Voronoi diagrams in information geometry: Statistical Voronoi diagrams and their applications
Browsing large image datasets through Voronoi diagrams
description
Transcript of Browsing large image datasets through Voronoi diagrams
Browsing large image datasetsthrough Voronoi diagramsPaolo Brivio, Marco Tarini, Paolo Cignoni
• Fairly large datasets (i.e. 1000s images)• cannot be all visible at the same time
• Non-uniform image aspect ratio• landscape vs portrait• image orientation
• Total ordering• e.g. time of shot, some ordering defined over calibration,
user-defined sequence, etc.• Allow to specify per-image importance• i.e. each image represents a subset of the dataset
Targeted image datasets
• Rectangular grid of image thumbnails• [opt] on scrolling panels
Conventional image browsers (fullscreen)
Explorer
by Microsoft
Image
by Google
FastStone
Picasa3
by Google
• Sequence of image thumbnails• [opt] scrollbars or buttons
PhotoC
loudby IS
TI-CN
RFastS
toneConventional image browsers (thumbnail bars)
Picasa3 by G
oogle
Other drawbacks: non-uniform aspect ratios
wasted space
Google Im
age
A new type of thumbnail bar
focusimage
Thumbnail sizes
focusimage
far from focus:small thumbnails
near to focus:large thumbnails
Thumbnail sizes
focusimage
thum
bnai
l siz
e
distance from focusin image list0
(focus image)±10 ±20
Clustering images
focusimage
far from focus:each thumbnail
represents many images
near to focus:1 thumbnailfor 1 image
Selecting visible images
focusimage
41 2 3 5 6 7
visibleimage
hiddenimage
repr
esen
tativ
enes
s
imagenumber
custo
m
fuctio
n
focus
Spatial ordering
focusimage
previous imagesin the ordering
following imagesin the ordering
x-axis: image ordering respected
y-ax
is:
arbi
trar
y
• Define a parametric domain in which the ordering is enforced• Arbitrary thumbnail-bar shape
custom parametric
function
Not only horizontal thumbnail bars
Parametric domain
Thumbnail-bar shape
enforce ordering
Transitions
focusimage
new focus
focusimage
Packing of thumbnails• arbitrary bar shape• irregular shaped
thumbnails• varying size• fitting
aspect/orientation• image ordering respected• 1 thumbnail per image
cluster
Transitions
newfocus
Packing of thumbnails• arbitrary bar shape• irregular shaped
thumbnails• varying size• fitting
aspect/orientation• image ordering respected• 1 thumbnail per image
cluster
Animated transition
withtemporal
coherence
Autorecentering Voronoi diagrams
• Voronoi diagram:• given a set of 2D “seeds” inside a 2D figure F• partition F into as many “regions”• a point belongs to the region of the closest seed
• Autorecentering step (Lloyd relaxation):• move seed (●) of each region in its barycenter (+)
x nx 1
Taming autorecentering Voronoi diagrams
Taming autorecentering Voronoi diagrams 1/2
• Weighting for region size differentiation• Power Diagram
• Dynamic weight balancing • match required region sizes• smooth transitions
• including: smooth appear/disappear of regions• Ordering enforcing (over “x”)• interleaved with recentering step
• Anisotropy: make regions appropriate• …aspect ratio• …orientation (non axis-aligned)
Taming autorecentering Voronoi diagrams 2/2
• Stabilization• prevent oscillations
• Small extra forces• pulling regions toward expected positions• accelerate convergence
• Accept user “dragging” mouse gesture• Real time computation• efficient GPU implementation
Tamed autorecentering Voronoi diagrams
Packing of thumbnails• arbitrary bar shape• irregular shaped
thumbnails• varying size• fitting
aspect/orientation• image ordering respected• 1 thumbnail per image
cluster
optional bulge-out effect
Animated transition
withtemporal
coherence
Thumbnail creationor
igin
al
imag
ere
gion
sh
ape
+ resizing- cropping
- resizing+
cropping
+
Thumbnail creation: with per-image orientationor
igin
al
imag
ere
gion
sh
ape
+ resizing- cropping
- resizing+
cropping
+
Example
More examples