Reachability Embeddings Scalable Self-Supervised Representation Learning from Spatiotemporal Motion Trajectories for Multimodal Computer Vision

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Reachability Embeddings: Scalable Self-Supervised

Representation Learning from Spatiotemporal Motion

Trajectories for Multimodal Computer Vision

Swetava Ganguli∗

, C. V. Krishnakumar Iyer, Vipul Pandey

Apple

{swetava,cvk,vipul}@apple.com

1 Introduction

GPS Record

Deduced Trajectory

s′

s′ ′

Absorption

Transition

(s,s′ ′ )

Emission

Transition

(s′ ,s)

Nodes Zoom-24 Tiles Pixels

↔

T7Trajectories

Node,

Neighbor Nodes,

s′ ∈NδR

δR

NδR

Only influence

computation of

{T1,T2,T3}

Ψea

Emission Nodes,

s′ ∈Ξs

Absorption nodes,

s′ ∈Λs

Nodes part of both and

Ξs

Λs

Gaussian distance and

time weight decay not

computed

Algorithm 1

Ψa

Ψe

Ψea

Emission Channel of

Absorption Channel of

Reachability Summary of

ℱe

Reachability

Encoder

Reachability Embedding of

h(s)∈ ℝdR

Pixel&=&Zoom-24&Tile

Each&number&along&the&channel&dimension&

corresponds&to&a&meaningful&real&number&

associated&with&the&zoom-24&tile&

Image-like Representation using

Reachability Embeddings as

Input for Downstream Task-

Specific Models

Pixel&=&Zoom-24&Tile

Each&number&along&the&channel&dimension&

corresponds&to&a&meaningful&real&number&

associated&with&the&zoom-24&tile&

Nodes Zoom-24 Tiles Pixels

↔

Figure 1: Generation of reachability embeddings.

Graphs are natural data structures for representing geospa-

tial datasets (e.g., road networks, point clouds, 3D ob-

ject meshes) with natural deﬁnitions of nodes and edges.

Instead of hand-engineering task-speciﬁc and domain-

speciﬁc features for nodes in graphs, recent methods

[

] have focused on automatically learning low-

dimensional, feature vector representations called node

embeddings. In parallel, self-supervised learning has been

an area of active and promising research. Self-supervised

representation learning techniques utilize large datasets

without semantic annotations to learn meaningful, univer-

sal features that can be conveniently transferred to solve

a wide variety of downstream supervised tasks. In [

we propose a novel self-supervised method for learning

representations of geographic locations from observed un-

labeled GPS trajectories that can be used by itself or can

be combined with other image-like data modalities to solve downstream geospatial computer vision tasks. A spatial

proximity-preserving graph representation of the earth surface is inferred from observed mobility trajectories that is used

to cast the geospatial representation learning task into a task of learning self-supervised node embeddings. Reachability

embeddings serve as task-agnostic, feature representations of geographic locations. Using reachability embeddings as

pixel representations for ﬁve different downstream geospatial tasks, cast as supervised semantic segmentation problems,

we quantitatively demonstrate that reachability embeddings are semantically meaningful representations and result in

4–23% gain in performance, as measured using area under the precision-recall curve (AUPRC) metric, when compared to

baseline models that use pixel representations (called Local Aggregate Representations (LAR)) that do not account for the

spatial connectivity between tiles [

]. Reachability embeddings transform sequential, spatiotemporal motion trajectory

data into semantically meaningful image-like tensor representations that can be combined (multimodal fusion) with other

data modalities (on machine learning platforms such as Trinity [

]) that are or can be transformed into image-like tensor

representations (for e.g., RBG imagery, graph embeddings of road networks, passively collected imagery like SAR, etc.) to

facilitate multimodal learning in geospatial computer vision. Multimodal computer vision is critical for training machine

learning models for geospatial feature detection to keep a geospatial mapping service up-to-date in real-time and can

signiﬁcantly improve user experience and above all, user safety.

2 The Reachability Embeddings Algorithm Proposed in [4]

AGPS trajectory encodes spatiotemporal movement of an object as a chronologically ordered sequence of GPS records (a

tuple of timestamp and the location’s zoom-24 tile [

]). Let

represent the set of all available GPS trajectories during the

time interval

[t0, t0+ ∆t]

such that all GPS records in each trajectory are associated with the same motion modality (e.g.,

driving, walking, biking). The Earth Surface Graph (ESG),

GES (VES ,EES )

, is deﬁned as the inferred graph obtained

from a raster representation of the earth’s surface based on zoom-24 tiles with these tiles as nodes,

VES

. GPS trajectories

are modeled as allowed Markovian paths on the ESG thereby deﬁning the edges of the ESG,

EES

, as the observed

transitions between nodes in

. In summary, the following equivalences are deﬁned: (i) zoom-24 tile

↔

Markovian state

∗Corresponding author. Alternative EMail: swetava@cs.stanford.edu

Abstract accepted for poster presentation at BayLearn 2022.

arXiv:2210.03289v1 [cs.CV] 7 Oct 2022

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ReachabilityEmbeddings:ScalableSelf-SupervisedRepresentationLearningfromSpatiotemporalMotionTrajectoriesforMultimodalComputerVisionSwetavaGanguli,C.V.KrishnakumarIyer,VipulPandeyApple{swetava,cvk,vipul}@apple.com1IntroductionFigure1:Generationofreachabilityembeddings.Graphsarenaturaldatastructuresf...

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Reachability Embeddings Scalable Self-Supervised Representation Learning from Spatiotemporal Motion Trajectories for Multimodal Computer Vision

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