Phobrain

Image Analysis 3 - Distances in Poincare Spherical Space

Paper: Poincaré Embeddings for Learning Hierarchical Representations

Earlier image distance analysis.
Results for various image histogram methods applied to a sampling of 328 photos with '11' in their sequence number,
from a collection of 8K photos by Bill and Elle, and a sampling of 568 photos with '33' in their sequence number from 16K
photos, including photos from Ellen and Raf & Skot as well. Units are scaled to give a reasonable integer range.
Pair distances stratify into three groups in each case. In the two extreme cases examined, Greyscale and RGB 32^3,
all the photos in the sample are found in the central Group 2 layer of pairs, while Groups 1 and 3 have fewer unique
photos and pairs, and there is a disjoint split of all photos between Groups 1 and 3. This holds for both samples.

Photo/Pair counts per Group

MetricN PhotosGroup 1Group 2Group 3
Greyscale328189/9142328/13538139/4893
RGB 32^3328167/7231328/13832161/6510
Greyscale568336/28456568/39696232/13664
RGB 32^3568293/21426568/40865275/19525

Groups 1 & 3: Intersections between Greyscale and RGB 32^3 (photos/aggregate)

N PhotosGroup 1Group 3
328107/24979/221
568175/454114/393

Intersection of Pairs between Greyscale/RGB32 Groups (pairs/aggregate)

N PhotosGroup 1Group 2Group 3
328217/13324457/20408150/9810
5682061/4227112193/607971565/29801

Sorted picture-picture distances

Greyscale

Group 1,2,3 example pairs

Hue*Saturation 24x24

Hue*Saturation 48x48

RGB 12x12x12

RGB 24x24x24

RGB 32x32x32

Group 1,2,3 example pairs

Sample size 568 photos from 16K

With '33' in sequence number.

Greyscale

RGB 32x32x32


Numerical differences due to color profiles, and distributions

There are significant numerical diffs between Oracle and OpenJDK for a lot of pairs' distance calculations, due to different default color profiles used.
These diffs don't affect the overall distributions, but they can affect which Group an individual pair falls into.. OpenJDK vs. Oracle:

< 1:1 1:499 513731
> 1:1 1:499 513732

< 1:1 1:776 505618
> 1:1 1:776 505599

< 1:1 1:793 505533
> 1:1 1:793 723759

< 1:1 1:1690 722604
> 1:1 1:1690 509486

< 1:1 1:1869 735261
> 1:1 1:1869 517035

Overall greyscale distributions for ~118M pairs are the same for the two JDK's:

Oracle Greyscale distribution


OpenJDK Greyscale distribution


For some images, ImageIO.read() returns e.g. 673/58903 differing bytes, including these from a stretch of about 100 pixels:

< -9876933
> -9942469

< -9876931
> -9942467

< -4279385
> -4344921

Here is the image:






Software
Histograms from BoofCV.



What use to cry for Capricorn? it sails
Across the heart's red atlas: it is found
Only within the ribs, where all the tails
The tempest has are whisking it around.


— Mervyn Peake, Titus Alone

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