Using Sensors to Detect Landmines CoVar Applied Technologies The - - PowerPoint PPT Presentation

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Using Sensors to Detect Landmines CoVar Applied Technologies The - - PowerPoint PPT Presentation

Sep 29, 2023 157 likes •514 views

Using Sensors to Detect Landmines CoVar Applied Technologies The CoVar Group 1 Duke University MPI, 2016 The CoVar Group (MPI 2016) Using Sensors to Detect Landmines MPI, 2016 1 / 33 Overview Confidence Sensor Score Alarm Set Map Data

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SLIDE 1

Using Sensors to Detect Landmines

CoVar Applied Technologies The CoVar Group

1Duke University

MPI, 2016

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SLIDE 2

Overview

Sensor Data Confidence Map Alarm Set Score Alarm Set Sensors collect data over a given region Confidence maps are generated over data typically by target detection algorithms Alarms are placed using information provided by confidence map Placement of alarms is compared with ground truth locations of known targets Detection performance is estimated

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SLIDE 3

A Topological Data Analysis

x

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

C(x)

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 threshold1 threshold2 threshold3

Lower the threshold → Find region topologically connected For each region sufficiently large

Keep the prominent peak Lower the remaining peaks

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SLIDE 4

Confidence Map - Before & After

(a) (b) Figure: (a) Before (b) After

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SLIDE 5

Alarm Set - Before & After

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.1 0.2 0.3 0.4 0.5 0.6 0.7 FAR Pd CoVar Algorithm Topological Algorithm

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SLIDE 6

Denoise by local averaging

Motivation: Noise levels are different at different places. Algorithm: For each point (x, y), the confidence level is C(x, y). Define the noise level at (x, y) as noise(x, y) =

1 m(D(x,y))

  • D(x,y) C(s, t)dsdt, where

D(x, y) is the rectangle centered at (x, y) and m() is the area. The new confidence level is defined as Cnew(x, y) = C(x, y)/noise(x, y). Before denoise After denoise

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Denoise by local averaging

ROC-FAR curve with 5000 alarms

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SLIDE 8

Alarm Aggregation: Hierarchical Clustering

200 400 600 800 1000 1200 1400 −1.5 −1 −0.5 0.5 1 1.5 CoVar AlarmSet Reduced AlarmSet

Find the similarity among alarms based on their distance. Group the alarms into clusters. Keep only the alarm with the highest confidence in each cluster.

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.1 0.2 0.3 0.4 0.5 0.6 0.7 FAR Pd CoVar Algorithm Clustering

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SLIDE 9

Iterative Centroid Alarm Set Generation

Possible Concern: Placing alarms at the location of a local maximum does not consider asymmetry in the confidence map about the local maximum. Possible Solution: Centroid Location Scheme

Assume digger will (eventually) dig a circle of radius r about a given alarm For a given alarm, consider the neighborhood of radius r about the location of the alarm Consider the confidence map, c(x, y), as a mass-density function and calculate the centroid over the neighborhood Use centroid location as new alarm location Repeat process until centroid location is fixed

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Example

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SLIDE 11

Diligent Digger

Sensor based algorithm performs well for easily identifiable targets Low confidence alarms perform no better than randomly placed alarms Can we design a Diligent Digger that performs better than the low confidence data informed alarms?

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SLIDE 12

Recall

FAR

0.2 0.4 0.6 0.8 1 1.2

Pd

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

roc far roc quiver

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Naive Diggers

Random and grid uninformed alarm sets developed to test benchmark performance Confidences randomly assigned for alarm locations Grid alarm placement superior to random placement on average

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Augmented Algorithm

Replace low confidence alarms with uninformed alarms based on a confidence threshold Identify threshold that informed alarms perform no better than random alarms Can we perform better below this threshold?

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Diligent Digger

1) Sensor based algorithm positions 2) Remove least confident alarms 3) Augment remaining alarms with uniform grid 4) Remove redundant grid alarms 1 2 3 4

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SLIDE 16

Diligent Digger

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SLIDE 17

Alternative method for alarm generation using a combinatorial approach.

Discretize search area (road) into nx × ny squares. (First we treat ny = 1, i.e. a one dimensional road.) Treat bombs as rectangles that are bx × by squares. Treat each non-overlapping placement of nb bombs as equally likely. Below, search area is 42 × 8, three bombs that are 4 × 2.

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SLIDE 18

Place bomb randomly along road with a fixed signal strength of µ.

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SLIDE 19

Add Standard Normal noise at each point along the road.

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SLIDE 20

Sweep a bomb width interval along the road. Find the one with the most area.

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SLIDE 21

Sweep a bomb width interval along the road. Find the one with the most area.

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Sweep a bomb width interval along the road. Find the one with the most area.

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Sweep a bomb width interval along the road. Find the one with the most area.

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SLIDE 24

(new) AREA method places alarm at midpoint of interval that maximizes area. (CoVar) PEAK method places alarm at the highest peaks.

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SLIDE 25

Bomb signal strength is Normal(µ, 1) Background noise is Normal(0, 1) For each µ ∈ [0, 5], we compare the average performance of the AREA and PEAK alarm generation algorithms over 1000 simulations With one bomb and one alarm, AREA performed better than PEAK for all fixed (known) sizes of bomb

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SLIDE 26

2d Area Method

Difference even more pronounced in higher dimension and with increased number of bombs Persists regardless

  • f whether

clustered peaks are suppressed in alarm set Right: Three 1x3 bombs in 2x10 domain

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SLIDE 27

2d Area Method

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As we let nx and ny approach infinity, the discrete distribution of bomb locations approaches the following continuous one.

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Hypothesis Test of Independence

Confidence Maps vs. True Targets

Hypothesis Test of Independence: H0 : Alarmpdf ⊥ ⊥ Truthpdf vs. H1 : Alarmpdf ⊥ ⊥ Truthpdf

Table: Hypothesis Test of Independence: Confidence Maps vs. True Targets

n Test Mean P-Value Median P-Value 5000 Distance Correlation 0.2476 0.0100 1000 Distance Correlation 0.3774 0.1300 200 Cross-Match 0.8782 1000 Cross-Match 0.1286 2100 Cross-Match 0.719339 4000 Cross-Match 0.2886 5000 Cross-Match 0.3085 7000 Cross-Match 0.3373

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SLIDE 33

Figure: DC Test (n = 5000): P-Values of various samples with replacement

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Summary

Filtered confidence map data in a variety of different ways Given this filtering, came up with different ways of placing alarms Improved up random performance for higher FAR levels Proposed a more concise algorithm scoring method Thank you CoVar!

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