Experiments Test different parking lot images captured in different luminance conditions The test samples include 1300 available parking spaces and 1500 occupied spaces The final false-acceptance rate (FAR) and false-rejection rate (FRR) are 0.032 and 0.02 In comparison, Dan’s method, which is a single-space detection method based on a SVM

classifier, has FDR = 0.048 and FRR = 0.071 3 seconds to perform the detection and segmentation of parking spaces for a 320x240

color image on a PC with a 1.6GHz Pentium-4 CPU The world projection information is well-learned and embedded in the semantic knowledge

so that the inter-object occlusion problem can be properly handled

BHDF: one-row space detection As an optimal inference problem

The statistical properties embedded in the BHDF graphical model D, S are conditional independent given H

p(si) is assumed to be a uniform distribution• “Occupied” status and “available” status are equally

possible • Ignore the effect of ln(p(SL)) due to uniform assumption

L L

o oL L L L L

H ,SH ,S =arg max p(H ,S |D )

L L L L Lp(D |H ,S )=p(D |H ) Rs(hi) is the set of semantic nodes connecting to h i

in the graph; Ni is the neighbors of the ith pixel Optimal inference

Belief propagation technique

L L

L L

L L

i

L L L L L LH ,S

i i L LH ,S

i M

i i i S ii M

H ,Si j

i M j N

arg max p(D |H ,S )p(H |S )p(S )

arg max [ ln(p(d |h ))]+ln(p(H |S ))

[ ln(p(d |h ))+ln(p(h | R (h )))]

arg maxln(p(h ,h ))

BHDF: graphical learning 3-layer BHDF is a well-defined graphical model Graphical topology is learned in advance

One-to-one connections between the D layer and the H layer Four-neighboring connections inside the H layer Topological connections between the S layer and the H layer

are learned based on training samples and camera calibration• Note that a car can occlude only its neighbors, each semantic node only

connects to its relative nodes on the H layer Inter-layer and intra-layer message propagations are

defined by using three trainable models (A,B,C)

Analyze the statuse of each row As an optimal inference problem which is

subject to three aspects• Local regions should be correctly classified p(DL|HL) • Adjacent regions should follow neighboring constraints

p(HL) • Parked cars in the same row would match the inter-

occluded patterns p(HL|SL) One row of parking space

Row-by-Row fashion Select one row of parking space

Assume each parking space as an equal-sized cube on the ground of the 3D scene

Projection one row of parking space from 3D to 2D based on camera calibration

BHDF: three trainable models Local classification model p(DL|HL)

Assume each image pixel has the identical local model; We aim to calculate p(di|hi={G,O,C})

Non-parametric density estimation for hi={G,O}• NG and ND: normalization terms; (.) is a symmetric kernel

function• dGj/ dDj denotes one of the Tn/ Tm “ground/ otherwise” pixel

samples

Overcome the luminance variation problem• Train different probability models for p(d|h=G) and p(d|h=O)

under different luminance conditions • Select a suitable classification model dynamically

Parametric density estimation for hi={C}• Converted to a new color domain: x=[u p] = T( d=[R G B] )

Combat the luminance variation problem• Only the chromatic information (u,p) is used • The distribution can be approximated by a Gaussian function

Adjacency model p(HL) Accumulated histogram to approximate the probability table p(hi,hj) based on 5000 pseudo training samples

•Most of the neighboring pairs follow the smoothness constraints

•Boundary regions, such as between “car” pixels and “ground” pixels, have quite different statistical distributions

Goals Available space number Available space locations Parking guidance Monitor the changes of space status

MotivationsParking has become a problem Intelligent parking lots surveillance

systems is becoming practical Assist users in efficiently finding

empty parking spaces

A BAYESIAN HIERARCHICAL DETECTION FRAMEWORKFOR PARKING SPACE DETECTION

Ching-Chun Huang1,3, Sheng-Jyh Wang1, Yao-Jen Chang2,3, and Tsuhan Chen3

1 Department of Electronics Engineering, National Chiao Tung University, Taiwan.2Advanced Technology Center, Industrial Technology Research Institute, Taiwan

3Department of Electrical & Computer Engineering, Carnegie Mellon University, USA.

Key ideas Background

Traditional methods: P(S|D)• Given one space observation (D)• Decide the status of the space (S)

Consider occlusion• Different spaces have different occlusion

patterns• Occlusion is a “pixel-level” problem• Owing to the occluded regions, adjacent

spaces become highly relative• Decide the status “space by space” is not

suitable

Proposed method: Bayesian hierarchical detection framework (BHDF) to combine (D,L,S) Introduce a hidden pixel labeling

layer “L” Analyze from pixel level to space

level Infer the statuses of multiple spaces

all together

Challenges Luminance variations Inter-occlusions among cars Occlusions caused by obstacles

System flow

Labeling results under different lighting conditions

Tn

i i Gjj=1G

Tm

i i Djj=1D

1p(d |h =G)= (d-d )

N

1p(d |h =O)= (d-d )

N

(Left) A pseudo training sample of parking lot status for global semantic model. (Right) Pre-defined “ground” regions in the black color and “otherwise” regions in the light-gray color

Z=(R+G+B)/3

u=(2Z-G-B)/Z

p=Max{(Z-G)/Z,(Z-B)/Z}

i ic

1p(d |h =C) p(T(d)|vehicle)

N

t1 1 1p(x|vehicle) exp(- x-m x-m )v v22πv

v

3D->2D occlusion

Obstacleocclusion

Global semantic model p(HL|SL) Accumulated histogram to approximate the

probability table p(hi|Rs(hi)) based on pseudo training samples• Pseudo training samples represent the inter-occluded patterns• Pseudo samples can be automatically generated based on

camera projection parameters and projecting 3D-cubes to 2D