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Proceedings ArticleDOI

A novel method for radio propagation simulation based on automatic 3D environment reconstruction

26 Mar 2012-pp 1445-1449

TL;DR: A novel method to simulate radio propagation that makes contributions on reducing human efforts and cost in constructing 3D scene and proves its potential in both accuracy and efficiency.

AbstractIn this paper, a novel method to simulate radio propagation is presented. The method consists of two steps: automatic 3D scenario reconstruction and propagation modeling. For 3D reconstruction, a machine learning algorithm is adopted and improved to automatically recognize objects in pictures taken from target region, and 3D models are generated based on the recognized objects. The propagation model employs a ray tracing algorithm to compute signal strength for each point on the constructed 3D map. By comparing with other methods, the work presented in this paper makes contributions on reducing human efforts and cost in constructing 3D scene; moreover, the developed propagation model proves its potential in both accuracy and efficiency.

Topics: Beam tracing (57%), 3D reconstruction (53%), Radio propagation (53%), Iterative reconstruction (52%), Ray tracing (graphics) (51%)

Summary (2 min read)

1. Introduction

  • It consists of two steps: 3D scenario reconstruction and radio propagation simulation.
  • The recognized objects are segmented and then vectorized to build the 3D environment database, in which the locations and materials of different objects are stored.
  • The results from the proposed model indicate both efficiency and accuracy by comparing it to other advanced methods in the Munich scenario [1] .
  • In Section 3, the authors describe the ray-tracing based radio propagation model, from which the evaluation procedure is implemented on the Munich scenario.

2. 3D Reconstruction Method

  • In Fig. 2 (b), although most of the pixels are classified correctly, the edges between adjacent objects are not accurate enough.
  • The authors in [6] solve this problem by manually indicating the misclassified parts, and then another classifier is used to adjust those pixels into the right classes.
  • As it's intended to finish this procedure automatically in this work, the performance is improved by using color cues, which are frequently used for edge detection.
  • A graph cut algorithm [8], [9] is employed to smoothly cut the edges based on cluster information.
  • Dominant class is calculated by selecting maximum likelihood among all the classes for each cluster (see ( 3) and ( 4)),.

5. Each virtual point serves as new transmitter, and the

  • All the reflected points are seen as virtual sources with same transmission power as real source, while with constraints in transmission angle.
  • As shown in Fig. 8 , the reflection region is constrained by combining maximum transmission range and angle ¿V\0'V2-According to the Geometrical Theory of Diffraction [16] , diffracted rays are produced by incident rays which hit edges, corners or vertices of boundary surfaces.
  • All the vertices and corners are obtained as a form of V¿ while searching for the reflected rays.
  • Therefore, those vertices are automatically introduced as diffracted virtual sources.

3.2 Radio Propagation Model

  • For a direct path d is the distance between TX and RX, for a reflected path and diffracted path, d is the distance between the virtual source and RX.
  • This is calculated by accumulating the power reduction of each obstacle along the path.
  • A(/) !_1 decreases when / increases, which means that the first object, with which the signal intersects, produces the most significant power loss.
  • The signal first penetrates through a glassmade object, then through a concrete obstacle.
  • At the end, the power loss at the receiver is the accumulated value among the directed, reflected and diffracted paths.

4. Experimental Results

  • Tab. 2 compares the proposed method with other stateof-the-art technologies.
  • The STD and ME of the proposed method are the smallest on METRO 200 and METRO 201, while they are slightly greater than CNET in METRO 202.
  • The experimental results indicate that this novel approach has good efficiency and accuracy.
  • A quantitative explanation for this improvement can be directed towards three reasons: the construction accuracy of the environment database is 82 %, the miss-classified pixels are 18 %.
  • Furthermore, the propagation model is adequate in describing reduced dimensionality environments, and most of the.

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A Novel Method for Radio Propagation Simulation
Based on Automatic 3D Environment Reconstruction
Danping
HE,
Guixuan LIANG, Jorge PORTILLA,
Teresa
RIESGO
Centro de Electrónica Industrial, Universidad Politécnica de Madrid
Abstract. In this paper, a novel method to simulate ra-
dio propagation is
presented.
The method consists of two
steps: automatic 3D scenario reconstruction and propaga-
tion modeling. For 3D reconstruction, a machine learning
algorithm is adopted and improved to automatically recog-
nize objects in pictures taken from target regions, and 3D
models are generated based on the recognized objects. The
propagation model employs a ray tracing algorithm to com-
pute signal strength for each point on the constructed 3D
map.
Our proposition reduces, or even eliminates, infras-
tructure cost and human efforts during the construction of
realistic 3D scenes used in radio propagation modeling. In
addition, the results obtained from our propagation model
proves to be both accurate and efficient.
1.
Introduction
Radio propagation modeling has been researched for
decades in an effort to estimate signal strengths more accu-
rately in wave propagation environments. Most of the ad-
equately designed propagation models lack efficiency when
a priory knowledge of the physical environment is not pre-
sented by a database. The accuracy of such propagation
models has strong dependencies on the accuracy of the in-
formation captured from the database. The traditional recon-
struction process, in which the environment is extracted me-
ter by meter, is usually tedious and prolonged. Alternatively,
people may purchase expensive digital maps from profes-
sional companies in order to save time and attempts on non-
propagation related issue. As a result, either time or money
is needed in traditional methods. In order to make the whole
simulation procedure time efficient and accurate with lower
cost, a novel approach is proposed in this paper.
A simplified overview of the methodology is indicated
in Fig. 1. It consists of two steps: 3D scenario reconstruc-
tion and radio propagation simulation. At the beginning, 3D
environment database is automatically constructed from the
pictures taken by hand-held camera or by satellite. The un-
supervised image understanding algorithm is developed to
recognize different objects in the images. The recognized
objects are segmented and then vectorized to build the 3D
environment database, in which the locations and materials
of different objects are stored. This approach allows recon-
structing large scale 3D maps at low computational com-
plexity, high accuracy and low cost. In the second step, an
improved ray-tracing propagation model is run on the gen-
erated 3D database to simulate the path loss for each point
within the target region. The method not only considers the
attenuation parameters of different materials but also con-
siders the orders of obstacles along the signal path. The re-
sults from the proposed model indicate both efficiency and
accuracy by comparing it to other advanced methods in the
Munich scenario [1].
3D scenario
reconstruction
Radio
propagation
simulation
Input Images
Fig. 1. Work flow of the proposed method.
The rest of this paper is organised as follows: The
3D environment reconstruction method is introduced in Sec-
tion 2, and preliminary tests are evaluated on some image
sets.
In Section 3, we describe the ray-tracing based radio
propagation model, from which the evaluation procedure is
implemented on the Munich scenario. The results of sim-
ulation are compared with other related methods in Section
4.
Finally, we state the conclusions and future work in Sec-
tion 5.
2.
3D Reconstruction Method
A large part of physical signal degradation is caused by
obstacles interfering with the signal path. In urban scenarios,
obstacles have architectural bearing, whereas in indoor envi-
ronments, walls, doors, desks or even humans are regarded
as obstacles. In this paper, we focus on constructing large

(a) Input image
|^^ t<|
(b)Preliminary recognition and
segmentation
Fig. 2. Multi-object recognition procedure.
(c) Edge refined by
Graph-Cut algorithm
(d) Improved result by
subdividing the clusters
outdoor scenarios. As previously mentioned, our obstacles
will not be manually labeled and measured as demonstrated
in traditional method. Instead, they are reconstructed auto-
matically in order to reduce time and efforts on the database
reconstruction and constraints.
In [2] and [3], the identification of objects is made by
a shape feature descriptor. The method in [4] uses color
and texture features. Furthermore, [5] and [6] recognize
different obstacles based on machine learning incorporat-
ing texture, layout, and context information. Our method
employs and improves the machine learning procedure de-
veloped in [6]. Fig. 2 indicates the procedure of object
recognition and segmentation. Given pictures taken from
the target areas (from hand-held camera or satellite images
such as those from Google Earth, see Fig. 2(a)), the prelimi-
nary results (see
Fig.
2(b)) are obtained by adapting the Joint
Boost algorithm [6] (JBA) which iteratively selects discrim-
inative texture-layout filters
V[
ri
]
(/) to compute weak learn-
ers,
and combines them into a strong classifier of the form
H(c,
i)
= Lm=i
hf(c).
Each weak learner h¡(c) is a decision
stump based on the feature response.
hi(c) :
\a[v[
r
^(i)>6]+b if c<C,
otherwise.
(1)
For those classes that share the feature c e C, the weak
learner gives h¡(c) e {a + b,b} depending on the compari-
son of the feature response to a threshold 0. For classes not
sharing the feature, the constant k
c
makes sure that unequal
numbers of training examples of each class do not adversely
affect the learning procedure. We use sub-sampling and ran-
dom feature selection techniques for the iterative boosting
[6].
The estimated confidence value can be reinterpreted as
a probability distribution using soft max transformation [7]
to give the texture layout potentials:
P{c\x,i)°cexpH(c,í). (2)
In Fig. 2(b), although most of the pixels are classified
correctly, the edges between adjacent objects are not accu-
rate enough. The authors in [6] solve this problem by manu-
ally indicating the misclassified
parts,
and then another clas-
sifier is used to adjust those pixels into the right classes.
As it's intended to finish this procedure automatically in
this work, the performance is improved by using color cues,
which are frequently used for edge detection. A graph cut al-
gorithm [8], [9] is employed to smoothly cut the edges based
Fig. 3. Example of implementing K-means clustering and Graph
Cut algorithm.
on cluster information. By using K-means clustering, the
first stage identifies k distinct clusters in the color space of
the image, k ranges from 5 to 8 depending on the complexity
of the target area. Then each pixel is assigned to its cluster
and the graph cut algorithm poses smoothness constraint on
this labeling by employing expansion algorithm finds a la-
beling within a known factor of the global minimum. Hence
a label map is generated as shown in Fig. 3. Dominant class
is calculated by selecting maximum likelihood among all the
classes for each cluster (see (3) and (4)),
ClassGc(k) = Max(P(ci\k))
(4)
where P(c¡\k) is the likelihood of class a given cluster k.
C(j) is the class label of pixel j decided by TBA. Classoc(k)
is the class decision for cluster k. Therefore, the inaccurate
edge issue is solved as shown in Fig. 2(c). However, sev-
eral objects are misclassified because of the color similarity
among different classes, for instance, the color of sky and
that of the windshields of cars are similar, some parts of
buildings and the road have similar colors. To tackle this
problem, we further subdivide each cluster into variety num-
bers of sub-clusters based on the connectivity property (see
Fig. 4). The selection of dominant class is repeated for each
sub-cluster by using (3) and (4). At the end, objects are seg-
mented and the final decision is obtained (see Fig. 2(d)).
To increase accuracy and reduce computational cost,
researchers may choose a subset of labeled images that is the
closest to the given testing sequence to train the classifier. In
this work, the classifier will not be trained from the MSCR
21-class full labeled data which is too huge and consist of
many redundant classes (e.g. animals, road signs, furnitures)
that are trivial for outdoor environment. We performed ex-
periments on a subset of the database, and only focus on 6
out of the 21 classes: building, grass, tree, sky, car, road,

Fig. 4. Example of sub-clustering based on connectivity prop-
erty.
Input Images Results of [6] Improved Result
Fig. 5. Comparison of classification results.
-
True class «- o
Building
Grass
Tree
Sky
Car
Road
00
c
'3
pq
75.7
2.4
16.8
10.0
12.8
7.1
s
0.1
44.3
0.6
0
0
0
8.1
35.0
71.6
5.7
6.0
1.5
4.9
0
8.9
84.3
0.4
0
S3
¡J
9.5
1.1
1.8
0
76.0
2.6
o
Pá
1.7
17.2
0.3
0
4.9
88.8
Tab.
1. Confusion Matrix. The number of clusters in texton
booster is 400, the average accuracy is 76.1 %.
which might be the main objects that affect outdoor radio
propagations. The experiment results are given in Tab. 1 in
a format of confusion matrix. With 1000 rounds of boost-
ing 45
%
of training images in the database, the number of
texton clusters is set to be 400 to achieve the best average ac-
curacy of
76.1
% whereas the JBA gives an overall accuracy
of 69.2 %. The authors of [6] then manually moved the mis-
classified parts to the right classes and the improved result
has an accuracy of 72.2 %. A small set of results is visually
shown in Fig. 5. It is noticed that the developed method
outperforms the JBA algorithm and the edges of adjacent
objects are much more accurate and clearer. Moreover, the
proposed method has the capability to adjust the misclassi-
fied pixels to the correct classes. For instance, in the second
image, some pixels belonging to the building are recognized
as car by JBA. The proposed method is able to change the
decision and move the pixels to the correct classes, such as
some are moved to the building and some are moved to trees.
Hence, the proposed multi-object recognition method is fully
automatic and more accurate, and it can be used to decide
the location of objects and automatically assign the attenu-
ate coefficient for each object, which will be useful during
the simulation of radio propagation.
In order to utilize the aforementioned algorithm to con-
struct the real propagation environment, we build a new
training image set from randomly cut images from Google
map.
Each image has a size of 800 x 550 pixels and they
are manually labeled with color codes and form the ground
truth, as illustrated in Fig. 6, where only buildings, trees and
roads are considered this time to ignore trivial obstacles in
outdoor environment. Afterwards, the image set is trained
by the proposed algorithm. It took around half an hour to
finish 1000 rounds of boosting process for 7 images. A toy
example of the reconstructed 3D scene is shown in Fig. 7,
and the accuracy is 85 %.
3.
Radio Propagation Simulation
3.1 Computational Geometry Part
Many methods are developed to simulate radio prop-
agation, where the objective is to reduce computation time
while maintaining good accuracy. Generally speaking, the
ray-tracing algorithm have very high accuracy [10], [11],
[12],
while the computation load is also very high as the
method tests every intersection along the ray path. When the
scenario area becomes large, traditional methods might take
longer than anticipated. Several algorithms are developed to
overcome the aforementioned drawback by slightly reduc-
ing accuracy. Beam tracing algorithms [13] extends the ray-
tracing algorithm to reduce intersection tests, as well as to
overcome sampling problems. The dominant path tracing al-
gorithm in [14] is developed to avoid redundant calculation,
since the authors believe that 98
%
of the received power
is contributed by only a few radio rays. The ray tube tree

v*>
Orignal
images I
***
w>^J
r
s^*
y *•'
mJf. mfmMñ mmm
Fig. 6. Training image set and the ground truths.
method described in [15] increases the preprocessing speed
in constructing trees for ray-tracing.
Our method takes advantage of automatic map recon-
struction described in Section 2 by utilizing the ray-tracing
algorithm. All the ray paths are calculated based on im-
age concept which is more efficient than traditional geom-
etry method. Basically, there are three types of
rays:
direct
ray, reflected ray and diffracted ray. Other rays such as over-
rooftop ray and ground reflected ray are not discussed here.
The roofs of buildings are assumed flat and thickness of wall
is uniform. Each object is labeled with unique index to ease
ray tracing procedure.
The algorithm searches for a direct path at each loca-
tion. All the obstacles which intersects the transmitted ray
in the Tx-to-Rx path, will provoke signal power attenuation.
For a location q, the direct path loss information is stored as
L
q
= [^1,^2,^3,
• •
,<z
w
],
a\ ~ a
n
are the attenuation param-
eters for the corresponding obstacles sorted along the path
from Tx to q.
After all the direct paths have been calculated, each lo-
cation in the target region has L
q
, q e targetregion, L
q
not
only provides path loss information, but its length also in-
dicates the number of obstacles that exist between Tx and
q. Based on the length of L
q
at each location q, visible seg-
ments from Tx are swept by selecting pixels belonging to
objects with length(L
p
) = 1. Reflections happen on the vis-
ible edges of those visible segments.
Traditionally, maps offer structural information, in-
cluding vertex locations for planes and polygons, and ma-
terial property of each obstacle. However, in this work, the
map is automatically constructed from images, although ob-
jects are correctly labeled, feature points to represent poly-
gons are not calculated. One of the benefits of this method
is that only the visible segments are needed to be vectorized,
which reduces redundant calculation for the whole map. The
Canny edge detector is employed to detect visible lines along
each visible segment, and the Harris corner detector searches
the feature points for each visible line, by combining the
feature points and edge information together we have pairs
of vertexes representing visible vectorized lines. Reflected
Reconstructed
3D view
Fig. 7. 3D reconstruction based on object recognition and seg-
mentation.
sources are calculated by mirroring the TX along this visible
line.
The details are introduced below:
1.
Visible segments are highlighted in the image, others
are considered as background.
2.
Canny edge detector is tested on each visible segment,
the visible lines are obtained in the image.
3.
Harris corner detector is used to find feature points
along detected edges, and
V¿
is used to represent posi-
tion of the feature point i. Edge is expressed by a pair
of vertexes of the form
E(V¿,
Vj•).
4.
Reflected image sources are calculated by mirroring
Tx along the edges, and stored as Reflections =
(xi,yi),(x2,y2),(x3,y3),'" ,(
x
n,y
n
) for Tx, n is lim-
ited by the maximum reflection number.
5.
Each virtual point serves as new transmitter, and the
whole procedure is repeated until reaches the maxi-
mum iteration number.
All the reflected points are seen as virtual sources with
same transmission power as real source, while with con-
straints in transmission angle. As shown in Fig. 8, the re-
flection region is constrained by combining maximum trans-
mission range and angle ¿V\0'V2-
According to the Geometrical Theory of Diffraction
[16],
diffracted rays are produced by incident rays which hit
edges,
corners or vertices of boundary surfaces. All the ver-
tices and corners are obtained as a form of
V¿
while searching

for the reflected
rays.
Therefore, those vertices are automati-
cally introduced as diffracted virtual sources. The diffracted
region is also determined.
3.2 Radio Propagation Model
A radio propagation model is developed in this paper to
estimate the power loss between the Tx and Rx points. The
developed model can be used to calculate and produce a path
loss profile of the transmitted signal, reflected and diffracted
signal respectively by
L
p
= lOnlogwd + L
obst
acle (5)
v'-i
(6)
^obstacle = £/(/)(*(/)
(=1
where n is path loss coefficient with range between 2 and 5.
The value of n is decided by the environment, i.e. in free
space n = 2, in others such as urban or rural environments
2 < n < 5. For a direct path d is the distance between TX
and RX, for a reflected path and diffracted path, d is the
distance between the virtual source and RX. L
0
t,
stac
i
e
is the
power loss due to obstacles encountered on the signal path.
This is calculated by accumulating the power reduction of
each obstacle along the path. /(/) is attenuation exponent of
the i
th
obstacle, and oc(/) ranges from 0 to 1, which is the
penetration rate of the material of i
th
obstacle.
a(/)
!_1
de-
creases when / increases, which means that the first object,
with which the signal intersects, produces the most signifi-
cant power loss. Fig. 9 gives an example of calculating (6)
in the direct path. The signal first penetrates through a glass-
made object, then through a concrete obstacle. By assuming
that /(1) = 2 dB, 1(2) = 23 dB, we can set a = 0.9 as a con-
stant value, we then have L
0
t,
stac
i
e
=
2
+
23
x 0.9 = 22.7 dB.
Equation (5) indicates that not only distance, but also the
material property of obstacles and their orders can affect the
received signal strength. At the end, the power loss at the re-
ceiver is the accumulated value among the directed, reflected
and diffracted paths.
4.
Experimental Results
The proposed method was verified by comparing the
results to that of Munich scenario [1], which was com-
prehensively studied by the European COST 231 working
group. Fig. 10 illustrates the top view of the target region in
Munich city. The size of the region is 2400 m x 3400 m and
there are 3 different routes measured by COST 231 group
(e.g. the red color is the first route named as METRO200,
the black one is the second route METRO
201,
and the green
one is the third rout METRO 202).
A new training database is created through similar
methods described in Section 2. The training images are
fetched randomly from Google Maps within the region of
Munich city. Buildings, roads and trees are labeled in order
to guarantee the learning of reliable and transferable knowl-
edge.
Fig. 11 shows the evaluation procedure: At the begin-
Reflection
Reijion d
Fig. 8. Reflection region and diffraction region.
Glass
Concrete
T
>-3i
>
T
Fig. 9. Example of propagation.
2300
-
Fig. 10. Building geometry of Munich city and 3 different routes
that measured by COST
231
group.
ning, the same area in which the COST 231 group did mea-
surements is captured on Google
map.
The images are down-
loaded and divided into small sub-images, each of which is
of the same size as the training images.
Afterwards, they are passed through the image classi-
fier to recognize and segment the three objects. The recog-
nized objects are then vectorized and the 3D database is au-
tomatically generated. Then the propagation simulator is run
to simulate the signal transmission in the target area. Finally,
the signal coverage map is visually presented to the user.
The proposed method is programmed by combining
C#, Matlab and C++ code. It was run on a PC equipped with

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  • ...Besides, a weighted multi-objective fitness function (WMOGA) developed in the authors' previous work by He et al. (2013) is modified and implemented to evaluate the impacts of NSGA-II on the final solutions, the formula of the weighted function is: / = w\Dc + u>2Dcost + u)3DL + u>4DPl + w5DPd (16)...

    [...]

  • ...The proposed method employs a ray-tracing method described in the authors' previous work (He et al. 2012) to emulate the propagation paths of both radio and sensing signals....

    [...]


References
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Journal ArticleDOI
TL;DR: This work presents two algorithms based on graph cuts that efficiently find a local minimum with respect to two types of large moves, namely expansion moves and swap moves that allow important cases of discontinuity preserving energies.
Abstract: Many tasks in computer vision involve assigning a label (such as disparity) to every pixel. A common constraint is that the labels should vary smoothly almost everywhere while preserving sharp discontinuities that may exist, e.g., at object boundaries. These tasks are naturally stated in terms of energy minimization. The authors consider a wide class of energies with various smoothness constraints. Global minimization of these energy functions is NP-hard even in the simplest discontinuity-preserving case. Therefore, our focus is on efficient approximation algorithms. We present two algorithms based on graph cuts that efficiently find a local minimum with respect to two types of large moves, namely expansion moves and swap moves. These moves can simultaneously change the labels of arbitrarily large sets of pixels. In contrast, many standard algorithms (including simulated annealing) use small moves where only one pixel changes its label at a time. Our expansion algorithm finds a labeling within a known factor of the global minimum, while our swap algorithm handles more general energy functions. Both of these algorithms allow important cases of discontinuity preserving energies. We experimentally demonstrate the effectiveness of our approach for image restoration, stereo and motion. On real data with ground truth, we achieve 98 percent accuracy.

7,060 citations


Journal ArticleDOI
TL;DR: This paper presents work on computing shape models that are computationally fast and invariant basic transformations like translation, scaling and rotation, and proposes shape detection using a feature called shape context, which is descriptive of the shape of the object.
Abstract: We present a novel approach to measuring similarity between shapes and exploit it for object recognition. In our framework, the measurement of similarity is preceded by: (1) solving for correspondences between points on the two shapes; (2) using the correspondences to estimate an aligning transform. In order to solve the correspondence problem, we attach a descriptor, the shape context, to each point. The shape context at a reference point captures the distribution of the remaining points relative to it, thus offering a globally discriminative characterization. Corresponding points on two similar shapes will have similar shape contexts, enabling us to solve for correspondences as an optimal assignment problem. Given the point correspondences, we estimate the transformation that best aligns the two shapes; regularized thin-plate splines provide a flexible class of transformation maps for this purpose. The dissimilarity between the two shapes is computed as a sum of matching errors between corresponding points, together with a term measuring the magnitude of the aligning transform. We treat recognition in a nearest-neighbor classification framework as the problem of finding the stored prototype shape that is maximally similar to that in the image. Results are presented for silhouettes, trademarks, handwritten digits, and the COIL data set.

6,426 citations


"A novel method for radio propagatio..." refers background in this paper

  • ...In [2] and [3], the identification of objects is made by shape feature descriptor....

    [...]


Journal ArticleDOI
TL;DR: This work shows that this seemingly mysterious phenomenon of boosting can be understood in terms of well-known statistical principles, namely additive modeling and maximum likelihood, and develops more direct approximations and shows that they exhibit nearly identical results to boosting.
Abstract: Boosting is one of the most important recent developments in classification methodology. Boosting works by sequentially applying a classification algorithm to reweighted versions of the training data and then taking a weighted majority vote of the sequence of classifiers thus produced. For many classification algorithms, this simple strategy results in dramatic improvements in performance. We show that this seemingly mysterious phenomenon can be understood in terms of well-known statistical principles, namely additive modeling and maximum likelihood. For the two-class problem, boosting can be viewed as an approximation to additive modeling on the logistic scale using maximum Bernoulli likelihood as a criterion. We develop more direct approximations and show that they exhibit nearly identical results to boosting. Direct multiclass generalizations based on multinomial likelihood are derived that exhibit performance comparable to other recently proposed multiclass generalizations of boosting in most situations, and far superior in some. We suggest a minor modification to boosting that can reduce computation, often by factors of 10 to 50. Finally, we apply these insights to produce an alternative formulation of boosting decision trees. This approach, based on best-first truncated tree induction, often leads to better performance, and can provide interpretable descriptions of the aggregate decision rule. It is also much faster computationally, making it more suitable to large-scale data mining applications.

6,068 citations


"A novel method for radio propagatio..." refers methods in this paper

  • ...The estimated confidence value can be reinterpreted as a probability distribution using soft max transformation [7] to give the texture layout potentials:...

    [...]


Journal ArticleDOI
TL;DR: This paper compares the running times of several standard algorithms, as well as a new algorithm that is recently developed that works several times faster than any of the other methods, making near real-time performance possible.
Abstract: Minimum cut/maximum flow algorithms on graphs have emerged as an increasingly useful tool for exactor approximate energy minimization in low-level vision. The combinatorial optimization literature provides many min-cut/max-flow algorithms with different polynomial time complexity. Their practical efficiency, however, has to date been studied mainly outside the scope of computer vision. The goal of this paper is to provide an experimental comparison of the efficiency of min-cut/max flow algorithms for applications in vision. We compare the running times of several standard algorithms, as well as a new algorithm that we have recently developed. The algorithms we study include both Goldberg-Tarjan style "push -relabel" methods and algorithms based on Ford-Fulkerson style "augmenting paths." We benchmark these algorithms on a number of typical graphs in the contexts of image restoration, stereo, and segmentation. In many cases, our new algorithm works several times faster than any of the other methods, making near real-time performance possible. An implementation of our max-flow/min-cut algorithm is available upon request for research purposes.

4,298 citations


Proceedings ArticleDOI
01 Jan 1999
TL;DR: This paper proposes two algorithms that use graph cuts to compute a local minimum even when very large moves are allowed, and generates a labeling such that there is no expansion move that decreases the energy.
Abstract: In this paper we address the problem of minimizing a large class of energy functions that occur in early vision. The major restriction is that the energy function's smoothness term must only involve pairs of pixels. We propose two algorithms that use graph cuts to compute a local minimum even when very large moves are allowed. The first move we consider is an /spl alpha/-/spl beta/-swap: for a pair of labels /spl alpha/,/spl beta/, this move exchanges the labels between an arbitrary set of pixels labeled a and another arbitrary set labeled /spl beta/. Our first algorithm generates a labeling such that there is no swap move that decreases the energy. The second move we consider is an /spl alpha/-expansion: for a label a, this move assigns an arbitrary set of pixels the label /spl alpha/. Our second algorithm, which requires the smoothness term to be a metric, generates a labeling such that there is no expansion move that decreases the energy. Moreover, this solution is within a known factor of the global minimum. We experimentally demonstrate the effectiveness of our approach on image restoration, stereo and motion.

3,195 citations