Interactive Model Prototyping in Visualization Space

Identifying and building models, and quantifying model parameters

-- Ove Daae Lampe and Helwig Hauser

Who am I?

Ove Daae Lampe

+Ove Lampe | ii.uib.no/vis | cmr.no/cmr_computing

Researcher at CMR Computing and PhD Student at UiB

Slides are available here: http://folk.uib.no/ola062/sigrad2011

Interactive Model Prototyping in Visualization Space

Model Building

Understanding underlying behaviour of the data
Abstracting data
Quantifying controlling parameters

Model Constructs

Point Construct
Linear Construct
Exponential Construct

Visualization Space

Model prototyping in Visualization Space analyzes visual representations of the data rather than the data.

In effect we rasterize the data once, and optimize the difference between this and a rasterized version of a model

But WHY Visualization Space

The data is rasterized once
Optimize and fit multiple models efficiently
Local models can be sketched
Directly observe convergence / divergence and the Residual

User sketching and Automated Fitting

Interactive Convergence

Constant-step iterations while interacting. Newton's optimization applied afterwards.

Optimizing:

Position / mean / μ
Radius / std.dev / σ
Scale / integral

Workflow I

Workflow II

Visualize and Observe
Sketch and Fit
Externalize and Subtract
Iterate

Test Dataset

A(x) = N(0,1)
C(x) = 0.05N(1,0.2)
B(x) = A(x)+C(x)

Step 1. Visualize and Observe

Step 2. Sketch and Fit

Step 3. Externalize ...

Modeled:

μ = (0.02,0.01)
σ = (1.035,1.04)

Reference:

μ = (0.0,0.0)
σ = (1.0,1.0)

Step 3. ... and Subtract

Step 4. Iterate

Modeled:

μ = (1.004,1.004)
σ = (0.1989,0.2015)

Reference:

μ = (1.0,1.0)
σ = (0.2,0.2)

Domain

Example

Drilling Data I

Drilling Data II

Torque measured in kN.m over time in seconds.

Step 1: Visualize and Observe

Step 2+3: Sketch, Fit, ... and Subtract

Step 4: Iterate

Externalized Result

Result: a quantitative plot of mean torque over depth and error (one standard deviation ≅ 68% of the measurements).