI 2006 submission

Next Stages

• Awaiting results from registration in VXL, which is needed for extensive evaluation experiments
• Continued experiments to improve the ability to propagate segments based on registration/model-building
• Possibly test segmentation propagation in the context of 2-D registration
• Consider using segmentation to place control points more cunningly
• Add Liwei's Euclidean image distance to VXL if time allows