Reverse geocoding is one of HERE Technologies most heavily used services. From its access logs geocodes can be extracted and then counted with respect to some cellulation of the earth–-creating a sparse heat map. For our Place & Address Search products we use such a heat map to define a notion of relative place importance to rank and index addresses and places. However, the large data size, sparsity, and variations in traffic from which different global heat maps may be derived, makes faithful visualization and comparison a challenge. Additionally, common implementations of spatial image processing techniques that can help address the aforementioned challenges don’t map directly onto Spark’s computing engine. In this talk Arvind Rao will describe implementations of histogram equalization and kernel-based sparse image processing methods on Spark. Histogram equalization, which is best known as a method of contrast enhancement, automatically normalizes images, facilitating comparison. Along the way, Arvind will talk about how HERE uses heat maps as a feature in their autocompletion service, and say just enough about perception of contrast to put histogram equalization in context.

1. Arvind Rao, HERE Technologies
@cwcomplex
Spatial Processing of
Global Heat Maps with
Apache Spark
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2. Agenda
• Definition of the heat map
– How its built from access logs
• Contrast enhancement
– Description of histogram equalization
• Kernel based image processing
– Gaussian blur. Motivated by noise removal
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5. Heat Map is a Spatial Histogram
• The earth is partitioned into cells
– Defined by fixed latitude & longitude increments
• Reverse geocodes within each cell are summed
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6. Aggregation of Request Coordinates
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7. Caveat: Cell Areas Vary by Latitude
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India
Europe

8. Definition & Data
• Not a conventional image
– Not acquired by a camera or sensor
– ~ 6.5 trillion tiles
• High Resolution
– For perspective a 4k display has ~ 8 million pixels
– By comparison the heatmap is ~ 1 million times more
detailed
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9. How is it used in HERE Search
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10. The Histogram is SUPER Skewed
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11. The Histogram is SUPER Skewed
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12. Loose Description of Histogram
Equalization (HE)
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13. Loose Description of Histogram
Equalization (HE)
Literally mapping data to percentile rank.
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14. Loose Description of HE
𝑙 ↦ 𝑃(𝐿 < 𝑙)×𝑁
Max Pixel Value
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15. Loose Description of HE
T
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16. Log Scaled vs. Histogram Normalized
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17. HE – Well- Defined Comparison
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18. HE Implementation
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Heat Map DF
Row(latitude, longitude,
count)
Map Row(latitude, longitude, density)
Row(latitude, longitude,
CDF(density) × N)
Map

19. Cumulative Distribution Function
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Row(latitude, longitude, density)
Histogram
Row(density, count)
group by
on density
collect locally &
accumulate CDF
Array of (density, count)
CDF
Broadcast of CDF Array

20. HE Implementation
Binary search finds closest left bin to given
density in CDF.
Then linear interpolate
between left and right
bins
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21. Some Things To Know
• May increase the contrast of background noise,
while decreasing the usable signal
• HE often best in scientific images, like thermal,
satellite, or X-rays
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22. Spatial Processing
• Transform image pixel by a function of neighborhood
pixel values
• Examples of kernel based methods:
– Mean, median, Gaussian, etc.
– Also useful in edge-detection & segmentation
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23. Spatial Processing
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neighborhood
pixel of interest
Imperative solution:
Slide kernel window
over image
• Iterate pixel by pixel
• Each pixel knows its
neighborhood.

24. Spatial Processing – Kernel for Blur
Gaussian kernel with 𝜎 = 1,
𝐻 𝑥, 𝑦 =
1
273
1 4 7
4 16 26
4 1
16 4
7 26 41
4
1
16
4
26
7
26 7
16
4
4
1
Transformed image,
𝐼7(𝑥, 𝑦) = 8 𝐻(Δ𝑥,Δ𝑦)𝐼(𝑥 + Δ𝑥, 𝑦 + Δ𝑦)
;<,;=
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Implemented with
a GroupBy
kernel application
Implemented with
a GroupBy
kernel application

25. Spatial Processing
Functional approach: process each pixel
independently.
Sketch of Algorithm:
1. Explode heat map to DataFrame of pointers from
new pixel indices to all non-null neighbors in the
original image
2. Map over exploded DataFrame to apply kernel
3. GroupBy on pixel indices (latitude & longitude)
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26. Spatial Processing
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Exploding heat map
DataFrame gives all
indices of pixels in
the transformed
image.

27. Spatial Processing
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The smoothed image is larger
and less sparse.

28. Spatial Processing
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Being a
neighbor is
reciprocal.

29. Spatial Processing
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Should think of rows in the exploded
DataFrame as a pointer from any pixel
index in the image domain to its non-null
neighbor from input image.
Sparsity guarantees that a
pixel index exists in exploded
DataFrame iff it has a non-null
neighbor.

30. Spatial Processing
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𝚫x 𝚫𝐲 nb-x nb-y originating
value
0 0 34.23 120.56 120
1 -1 34.24 120.55 120
2 -2 34.25 120.54 120

31. Spatial Processing
Sketch of Algorithm
1. Explode heat map to DataFrame of pointers
from new pixel indices to all non-null neighbors
in the original image.
2. Map over exploded DataFrame to apply kernel.
3. GroupBy on pixel indices (latitude & longitude)
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32. Frankfurt – Without & With Blurring
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33. Berlin – Without & With Blurring
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34. Arvind Rao, HERE Technologies
@cwcomplex
Take Care!
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