Human Detection under Partial Occlusions using Markov Logic Networks

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Human Detection under Partial Occlusions using Markov Logic Networks

Raghuraman Gopalan and William Schwartz

Center for Automation ResearchUniversity of Maryland, College Park

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Human Detection

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Human DetectionHolistic window-based:•Dalal and Triggs CVPR (2005)•Tuzel et al CVPR (2007)

Part-based:•Wu and Nevatia ICCV (2005)•Mikolajczyk et al ECCV (2004)

Scene-related cues:•Torralba et al IJCV (2006)

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The occlusion challenge

* Probability of presence of a human obtained from Schwartz et al ICCV (2009)

Body parts occluded by objects Person occluded by another person

0.0059* 0.0816

0.14520.1272

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Related work

Bilattice-based logical reasoning: Shet et al CVPR (2007)

Integrating probability of human parts using first-order logic (FOL): Schwartz et al ICB (2009)

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Our approach: Motivation

A data-driven, part-based method1. Probabilistic logical inference using

Markov logic networks (MLN) [Domingos et al, Machine Learning (2006)]

2. Representing `semantic context’ between the detection probabilities of parts.

Within-window, and between-windows With and without occlusions

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Our approach: An overviewMultiple detection windows

Part detector’s outputs

Face detector outputs

Instantiation of the MLN

Inference

Final Result

Queries:

- person(d1)?- occluded(d1)?- occludedby(d1,d2)?

Learning contextual

rules

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Main questions

How to integrate detector’s outputs to detect people under occlusion? Enforce consistency according to spatial

location of detectors → removal of false alarms.

Exploit relations between persons to solve inconsistencies → explain occlusions.

Both using MLN, which combines FOL and graphical models in a single representation → avoids contradictions.

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Inference

Final Result

Queries:


Learning contextual

rules

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Part-based detectors To handle human detection under occlusion, our original detector is split

into parts, then MLN is used to integrate their outputs.

original

top

torso

legs

top-torso

torso-legs

top-legs

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Detector – An overview

Exploit the use of more representative features to provide richer set of descriptors to improve detection results – edges, textures, and color.

Consequences of the feature augmentation: extremely high dimensional feature space (>170,000) number of samples in the training dataset is smaller

than the dimensionality

These characteristics prevent the use of classical machine learning such as SVM, but make an ideal setting for Partial Least Squares (PLS)*.

* H. Wold, Partial Least Squares, Encyclopedia of statistical sciences, 6:581-591 (1985)

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Detection using PLS

fUqy

ETPXT

T

T, U are (n x h) matrices of h extracted latent vectors. P (p x h) and q (1 x h) represent the matrices loadings and E (n x p) and f (n x 1) are the residuals of X and Y, respectively.

PLS method NIPALS (nonlinear iterative partial least squares) finds the set of weight vectors W(p x h) ={w1,w2,….wh} such that

PLS models relations between predictors variables in matrix X (n x p) and response variables in vector y (n x 1), where n denotes number of samples, p the number of features.

2

1||

2 )],[cov(max)],[cov( yXwut iwiii

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Inference

Final Result

Queries:


Learning contextual

rules

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Context: Consistency between the detector outputs

topTorso(d1) ^ top(d1) ^ torso(d1) → person(d1) (consistent)

topTorso(d1) ^ (¬top(d1) v ¬torso(d1)) → ¬person(d1) (false alarm)First order logic rules:

Each detector acts in a specific region of the body. One can look at the output of sensors acting in the same spatial location to check for consistency – similar responses are expected.

Example:

top-torso top torso

Given that top-torso detector outputs high probability, top and torso detectors need to output high probability as well since they intersect the region covered by top-torso.

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Context: Understanding relationship between different windows

d1

d2

intersect(d1,d2) ^ person(d1) ^ matching(d1,d2) →

person(d2) ^ occluded(d2) ^ occludedby(d2,d1)

First order logic rule:

matching(d1,d2) is true if:

- Detectors at visible parts of d2 have high response.

- detectors at occluded parts of d2 have low response while sensors located at the corresponding positions of d1 have high response.

Low response given by a detector might be caused by a second detection window (a person may be occluding another and causing low response of the detectors).

- d1, and d2 are persons- d1 and d2 intersect

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Inference

Final Result

Queries:


Learning contextual

rules Fi

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3. Inference using MLN* - The basic idea A logical knowledge base (KB) is a set of

hard constraints (Fi) on the set of possible worlds

Let’s make them soft constraints:When a world violates a formula,It becomes less probable, not impossible

Give each formula a weight (wi)(Higher weight Stronger constraint) satisfiesit formulas of weightsexpP(world)

Contents of the next three slides are partially adapted from Markov Logic Networks tutorial by Domingos et al, ICML (2007)

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MLN – At a Glance

Logical language: First-order logic Probabilistic language: Markov networks

Syntax: First-order formulas with weights Semantics: Templates for Markov net features

Learning: Parameters: Generative or discriminative Structure: ILP with arbitrary clauses and MAP score

Inference: MAP: Weighted satisfiability Marginal: MCMC with moves proposed by SAT

solver Partial grounding + Lazy inference / Lifted inference

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MLN- Definition

A Markov Logic Network (MLN) is a set of pairs (Fi, wi) where Fi is a formula in first-order logic wi is a real number

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Example: Humans & Occlusions

patterns.y probabilitdetector out thereason toseir windowbetween thcontext analyze occlude, persons When two2)

parts. of presence implieshuman a of Presence 1)

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1.15.1

Two constants: Detection window 1 (D1) and Detection window 2 (D2)

)()(),(,)()(

yHumanxHumanyxOcclusionyxxPartsxHumanx

D1

D2

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1.15.1

Parts(D1)

Human(D1) Human(D2)

Parts(D2)


)()(),(,)()(


One node for each grounding of each predicate in the MLN

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1.15.1

Parts(D1)

Human(D1)Occlusion(D1,D1)

Occlusion(D2,D1)

Human(D2)

Occlusion(D1,D2)

Parts(D2)

Occlusion(D2,D2)


)()(),(,)()(


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1.15.1

Parts(D1)


Occlusion(D2,D1)

Human(D2)

Occlusion(D1,D2)

Parts(D2)

Occlusion(D2,D2)


)()(),(,)()(


One feature for each grounding of each formula Fi in the MLN, with the corresponding weight wi

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1.15.1

Parts(D1)


Occlusion(D2,D1)

Human(D2)

Occlusion(D1,D2)

Parts(D2)

Occlusion(D2,D2)


)()(),(,)()(


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1.15.1

Parts(D1)


Occlusion(D2,D1)

Human(D2)

Occlusion(D1,D2)

Parts(D2)

Occlusion(D2,D2)


)()(),(,)()(


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Instantiation MLN is template for ground Markov nets Probability of a world x:

Learning of weights, and inference performed using the open-source Alchemy system [Domingos et al (2006)]

Weight of formula Fi No. of true groundings of formula Fi

iii xnw

ZxP )(exp1)(

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Inference

Final Result

Queries:


Learning contextual

rules

Results

Results

Results

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Comparisons

Dataset details: •200 images•5 to 15 humans per image•Occluded humans ~ 35%

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Comparisons

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Conclusions

A data-driven approach to detect humans under occlusions

Modeling semantic context of detector probabilities across spatial locations

Probabilistic contextual inference using Markov logic networks

Question of interest: Integrating analytical models for occlusions and context with this data-driven method

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Questions ?

Documents

Human Detection under Partial Occlusions using Markov Logic Networks