6.2.1
Online Updating of Travel Time Models Using Confidence
Score
For traffic scenarios, the travel times may change during different times of the day. The Gaussian models of travel time need to be updated adaptively with changing traffic condi- tions. If a GMM is employed and trained during the training stage, the mean and variance
of each Gaussian are updated online by using the travel time of the matched object. Con- sidering the existence of false positives, the matched object with a higher similarity score, which indicates higher confidence in matching, should have more impact on the travel time model; or vice versa. The mean and variance are updated by
μnew = (1− λ)μold+ λtmatch (6.12)
σnew2 = (1− λ)σold2 + λ(tmatch− μnew)2 (6.13)
where tmatch is the travel time of the matched object; λ is the update parameter in the range of [0, 1], which is defined as λ = α· S. α is a constant update factor which is a small number such as 0.05. S is the confidence factor, which is equal to the overall similarity of a matched pair. Thus, the matched objects with high similarity scores contribute more to the parameter updating.
6.2.2
Adaptive Weight Estimation
There are many different cues that could be used for object re-identification. An individual similarity for each cue can be evaluated, and then these similarities need to be combined for a final evaluation. Weighted sum is a simple but effective way to achieve the information integration. The problem is how to assign the weight to each cue. It is intuitive that a more reliable cue should be assigned a higher weight. Observers or algorithms must evaluate the degree of reliability of each cue and assign higher weights to the more reliable cues. The reliability is normally context sensitive and changes with the environment [90]. There have been some work to explore evaluating the reliability of the cues and combine them in a self- organized manner. [113] proposed a method to integrate five visual cues for face detection. In their work, each feature generates a two-dimensional salient map by comparing with a prototype that describes the appearance of the face. Then, different features are combined
by a method called Democratic Integration. We apply a similar method in our system to evaluate the weights of the multiple features, and extend this method to an online adaptive weight estimation, which suits the real-time systems.
To find a match among the received candidates for an incoming object, an overall simi- larity score is calculated between the object and each candidate. The overall similarity score is the weighted sum of various features, and we evaluate the reliability of each feature as follows: if the similarity of a feature is in accordance with the result of the overall similarity score, this feature is considered as reliable. For a correctly matched pair of an object and the candidate, the higher the similarity of a single feature, the more reliable that feature is. On the contrary, if the similarity of a feature is low enough, it is considered having zero reliability. To compute the reliability quantitatively, the quality of a feature is introduced. The similarity score of a feature for the best matched candidate is compared with the av- erage score of this feature over all candidates. The higher the score (as compared to the average), the more it contributes to the running evaluation of the reliability of this feature. The quality of this feature is the difference between the similarity score and the average. On the other hand, if the similarity score is lower than the average, the quality is set to zero. The quality of each feature is calculated in this way, and then normalized over all the features. The reliability of a feature is the running average of the quality of this feature. Since the qualities are normalized, the reliability scores will add up to 1. The formulation of the method is described below.
For Object o, given C candidates, a similarity score Sj(c, o) is calculated for each feature
j ∈ F = {CH, H, L, A, S, T T } of each candidate c ∈ {1 . . . C}. From the descriptions in
Section 6.1, we know that 0 ≤ Sj(c, o) ≤ 1. The overall similarity result of each object- candidate pair is
R(c, o) =
j∈F
where rj is introduced as the reliability of the jth feature, with
jrj = 1. Then the best match for Object o is found by
ˆ
O(o) = arg max
c∈{1...C}{R(c, o)} (6.15)
When (6.11) is compared with (6.14) and (6.15), we can see that the weight wj assigned to each feature is the reliability rj of that feature.
To estimate rj, the quality ˜qj(o) is introduced, and 0 ≤ ˜qj(o) ≤ 1. The quality ˜qj(o) measures how successful the feature predicts the result or how much it agrees with it. It is calculated by
˜
qj(o) =R(Sj( ˆO(o), o)− < Sj(c, o) >)) (6.16) where < . . . > denotes an average over all candidate similarity scores for Object o; R is the ramp function: R(x) = ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ 0 if x≤ 0 x if x > 0
In (6.16), the similarity score of each feature for the best matched candidate is compared to the average score of this feature over all candidates. If the score of this feature is greater than the average, the quality is the distance to that average; otherwise the quality is zero.
Normalized qualities qj(o) are computed by
qj(o) = ˜ qj(o) k∈Fq˜k(o) (6.17)
This definition ensures that
j∈F
qj(o) = 1 (6.18)
qj(o), rj is also normalized. The sum of reliabilities over all features will be 1. Thus, the reliabilities can be used as weights. A feature with a normalized quality higher than its current reliability will tend to increase its reliability, and a feature with a normalized quality lower than its current reliability will have its reliability lowered [113].
An initial set of rj can be estimated beforehand. With the system running, the environ- ment conditions may change over time. For example, the light conditions may be different during different times of the day. Then the reliability of color information might change. When the color shift between two cameras is larger, a lower weight should be assigned. To adapt to the changes in the environment, an online weight updating is applied. Since rj is the running average of qj(o) over all object o, it is easily updated by incorporating the results of newly matched objects. However, to reduce the impact of the false positives that may corrupt the reliability of features, only the matched objects with the overall similarities higher than a threshold are used to update the reliability scores.
6.3
Conclusions
Compared to the object re-identification method that is used in Chapter 5, a more robust algorithm combining multiple features with adaptive weights is proposed. These features include 3D color histograms, HOG and LBP descriptors, object sizes, aspect ratios and travel times. The travel times can be modeled by the GMM or a single Gaussian model depending on the domain knowledge in the blind region. The parameters of GMM are trained using the EM algorithm in the training stage and updated online taking the confidence score of the matched objects into account. The weight of each feature is estimated based on the reliability of each feature and also trained in the training stage. Like the parameters of the Gaussian models, the weights are also updated after every newly matched object is found, which makes this system adaptive to environment changes.