IbPRIA 2009: 4th Iberian Conference on Pattern Recognition and Image Analysis

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"IbPRIA 2009——第四届伊比利亚模式识别与图像分析会议的论文集" 本文档汇集了2009年在葡萄牙Póvoa de Varzim举行的第四届伊比利亚模式识别与图像分析会议（IbPRIA 2009）的经过同行评审的论文。这次会议共收录了33篇修订后的完整论文和29篇修订后的海报论文，以及3场邀请报告，从106份提交的稿件中精心挑选出来。这些论文围绕计算机视觉、图像分析与处理以及模式识别这三个主题进行了组织。模式识别是人工智能和机器学习领域的一个关键分支，涉及让计算机理解并分类数据中的模式。在IbPRIA 2009会议上，参与者探讨了如何通过算法和技术使计算机能够自动检测、识别和理解图像、视频和其他感官输入中的模式。这些模式可能包括形状、纹理、颜色分布等特征，对理解复杂的数据集至关重要。图像分析则侧重于处理、解释和理解图像内容的过程。这可能包括图像预处理（如去噪和增强）、图像分割（区分图像的不同部分）、物体检测和识别，以及场景理解。在本次会议上，研究者分享了最新的方法和技术，以改进图像分析的精确度和效率。论文集中的内容涵盖了广泛的主题，可能包括但不限于以下几点： 1. **计算机视觉**：利用计算机模拟人类视觉系统，识别和解释视觉信息。这可能涉及到深度学习模型，如卷积神经网络（CNN），用于物体识别、目标检测和场景理解。 2. **图像分析和处理**：包括图像特征提取、图像配准、图像增强以及图像分类等技术，这些对于在各种应用中如医学成像、遥感或监控系统中分析图像至关重要。 3. **模式识别**：涉及创建统计模型和机器学习算法，以识别和分类数据中的模式。这些技术可以应用于语音识别、文本分类、生物信息学和金融数据分析等领域。 4. **邀请报告**：大会邀请的专家可能分享了他们在模式识别和图像分析领域的最新研究进展，推动了学术界和工业界的交流与合作。此外，本书出版于“Lecture Notes in Computer Science”系列，这是一个知名的学术出版系列，自1973年以来，一直致力于发表计算机科学领域的高质量研究成果。其编委会由来自全球顶级大学和研究机构的专家组成，他们确保了所收录论文的严谨性和影响力。 IbPRIA 2009会议的论文集不仅展示了当前模式识别和图像分析领域的前沿研究，也为该领域的学者和从业者提供了宝贵的参考资源，促进了理论研究与实际应用的结合。

2H.Kuecketal.

Theorem 1. If a preference relation  satisﬁes axioms 1 to 6 above, then there

exists a function u mapping outcomes to the real line with the properties that:

1. u(o

) ≥ u(o

) iﬀ o

 o

2. u([(o

), (o

),...,(o

)]) =



i=1

u(o

Expected utility does therefore arise as a rational consequence of fairly unassail-

able axioms. An agent expecting to behave optimally must maximize its expected

utility; see [14] for a more comprehensive treatment.

Following this result, it is reasonable that our goal in decision making under

uncertainty be one of ﬁnding an optimal strategy π

∗

that maximizes the expected

utility U(π) of the agent:

∗

=argmax

U(π), with U(π)=



u(x, π)p(x|π) dx (1)

Note, we are integrating over all possible unknown states x (that is we are con-

sidering all possible worlds and weighting them according to how likely we deem

them). U(π) then describes how useful we expect the outcomes of adopting a

policy to be based on the current beliefs encoded in p(x|π). In the MEU view, we

are assuming that we can solve the joint maximization and integration problem.

In general we can’t do this and are forced to make approximations. Theories

that take into account these approximations have appeared under the umbrella

of bounded rationality. The application domain of the MEU principle is very

broad. The principle can be used to guide the placement and control of a net-

work of sensors in a changing environment, to decide what data must be gathered

to improve a classiﬁer, to plan a sequence of gazes to dynamically understand a

visual scene, to plan the trajectory of a robot so as to minimize resources, and

so on. In this paper, we will present an inference and learning approach for solv-

ing MEU problems. This single approach will suﬃce to solve diﬃcult nonlinear,

non-Gaussian problems arising in myopic and sequential (multi-stage) decision

making. We discuss these two problems in the following subsections.

1.1 Myopic Decision Making

We will illustrate myopic decision making in the context of Bayesian experimen-

tal design. We don’t lose much generality doing this because Bayesian experimen-

tal design is a broad ﬁeld of study that is applicable to many problems, including

active vision, sensor network management and active learning. We assume that

we have a measurement model p(y|θ, π) of experimental outcomes y ∈Ygiven a

design π as well as a prior p(θ) on the model parameters θ ∈ Θ. The prior could

be based on expert knowledge or previous experiments. We recover the general

model presented in the previous section by noting that x = {y, θ}.

The model parameters as well as future observations are unknown so we have

to integrate out over their probability distributions. (In the simple case of learn-

ing a regression function or a classiﬁer, which is widely studied in active learning,

Inference and Learning for Active Sensing, Experimental Design and Control 3

π would correspond to the predictors (inputs) and y to the corresponding covari-

ates (outputs).) The general goal is then to choose the optimal design π

∗

∈ R

which maximizes the expected utility

U(π)=



u(y, π,θ) p(θ)p(y|θ, π) dy dθ (2)

with respect to some measure of utility u(y,π,θ). When the model parameters

are the objects of interest, which will be the case in Section 3.1, the negative

posterior entropy is commonly chosen as the utility function. That is, one aims

to maximize

u(y, π,θ)=



p(θ



|y, π)log p(θ



|y, π)dθ



This measures how concentrated the belief distribution over the parameters is

after conducting an experiment with design π and observing outcome y.Note

the diﬀerence between θ and θ



here. θ represents the true model parameters

of the possible world under consideration in which the hypothetical experiment

is conducted. The outcome y is generated according to p(y|θ, π). p(θ



|y, π)then

is the belief distribution over the model parameters that we would have after

observing y. Note that this particular utility function does not actually depend

on θ. It merely measures how peaked the posterior belief p(θ



|y, π)is,nothow

close it is to the ‘real’ θ. In the case of a linear-Gaussian model, this entropy

based utility function is referred to as Bayesian D-optimality [1].

In general, the choice of utility function should reﬂect the objective of the

experiment as well as costs and risks related to the experiment as well as possible.

For example in a medical trial the goal might be to gain the maximum amount

of information about the eﬀects of a new drug while at the same time keeping

the risk of people dying (or suﬀering severe side eﬀects) to a minimum and also

minimizing the monetary cost of the trial. The utility function would then consist

of several terms representing these (possibly conﬂicting) objectives. Another

interesting choice of utility is given in Section 3.2 of this paper.

1.2 Sequential Decision Making

In the previous section, we only considered integrating over the outcome at the

next step of decision making. In general, we would like to plan several steps

ahead. This type of planning can be modeled with a Markov decision process

(MDP); illustrated in Figure 1. Here we are integrating over an inﬁnite sequence

0:∞

= {z

,...},whereeachz

=(s

) represents a tuple of state,

action, and reward at time n.

The design parameter π in this setting determines a policy for choosing an

action a

based on the current state s

according to p(a

,π). Given a policy,

the states and rewards of the Markov process evolve according to an initial-state

model: s

∼ μ(s

), a transition model: s

n+1

∼ p(s

n+1

), and rewards:

∼ p(r

). We can then deﬁne the utility function for a single trajectory

as its discounted reward, u(z

0:∞



∞

n=0

. Intuitively the discount factor

Inference and Learning for Active Sensing, Experimental Design and Control 5

design and control has focused on the simple linear-Gaussian models, for which

closed form solutions exist [2,3]. Recently, however, there has been a ﬂurry of

work applying inference and learning techniques to more diﬃcult nonlinear prob-

lems. In the context of control this seems to have originated with [4], although

only immediate rewards are considered, thus making it perhaps more applica-

ble to the setting of myopic experimental design. In this section we will focus

on a promising sample-based technique originating in the experimental design

literature [10].

One possible strategy for solving these problems involves sampling policies π

and hidden states x from the artiﬁcial target distribution

h(π, x) ∝ u(x, π) p(x|π). (4)

We can see by marginalizing over x that this produces a distribution

h(π) ∝



u(x, π) p(x|π) dx = U (π)

proportional to the expected utility. In order to sample from this distribution we

must assume that u(x, π) is positive and ﬁnite but this is easy to ensure so long

as the utility is bounded. We may also be required to introduce a prior p(π)to

ensure that this distribution is well deﬁned, but typically a uniform distribution

over some bounded region is suﬃcient.

If U(π) happens to have a strongly dominant and highly peaked mode around

the global maximum π

∗

, we can justify sampling from (4) and deriving a point

estimate by averaging these samples. In the context of sequential decision making

this is the approach taken in [6]. However, in general the assumption of such a

favorable U(π) is unrealistic, and applying this strategy to a multimodal or fairly

ﬂat utility landscape will yield poor estimates.

Other strategies involve discretizing the policy space R

and approximating

the integrals with direct Monte Carlo methods. However, these approaches are

expensive and inadequate for high dimensional spaces. To eliminate the need for

discretization, M¨uller et al. [10] proposed a Markov chain Monte Carlo anneal-

ing technique for simultaneous maximization and integration. They deﬁne the

following artiﬁcial target distribution

(π, x

1:J

) ∝



j=1

u(π, x

)p(x

|π)

Marginalizing this distribution over the unknown outcomes and parameters gives

(π)=



(π, x

1:J

) dx

1:J





j=1

u(π, x

)p(x

|π) dx

1:J

= U (π)





j=2

u(π, x

)p(x

|π) dx

2:J



j=1

U(π)=U

(π).

6H.Kuecketal.

For large exponents J, the probability mass of this distribution will concentrate

on the global maximum for π

∗

. However, because the modes of this distribution

will typically be narrow and widely separated for large J, sampling from this

distribution using Markov chain Monte Carlo techniques directly is diﬃcult. We

must therefore take a simulated annealing approach in which we start sampling

from U

(π)forJ = 1 and slowly increase this exponent over time according

to some annealing schedule. Increasing J slowly enough allows the chain to

eﬃciently explore the whole parameter space before becoming more constrained

to the major modes.

In order to apply this technique to problems of sequential decision making we

must use reversible jump MCMC [5] to sample from trans-dimensional distribu-

tions such as (3); see [6,7] for more details on applying these ideas to control

problems. In the myopic experimental design setting we advise the use of se-

quential Monte Carlo samplers [8] (see also Figure 2).

3 Demonstrations

3.1 Active Sensing Example

As a ﬁrst example we study a synthetic problem that, despite its apparent sim-

plicity, exhibits complex multi-modality. In particular, we address the problem

of inferring the parameters of a sine wave. This non-linear experimental design

example is motivated by the problem of scheduling expensive astronomical ob-

servations [9]. The sine wave is parameterized by θ = {A, ω, ρ} where A is the

amplitude, ω the frequency and ρ the phase

y = f (π; A, ω, ρ)+ = A sin (πω+ ρ)+.

Here  denotes the normally distributed measurement noise. The objective is to

ﬁnd the optimal location π

∗

along the x-axis at which to make the next noisy y

measurement in order to maximally reduce uncertainty about the parameters θ.

In the example shown in Figure 2, two prior observations have already been made

and the design problem consists of choosing the optimal third measurement. That

is, the prior belief p(θ) here is actually the posterior parameter distribution after

these ﬁrst two measurements. Figure 2(a) shows some sine waves corresponding

to samples from this p(θ), visualizing the belief about possible sine waves.

The corresponding expected utility function U (π) shown in Figure 2(b) is

proportional to the uncertainty about y at a given point π along the x-axis.

This function is highly multi-modal, with most of the modes having similar

magnitudes. However exponentiating this function to a power of 50 concentrates

most of the probability mass on the major mode, so that samples distributed

proportional to this function provide a good basis for estimating π

∗

. When using

a single MCMC chain using the approach of [10], the chain often gets trapped in

the minor modes, as can be seen in Figure 2(c). The interaction between multiple

particles in the SMC samplers algorithm we proposed in [8] helps avoid this and

yields a much better estimate as shown in Figure 2(d).

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