2DOF POSE ESTIMATION OF TEXTURED OBJECTS WITH

ANGULAR COLOR COOCCURRENCE HISTOGRAMS

Thomas Nierobisch and Frank Hoffmann

Chair for Control and Systems Engineering, Department of Electrical Engineering and Information Technology

Universit

¨

at Dortmund, Germany

Keywords:

2DOF pose estimation, color cooccurrence histogram, probabilistic neural network

Abstract:

Robust techniques for pose estimation are essential for robotic manipulation and grasping tasks. We present a

novel approach for 2DOF pose estimation based on angular color cooccurrence histograms and its application

to object grasping. The representation of objects is based on pixel cooccurrence histograms extracted from

the color segmented image. The conﬁdence in the pose estimate is predicted by a probabilistic neural network

based on the disambiguity of the underlying matchvalue curve. In an experimental evaluation the estimated

pose is used as input to the open loop control of a robotic grasp. For more complex manipulation tasks the

2DOF estimate provides the basis for the initialization of a 6DOF geometric based object tracking in real-time.

1 INTRODUCTION

This paper is concerned with vision based 2DOF pose

estimation of textured objects based on monocular

views. Object pose estimation is an active area of

research due to its importance for robotic manipu-

lation and grasping. The literature reports two dis-

tinct approaches to solve the pose estimation prob-

lem. Model based methods rely on the extraction of

speciﬁc geometric features in the image such as cor-

ners and edges (Shapiro and Stockman, 2001). The

extracted features are then compared and related to

a known geometric model of the object. Efﬁcient

and reliable approaches for model-based pose esti-

mation with known correspondences have been pro-

posed by (Dementhon and Davis, 1992; Nister, 2003).

The drawback of this method is the lack of robust-

ness in the extraction of distinguishable features in

particular for textured objects. In addition, feature

based methods require the solution of the correspon-

dence problem, which becomes inherently more difﬁ-

cult in case of occlusion and undistinguishable fea-

tures. In contrast, global appearance based meth-

ods capture the overall visual appearance of an ob-

ject (Schiele and Pentland, 1999). Neither do they

depend on the extraction of individual features nor

do they face the correspondence problem. This pa-

per follows the latter approach for robust and compu-

tationally efﬁcient pose estimation of multi-colored,

textured objects. (Chang and Krumm, 1999) pro-

posed distance color cooccurrence histograms for ob-

ject recognition. They emphasize the conservation

of geometric information as the major advantage of

color cooccurrence histograms compared to regular

color histograms. Based on this fundamental idea,

(Ekvall et al., 2005) proposed color cooccurrence his-

tograms for object recognition as well as 1DOF pose

estimation. The angular extension of color cooccur-

rence histograms was suggested by (Nierobisch and

Hoffmann, 2004) in the context of pose estimation of

robot players (AIBO’s). In addition the 2DOF pose

estimation of objects with minimal texture and only

three distinct colors has been successfully demon-

strated. The aim of this paper is to investigate the

potential of angular color cooccurrence histograms

for 2DOF pose estimation of multi-colored, textured

objects. Recently (Najaﬁ et al., 2006) introduced a

method that combines appearance and geometric ob-

ject models in order to achieve robust and fast object

detection as well as 2DOF pose estimation. Their ma-

jor contribution is the integration of the known 3D

geometry of the object during matching and pose es-

timation by a statistical analysis of the distribution

of feature appearances in the view space. Nonethe-

52

Nierobisch T. and Hoffmann F. (2007).

2DOF POSE ESTIMATION OF TEXTURED OBJECTS WITH ANGULAR COLOR COOCCURRENCE HISTOGRAMS.

In Proceedings of the Second International Conference on Computer Vision Theory and Applications - IU/MTSV, pages 52-59

Copyright

c

SciTePress

less their approach requires a 3D model of the object,

which is difﬁcult to generate for objects of complex

shape.

This paper is organized as follows: Section II

provides an introduction to color cooccurrence his-

tograms with the focus on the angular extension of

the representation. Section III explains the signiﬁcant

steps of segmentation and 2DOF rotation estimation

based on color cooccurrence histograms. Section IV

introduces a method to predict the conﬁdence in the

2DOF rotation estimation. Experimental results for

pose estimation of textured objects are presented in

Section V and a summary is provided in Section VI.

2 COLOR HISTOGRAMS

0

1

2

3

4

5

6

7

B\B

<=45°

R/B

<=45°

R/R

<=45°

B/B

>45°

R/B

>45°

R/R

>45°

Frequency

Red-blue pixel pair <= 45°

Red-blue pixel pair >45°

45° Boundary

Reference pixel

Figure 1: Angular Color Cooccurrence Histogram.

Standard color histograms are often used to capture

and abstract the appearance of objects and environ-

ments, e.g. for localization tasks (Ulrich and Nour-

bakhsh, 2000). The drawback of conventional color

histograms is that geometrical information about the

color distribution is lost in the compression. As a

remedy to this detriment (Chang and Krumm, 1999)

introduce the color cooccurrence histograms (CCHs),

which summarize the geometric distribution of color

pixel pairs within the image of an object. An exten-

sion of CCHs are angular or distance color cooccur-

rence histograms (ACCHs or DCCHs, respectively),

which contain additional geometric information by ei-

ther including the orientation of a pixel pair or its dis-

tance. A CCH computes pixel pairs in a local envi-

ronment by starting at a reference. These pixel pairs

describe the color information of the reference pixel

in conjunction with all other pixels in its local en-

vironment. By linearly shifting the reference pixel

and its local environment pixel by pixel a geomet-

ric color statistics of a region of interest (ROI) is ob-

tained. In order to render the representation indepen-

dent of scale and size the histogram is normalized.

ACCHs augment the geometrical information in com-

parison to CCHs by additionally storing the orienta-

tion of the vector connecting the two pixels. Starting

from the reference pixel the angle between the ref-

erence frame and a pixel in the local environment is

computed and mapped on to a discrete set of angular

intervals. Accordingly, DCCHs include statistics on

discrete distances between pixels rather than angles.

Figure 1 illustrates the method of ACCHs calculation

for an image with only two distinct colors. The an-

gular range is discretized into two segments, below or

above 45°. Therefore, the histogram consists of six

separate bins, namely blue-blue, blue-red and red-red

pixel pairs at two distinct angles. The pose estimate

relies on the similarity between the stored histograms

of known poses with the histogram of the object with

unknown pose. Let h(d,a,b) denote the normalized

frequency of color pixels with the discrete colors a

and b oriented at a discrete angle d. The similarity of

two normalized ACCHs is deﬁned as

s(h

1

,h

2

) =

D

∑

d=1

C

∑

a=1

C

∑

b=1

min(h

1

(d, a, b), h

2

(d, a, b)), (1)

where h

1

denotes the angle color histogram of the seg-

mented patch in the test image and h

2

is the histogram

of a training image stored in the database. D corre-

sponds to the number of angular discretizations and C

characterizes the number of distinct colors in the his-

tograms. To obtain a scale invariant similarity mea-

sure, termed match value in the remainder of this pa-

per, the histogram counts are normalized by the size

of the ROI histogram #h

1

,

m(h

1

,h

2

) =

s(h

1

,h

2

)

#h

1

. (2)

3 2-DOF ESTIMATION OF

OBJECTS WITH TEXTURE

3.1 Experimental Setup

A 5-DOF manipulator and a turntable are used to au-

tomatically generate object views at constant distance

between camera and object across a view hemisphere.

The reference views cover the upper hemisphere, for

which due to the limited workspace of the manipula-

tor the elevation is restricted to a range from 45° to

90°. In the following the elevation is denoted by θ

and the azimuth by ϕ. Figure 2 shows the setup for

capturing sample images and indicates the view point

range. Prior empirical evaluations suggest that a suc-

Figure 2: Setup for generating spherical views of the object.

cessful open loop grasp requires an accuracy of 10°

in θ and 20° in ϕ for the reference pose. Larger pose

estimation errors result in a failure of the open loop

grasping controller. Therefore, our performance mea-

sure considers angular errors in θ above 10° and in ϕ

above 20° as failures.

3.2 Object Recognition and 1-D Pose

Estimation

In (Ekvall et al., 2005) the authors present an ap-

pearance based method for robust object recognition,

background segmentation and partial pose estimation

based on CCHs. The approach employs a winner-

take-all-strategy in which the appearance of an object

of unknown pose is compared with a set of training

images of known pose. The pose associated with the

best matching training image predicts the azimuth ori-

entation of the object around the vertical axis. This

prior, incomplete 1DOF pose estimate is subsequently

augmented to a complete 6DOF pose by a feature

based technique that facilitates a geometric model of

the object. In experimental evaluations the average

angular estimation error was 6°. Our work is an ex-

tension of the previous approach in that it estimates

2DOF spherical poses located on a hemisphere. In

addition to the azimuth estimate it also considers the

elevation of the camera along the hemisphere. For

typical objects with a small top surface the varia-

tion of colors along the elevation angle is substan-

tially smaller than for rotations around the vertical

axis. Due to this property standard CCHs are un-

able to capture variations of the object’s appearance

at large elevation angles. This observation motivates

the application of ACCHs for the task of 2DOF pose

estimation. Our approach employs the same scheme

proposed by (Ekvall et al., 2005) for object recogni-

tion and background segmentation to determine the

ROI prior to the CCH computation itself. For object

recognition the image is ﬁrst scanned and a matching

vote indicates the likelihood that the window contains

the object. Once the entire image has been searched,

the maximum match provides an hypothesis of the ob-

jects location. For background segmentation the best

matching window is iteratively expanded by adjacent

cells to obtain the ﬁnal ROI. In a region growing

process neighboring cells that bear sufﬁcient resem-

blance with the object’s CCH are added to the ROI.

3.3 2-D Pose Estimation

The purpose of this work is to analyze extended CCHs

for the task of 2DOF pose estimation. We assume that

the object stands on a planar, horizontally oriented

surface and the elevation and azimuth of the eye-in-

hand manipulator conﬁguration relative to the object

are unknown. From geometric reasoning it is straight-

forward to identify the type of color cooccurrence his-

togram (CCH, ACCH or DCCH) which captures the

geometric information relevant for 2DOF rotation es-

timation. CCHs do not contain sufﬁcient information

to discriminate between arbitrary poses, as they only

count the frequency of pixel pairs but not their rel-

ative orientation. In case of a birdseye perspective

(θ = 90°) a rotation of the object along the vertical

axis (ϕ) does not alter the frequency of color pairs in

the CCH. The same observation applies to DCCHs, as

they do not capture the orientation of the vector con-

necting the two pixels. Obviously, the rotation along

the vertical axis does not change the frequency of the

color pixels but only their orientation. Therefore AC-

CHs seem most suitable for 2DOF pose estimation as

they are sensitive to variations in appearance that are

purely related to the orientation of pixels.

In an experimental evaluation, object views are gener-

ated by moving the camera along the vertical axis (ϕ)

in 10° steps from 0° to 360° and along the horizon-

tal axis (θ) from 0° to 180° in 10° steps. To analyze

the potential of ACCHs independent of the problem

of proper background segmentation, the algorithm is

evaluated on a set of views of a textured object in front

of a homogeneous background that allows near op-

timal object segmentation. Compared to the 1DOF

pose estimation based on CCH’s the 2DOF results are

more susceptible to segmentation errors, because the

same amount of information is available to extract two

degrees of freedom rather than one. Due to the addi-

tional angular resolution of the histogram the num-

ber of bins in an ACCH is a magnitude larger than

for a CCH with the same set of colors. Therefore,

the statistics of bin counts in an ACCH deteriorates

in comparison to a CCH because the same number of

pixel pairs is distributed over a larger number of bins.

Figure 3 shows two match value responses across

StoredHistograms

0 36 72 108 144 180 216

0

0.2

0.4

0.6

0.8

1

0.88

0.890.89

0.91

0.92

0.87

0.93

Theta=0° Theta=90°Theta=75°Theta=15° Theta=30° Theta=45° Theta=60°

0 36 72 108 144 180 216

0

0.2

0.4

0.6

0.8

1

0.93

0.87

0.91

0.81

0.82

0.83

0.83

Theta=0° Theta=15° Theta=30° Theta=45° Theta=60° Theta=75° Theta=90°

Match value

Match value

Figure 3: Upper) Match value curve using the local neigh-

borhood for ACCH’s Calculation. Lower) Match value

curve using a modiﬁed approach for ACCH’s Calculation.

the training set of image-pose pairs for a test object

oriented at a true pose of approximate 183° in ϕ and

0° in θ direction. The training images are ordered in

the sequence {[θ = 0°, ϕ = 0°], [θ = 0°, ϕ = 10°], ...,

[θ = 0°, ϕ = 350°], [θ = 15°, ϕ = 0°], ..., [θ = 30°,

ϕ = 0°], ..., [θ = 90°, ϕ = 350°]}.

The match value plot is partitioned into seven slices,

each slice corresponding to a full scan along the az-

imuth ϕ in [0...360]° along seven different elevations

of θ in 0°, 15°, 30°, 45°, 60°, 75° and 90°. The

shape of the match value response resembles an am-

plitude modulated signal. The slower modulation cor-

responds to the horizontal rotation, whereas the faster

modulation contains the information about the verti-

cal rotation. The two match value responses corre-

spond to two different ways of computing the ACCH.

In the upper match value response pixel pairs origi-

nate from a local neighborhood region of the refer-

ence pixel. Local color pair statistics are useful to

distinguish between multicolored objects with a fair

amount of texture. The local statistics results in an

ambiguity along the θ rotation because the slow mod-

ulation does not discriminate well enough to ensure

a robust estimation. In our example the variation in

maxima along θ only ranges from 0.93 to 0.87. Pixel

pairs counted across a larger separation contribute

more information on the object’s pose. Nearby pixel

pairs, even though useful for object recognition, di-

lute the information of the object’s global appearance

as e.g. the likelihood of ﬁnding a same colored pixel

next to the reference pixel is fairly large. Therefore,

the second scheme only counts pixel pairs separated

by a minimal distance and ignores pixels in the imme-

diate neighborhood of the reference pixel. As a result

the 2DOF appearance of the object reﬂected through

the ACCHs becomes more distinguishable. In this

scheme the variation in maxima along θ ranges from

0.93 to 0.81, with a signiﬁcant decrease in the ampli-

tude of incorrect local maxima. The drawback is that

due to the deﬁnition of an excluded neighborhood re-

gion the scheme is no longer scale-invariant. There-

fore, the second approach is only feasible if the rela-

tive distance between the camera frame and the object

is approximately known in order to properly scale the

excluded region.

The test set contains 190 test images with random

2DOF poses that differ from the training set. The

mean angular error across the vertical axis is about

10° and 3.8° across the horizontal axis. The ACCHs

operate with a resolution of 12 discrete angles and 40

colors. The local environment comprises 20 pixels,

but only pixel pairs with a separation of more than 10

pixels contribute to the angular histograms.

4 CONFIDENCE RATING

Our experiments indicate that the major problem for

reliable appearance based 1DOF or 2DOF pose esti-

mation in natural scenes is the accuracy of the seg-

mentation in the preprocessing stage. In most cases

the 1DOF rotation estimation is fairly robust towards

segmentation errors. However if background objects

of similar colors are located next to the object the seg-

mentation partially or completely merges the two ob-

jects. Incorrect segmentation results in poor perfor-

mance of the subsequent pose estimation due to the

large amount of background noise introduced by the

misleading object. In order to detect such incorrect

rotation estimates we rate the conﬁdence in an esti-

mate based on the characteristics of the match value

response. Estimates that originate from ambiguous

match value responses with multiple local maxima of

similar magnitude are rejected. A multi-layered feed-

forward neural network is trained on match value re-

sponses which an expert previously manually classi-

ﬁed by visual inspection as either ambiguous or reli-

able. The match value responses constitute the input

vector x

n

, based on which the neural network rates

the conﬁdence in terms of a probability h(x

n

) that the

estimate is reliable. The input vector x

n

corresponds

to the match values of the test image over the set of

training images. The training method is similar to the

well known backpropagation algorithm, except that in

this case gradient descent minimizes the entropy

E

min

= min

w

ij

−

N

∑

n=1

d

n

ln(h(x

n

)) + (1− d

n

)ln(1− h(x

n

))

(3)

rather than the squared error (MacKay, 1992). The

term d

n

∈ {0,1} denotes the expert reliability clas-

siﬁcation of the training example x

n

. The term w

ij

denotes the synaptic weights that are subject to op-

timization. The entropy in Eq. 3 acquires its min-

imum, if h(x

n

) is equal to the relative frequency of

training pairs c(x

n

,d

n

= 1)/c(x

n

,d

n

= {0,1}). The

classiﬁer reject any rotation estimates with an am-

biguous match value response x for which the neural

network predicts a conﬁdence lower than h(x) < 0.8.

For the example shown in the left of ﬁgure 4 the rota-

Figure 4: Left top) overlapping objects merged during seg-

mentation. Left bottom) corresponding ﬂat match value re-

sponse due to incorrect segmentation. Right top) proper

segmentation from a different perspective. Right bottom)

corresponding match value curve with an unique maximum.

tion estimation fails because the segmentation merges

a part of book with similar colors with the object of

interest in the foreground. As a result of the poor ob-

ject segmentation the rotation estimate has an error of

about 60°. However, the neural network rejects this

rotation estimation due to its low conﬁdence rating

of h(x) = 0.69 caused by the incorrect segmentation.

The corresponding ﬂat match value curve shows two

local maxima of similar magnitude. in response to the

rejection, the manipulator moves the camera to a dif-

ferent pose in order to capture an image of the object

from a better perspective. In the new image shown

on the right side of ﬁgure 4 the two objects no longer

overlap and the segmentation succeeds. The rotation

estimation error is less than 20° which is sufﬁcient

for the subsequent model based reﬁnement step. The

corresponding match value response shows a unique

maximum, which the neural network conﬁrms with a

high conﬁdence rating h(x) = 0.98.

The conﬁdence rating of the 2DOF pose estimate

is based on the ambiguity of the match value response.

In order to distinguish between reliable and unreli-

able estimates, a neural network is trained on manu-

ally classiﬁed match value responses. In order to train

the neural network a small subset of features from the

match value response that best correlate with the clas-

siﬁcation has to be selected. From inspection of ex-

ample responses it turns out, that the distribution and

magnitude of global and local maxima are suitable

features to predict the conﬁdence.

Figure 5 shows a blue-colored box in the follow-

ing referred to as object A after being segmented from

the background. The pose estimation error in front of

the blue background is about 2° in θ and about 46°

in ϕ. The large pose estimation error in ϕ is caused

by the imperfect segmentation of the blue object from

the blue background. The error in front of the yel-

low background that is easier to separate from the ob-

ject only amounts to 2° in θ and 6° in ϕ. In the fol-

lowing we analyze the causes for incorrect pose es-

timates and how to detect potential outliers from the

match value response itself, so that these unreliable

pose estimates can be rejected beforehand. The cor-

Figure 5: Fruitbox under different background conditions.

responding match value responses of object A for the

two background scenarios are shown as a 2D-plot (up-

per graphs) and 1D folded plot (lower graphs) in ﬁg-

ure 6. The left top graph shows the ambiguous match

value response with several local maxima of similar

magnitude caused by poor segmentation in front of

the blue background. The noise introduced into the

ACCH by the blue background pixels is reﬂected by

the bimodal distribution in ϕ. In analogy to ﬁgure 3

the upper left graph shows the slow modulation corre-

sponding to the changes of θ and the fast modulation

corresponding to ϕ. The stars denote local maxima

of the response which magnitude exceeds a thresh-

old of 95 % relative to the global maximum. Addi-

tionally also the local maxima along the θ slices are

marked by stars in case exceeding 97 % of the abso-

lute maximum. Obviously, several local maxima of

similar magnitude in the ﬁrst slice might correspond

to the true object pose in ϕ.

The right part of ﬁgure 6 shows the 2D and 1D

match value responses for the image with proper ob-

ject background segmentation. The 2D match value

shows a unique maximum. In the 1D folded represen-

tation the local maxima are either in the vicinity of the

global maximum or correspond to similar values of ϕ

at different values of θ.

Based on this empirical observation the neural net-

work predicts the conﬁdence based on the following

four features extracted from the match value response:

1. R

ϕ

: ratio between the magnitude of the global

maximum and the second best match value out-

side a minimum separation of 20 ° within the same

θ slice that contains the global maximum

2. D

ϕ

: separation between the global maximum and

the second best match outside the minimum sep-

aration within the same θ slice that contains the

global maximum

3. R

θ

: ratio between the magnitude of the global

maximum and the second best match value across

all θ slices

4. D

θ

: separation between the magnitude of the

global maximum and the second best match value

across all θ slices

The purpose of the ﬁrst two features is to detect an

ambiguous response in ϕ, the other two features dis-

tinguish between ambiguous and disambiguous re-

sponses in θ. Notice, that D

θ

is speciﬁed in terms of

an integer that denotes the number of slices that sep-

arate the ﬁrst from the second maximum. A smooth

variation of the match value response with θ implies

that the second maximum should occur in the neigh-

boring slice D

θ

= 1. Larger values of D

θ

in partic-

ular in conjunction with a large ratio R

θ

indicate a

potential ambiguity in the θ estimate. The next sec-

tion reports experimental results of 2DOF pose esti-

mation and the improvement using the probabilistic

conﬁdence rating under real world conditions.

5 EXPERIMENTAL EVALUATION

The experimental evaluation of the proposed method-

ology in realistic scenarios is based on three test ob-

jects of different color and texture with views gener-

ated for various backgrounds. The experiments in the

previous section assumed an ideal, textureless object

with three distinguishable colors in front of a homo-

geneous background. The purpose of these experi-

ments is to analyze the robustness and accuracy of the

pose estimation for daily life objects in a realistic set-

ting. The three test objects are shown in ﬁgure 7 and

are referred to in the remainder of the text as object

A, B and C. The ACCHs operate with a resolution of

10 angles and 40 colors.

Figure 7: Test objects A, B and C.

In the following

¯

E denotes the mean error of the

pose estimate in θ and ϕ. The training images belong

to views at θ angles of 45, 50, 60, 70, 80 and 90°. In ϕ

the sample images are captured in 10° steps. The min-

imal

¯

E that is feasible in theory with a winner-takes-

all strategy depends on the density of samples, in our

case it amounts to 2.5° in ϕ and 2.4° in θ. The results

in table 1 indicate that for all test objects the actual

error along θ is close to the optimum. The mean er-

ror in ϕ is signiﬁcantly lower than the error bounds

for successful grasping deﬁned in section III. The ex-

perimental results in table 1 demonstrate that under

the assumption of near optimal segmentation an er-

ror rate of less than 4° in θ and 9° in ϕ is feasible

for all test objects. This error rate is small enough

for a successful open loop grasp within the speciﬁed

error bounds. The percentage of failures is approxi-

mately 7%. Table 2 reports the results of the pose

Table 1: 2DOF pose estimation with optimal segmentation.

Objects Object A Object B Object C

¯

E

(ϕ)

7.0° 8.9° 8.5°

¯

E

(θ)

4.0° 3.3° 3.7°

estimation under different background conditions and

the impact of the probabilistic conﬁdence rating on

the failure, error and acceptance rate. Background A

consists of a wooden material and shows a yellowish

textured surface (as shown in the left image in ﬁgure

5). The two other backgrounds B and C contain a tex-

tured blue and green surface, respectively. The ﬁrst

column speciﬁes the actual object and background,

the three following columns describe the mean errors

of the pose estimation in θ and ϕ and the percentage of

failures. The next two columns show the mean error

¯

E

for θ and ϕ for those views that were accepted by the

conﬁdence rating based on the match value response.

Finally, the percentage of failures and the rate of ac-

cepted views (FR) is provided in the last two columns.

To verify the methodology under realistic environ-

mental conditions the test set contains 50 images of

the three objects taken at random 2DOF positions for

the three different backgrounds. Based on the fact

that the color distribution of object A contains a large

portion of blue colors, segmentation errors with back-

45

50

60

100

200

300

0.45

0.5

0.55

theta

phi

Match value

45

50

60

100

200

300

0.6

0.65

0.7

0.75

theta

phi

Match value

0 50 100 150 200

0.44

0.46

0.48

0.5

0.52

0.54

Match value

Histograms

0 50 100 150 200

0.6

0.65

0.7

0.75

Match value

Histograms

R

φ

R

θ

D

φ

φ

R

θ

θ

θ

D

R

D

Figure 6: Left top) Ambiguous 2D match value curve based on segmentation noise. Left bottom) According 1D match value

response based on segmentation noise. Right top) Unique 2D match value response based on proper segmentation. Right

bottom) Corresponding match value response with an unique maximum.

Table 2: 2DOF pose estimation for the three objects under different background conditions.

Object / Background pose estimation pose estimation with conﬁdence

¯

E

(ϕ)

¯

E

(θ)

Failures

¯

E

(ϕ)

¯

E

(θ)

Failures FR

Object A / Backgrd. A 8.0° 11.8° 44% 5.3° 7.3° 27% 30%

Object A / Backgrd. B 22.2° 14.7° 66% 11.2° 9.8° 47% 34%

Object A / Backgrd. C 9.0° 7.2° 20% 4.6° 4.0° 0% 32%

Object B / Backgrd. A 9.1° 15.8° 42% 7.4° 9.2° 19% 42%

Object B / Backgrd. B 10.7° 25.7° 68% N.A. N.A. N.A. N.A.

Object C / Backgrd. A 12.4° 30.2° 72% 6.1° 19.5° 42% 15%

Object C / Backgrd. B 6.5° 9.1° 28% 4.8° 5.3° 11% 36%

ground B cause a substantial error

¯

E for θ as well as

ϕ. The results in table 2 demonstrate that for simi-

lar object-background colors the color information in

a CCH alone provides an insufﬁcient cue for object

segmentation and pose estimation. One possible rem-

edy to this problem is to integrate additional cues in

the segmentation process. The distance between cam-

era and object or background pixels can be estimated

from optical ﬂow or stereo-vision across multiple im-

ages taken from slightly different views. It is expected

that the segmentation accuracy improves substantially

if additional cues are integrated. The objective of the

conﬁdence rating is to gain accuracy in the pose esti-

mate, in particular to reduce the number of failures at

the cost of rejecting ambiguous object views. In the

context of robotic object grasping robust estimation

is more important than complete decision making. It

is acceptable to reject an ambiguous view and to de-

fer temporarily the grasping process. The manipulator

moves the camera to novel viewpoints until the algo-

rithm generates a pose estimate supported with sufﬁ-

cient conﬁdence. For object A the two backgrounds A

and C are less problematic in terms of segmentation

noise rejection of uncertain poses reduces the mean

error as well as the number of failures. In case of

background C the neural network is able to exclude

all failures, albeit at the cost of rejecting two out three

views. Notice, that for test object B in front of back-

ground B that coincides with the object color nearly

70% of the original estimates are failures. In this case

the neural network ultimately classiﬁes all estimates

as unreliable. Acceptable error and failure rates are

achieved for test object C in front of background B.

The mean estimation error

¯

E is small enough to al-

low an open loop grasp for 9 of 10 estimations. In

contrast pose estimation on background A fails al-

most completely with an failure rate of 72% due to

the similar colors of the object. Even if only 15 %

of the estimates are accepted, the failure rate of 42%

is still not acceptable. Instead of an open loop grasp

control based on a single image and pose estimate it

is more robust to operate in feedback mode by ac-

quiring additional images. A Kalman ﬁlter approach

fuses observed pose estimates with the known camera

motions. The experimental results demonstrate that

2DOF pose estimation based on ACCHs is feasible

under the assumption of proper segmentation. The

main drawback of the proposed method is the sensi-

tivity with respect to noise and segmentation errors.

As a 2DOF pose estimation with ACCHs is substan-

tially more difﬁcult, the approach does not achieve the

same level of robustness as in the case of 1DOF pose

estimation based on pure CCHs.

6 CONCLUSIONS

In this paper we presented a novel approach for 2DOF

pose estimation based on angular cooccurrence his-

tograms. Under the assumption of proper object back-

ground segmentation the accuracy of estimated poses

is sufﬁcient for object manipulation with a two-ﬁnger

grasp. The conﬁdence rating of the match value re-

sponse by the neural network is a suitable means to

further improve the robustness of pose estimation at

the cost of a reduced recognition rate. The quality of

the appearance based segmentation deteriorates sub-

stantially in the case of overlapping objects or back-

grounds with similar colors. The degradation reﬂects

itself in an ambiguous match value curve detected by

the neural network. In a robotic manipulation sce-

nario the camera is moved in order to capture an im-

age of the object from a presumably better perspec-

tive. The grasping motion is not executed until a sufﬁ-

cient conﬁdence in the prior pose estimation has been

achieved. Our experimental results show that earlier

appearance based methods for 1 DOF pose estimation

can be extended to a 2DOF pose estimation. How-

ever, 2DOF pose estimation based on ACCHs is no

longer scale invariant and therefore requires an ap-

proximate initial estimate of scale. For our task the

reach of the robot arm is limited so that the scale does

not vary much across different conﬁgurations. There-

fore, a single training set of ACCHs captured at an

intermediate camera to object range is valid across

the entire workspace of the manipulator. An avenue

for future research is the integration of appearance

based approaches with an image based visual servo-

ing scheme. In image based visual servoing the cor-

respondance problem is prevalent in particular if are

only partially visible. To solve the correspondence

problem for visual servoing tasks the objects are of-

ten labeled with artiﬁcial landmarks like color blobs.

These approaches are therefore constrained to struc-

tured, synthetic environments. To overcome all those

limitations visual servoing is established on the entire

appearance of an object.

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