### Table 7 : Results obtained with Discrete Hidden Markov Model

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### (Table 2). 2.3.2 Hidden Markov Model (HMM)

"... In PAGE 5: ....3.1 Video Analysis The video analysis was performed by two expert surgeons encoding the video of each step of the surgical procedure frame by frame (NTSC - 30 frames per second). The encoding process used a code-book of 14 different discrete tool maneuvers in which the endoscopic tool was interacting with the tissue (Table2 ). Each identified surgical tool/tissue interaction, had a unique F/T pattern.... In PAGE 8: ... 1b. (a) Forces (b) Torques Studying the magnitudes of F/T applied by R1 and ES during each step of the MIS procedures for the different tool/tissue interactions (Table2 ) using the grand median analysis showed that the F/T magnitudes applied by these groups were significantly different (p lt;0.05) and task dependent (Fig.... ..."

### Table 1 State Transition Matrix for a Hidden Markov Model

"... In PAGE 25: ...alues such as Sunny = 1.0, Rainy = 0, and Foggy = 0. 2. A state transition matrix ( Table1 ) that stores the probability of going from one state to another. For example, the first row gives the probability of a sunny day following a sunny day, a rainy day following a sunny day, a foggy day following a sunny day, and so on.... ..."

### Table 2. Accuracy of Hidden Markov Models to recognize haptic gestures

### Table 3: Results of 3 classes segmentation based on hidden Markov models.

"... In PAGE 6: ... Two successive frames will be shifted of 512 samples. Table3 shows results of 3 classes segmentation. Quality rates are better than with simple approaches reviewed in previous section.... ..."

### Table 2: Log-likelihood of the experiments on the hidden Markov simulation data

"... In PAGE 13: ...009 0.005 Table2 shows the mean and the standard deviation of log-likelihood of the test set using the naive method, the log-likelihood of the gated experts and the hidden Markov experts. It indicates that the likelihood of the gated experts and the hidden Markov experts are signi#0Ccantly better than the naive model.... ..."

### Table 1: Recognition results using Hidden Markov Models with di erent numbers of states 4.1 Hidden Markov Models for Object Recognition In the rst part of our experiments we implemented and tested Hidden Markov Models for 2D object recognition problems. The basic constraint for the use of Hidden Markov Models is the limitation to classi cation problems, where objects can be represented by feature sequences. We decided to use a ne invariant features, described in [6], based on closed contour lines of 2D objects. Hence, the sequence of features does not change if the object is rotated and translated. We took four objects, shown in Figure 4, and trained Hidden Markov Models with di ering numbers of states using 50 samples for each object. The classi cation results for 10 images of each object are shown in Table 4.1. For an e cient computation of the a priori probabilities for a given observation and a Hidden

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### Table 5.1: Cross-entropies for Hidden Markov Models treating the melody notes as observed events and the harmonic symbols as hidden states

### Table 1. Observations of a Hidden Markov Model for a meeting of 4 individuals

2005

"... In PAGE 2: ... One observation is a vector containing a binary value (speaking, not speaking) for each individual that is recorded. This vector is transformed to a 1-dimensional discrete code used as input for the HMM (see Table1 ). The automatic speech detector has a sampling rate of 62.... ..."

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