Large Scale Data Analysis - Scientific Visualization: Uncertainty, Multifield, Biomedical, and Scalable Visualization - page 323

of base elements (e.g. clusters) or as a collection of differences between features
at different parameters (e.g. regions above threshold a that are below threshold b )
respectively.
Feature families with a nested structure can be encoded and computed in an
efficient manner. In our system, we specify for each element in the hierarchy its life
span (in terms of the feature parameter), an arbitrary number of children , and a single
parent . As is common with hierarchies, the set of features at a particular parameter
p is then defined as all elements that are alive at parameter p combined with all their
descendants. More formally we define:

Definition 27.1 ( Element )An e lement e is defined by a unique id and minimally
contains a parameter range [ p min , p max ] , a direction, a collection of its children ids,

and the id of its parent:

e = ( id , direction , [ p min , p max ] , { child 0 ,..., child n } , parent ) ∈ E

Definition 27.2 ( Feature )A feature f is the union of an element e and all its descen-
dants

= e , ... }

children n f ∪ ( e ) | n ∈{ 1 , 2

The element id is simply a unique identifier that is typically stored implicitly, e.g.
based on the order in which elements are stored in a file. The direction indicates
whether the parent of an element is born at p

<

p min and consequently its children

>

are born at p p max or the opposite.

A feature family is a collection of features defined hierarchically as described
above:

Definition 27.3 ( Feature Family )A feature family F is a set of features

F ={ f 0 ,..., f m }⊂F

Finally, in a time-dependent simulation or an ensemble of simulations we have one
feature family per time or ensemble member:

Definition 27.4 ( Clan )A clan C is an ordered set of feature families

C ={ F 0 ,..., F n }⊂ F

We store feature families in a traditional multi-resolution graph that is updated
on-the-fly as the user changes parameter. At any time we maintain a set of living
elements that serve as the representatives for their corresponding features. Using the
parent and child information this set is progressively updated as the feature parame-
ter changes. Specifically, when an element dies it is removed from the set and either
its children or its parent are born and added to the set. Furthermore, we support the
encoding of multiple hierarchies associated with a feature family by storing multiple
parameter ranges and child/parent ids in each feature, one for each hierarchy.