IL-1 como marcador de metástasis a distancia

Pun and Lee (2003) have demonstrated how images converted from their Cartesian plane to a log-polar image before processing, eliminate the effects of rotation and scale. Consid- ering an image I with Cartesian coordinates denoted by I(x, y). This is transformed into a log-polar form dst(θ ,ρ) as in Equation 4.9. To obtain the log-polar image, a conformal mapping of the points in the Cartesian plane I(x, y) to the points in the log-polar plane (θ , ρ) was performed.

Figure 4.10: The top left image is the original image of a Cockatiel in RGB. This was transformed into grayscale (see top right of this figure) and used to form the grayscale histogram (see the bottom part of this figure). The histogram was created using the silhouette of the bird excluding background. The horizontal axis shows the intensity

values from 0 to 255 and the vertical the number of intensity values.

dst(θ , ρ) ← src (x, y) f or        ρ = logpx2+ y2 θ = arctan  x y  i f x> 0 (4.9)

To complement the colour features, the segmented image were converted to HSV space and a log-polar transform was applied to each channel separately (see Figure 4.12). Five statistics (including mean, standard deviation, skewness, entropy and energy) were computed from each channel. Similar to the previous process, these features were con- catenated to form the log-polar feature set, which comprises a total of 15 features. This approach is different from existing approaches because it considered colour information

4.3. EXPERIMENTS 99

Figure 4.11: Gabor filter features for four orientations. Five Statistical features were extracted from these and the results concatenated to form a feature vector.

Figure 4.12: Colour log-polar features obtained by extracting hue, saturation and value log-polars then extracting statistical features, which were concatenated to form a colour

log-polar feature vector.

whilst computing the log-polar features.

4.3

Experiments

Three sets of experimental evaluations were performed:

• Firstly, quantifying the effectiveness of the appearance feature set, across the dataset of seven classes (seven different species), using four different classifiers and com- paring this result with the feature sets proposed by Marini et al. (2013).

• Secondly, quantifying the effectiveness of the appearance feature set, across the ex- tended dataset of thirteen classes (eleven bird species, one with three colour forms), using four different classifiers. This was compared with the feature sets proposed by Marini et al. (2013).

• Finally, quantifying the effectiveness of the appearance feature set, across the CUB- 200-2011 dataset (using 5, 17 and 200 species), using four different classifiers. Again, this was compared with the feature sets proposed by Marini et al. (2013). Features for these experiments were selected randomly.

All experiments were performed on a Mac book pro laptop running OS X 19.5, with 2.5 GHz Processor and 4 GB RAM. The pre-processing and feature extraction algorithms were all implemented in C++ with XCode 5.1.1 and OpenCV 3.0, whilst the classification and feature selection algorithms were implemented in WEKA 3.7 (Hall et al., 2009).

For all experiments, a five-fold cross-validation scheme was used, in which the orig- inal videos for each class (species) were randomly partitioned into five equal sized sub- samples each. Of the five subsamples for each class (species), a single subsample was retained as the validation data for testing the model, and the remaining four subsamples were used as training data. The cross-validation process was then repeated five times (the folds), with each of the five subsamples used exactly once as the validation data (see fig- ure 4.13 for a diagram of a thirteen class five-fold cross validation). The five results from the folds were then averaged to produce the results (correct classification rates) for each experiment. The advantage of doing it this way was that all videos were used for both training and validation, and each video was used for validation exactly once.

For each experimental run, individual image frames were sampled (from the train- ing and test set), from which the corresponding appearance features were extracted (see Section 4.2). These features were concatenated to form the full appearance feature set, comprising 169 features. All features were stored in a WEKA compatible format.

Finally, the feature set was loaded into WEKA for classification. Four classifiers were then used (Naive Bayes (NB), Random Forest (RF), Random Tree (RT) and Support Vector Machine (SVM)) to perform the classification experiments, and results for each were reported in Section 4.4. The Naive Bayes classifier is based on the Bayes rule assuming conditional independence between classes. This is a multi-class classifier as when given an observation, the classifier estimates the conditional probabilities of classes using the joint probabilities of samples and classes and the observation is classified as

4.3. EXPERIMENTS 101

Figure 4.13: A sample five-fold cross-validation assuming the thirteen class dataset was used. Each fold of a class represents approximately one-fifths of the videos in that class. In each iteration, one fold of each of the classes is used for testing and the

remaining for training.

one of the N classes based on the conditional probabilities. The SVM classifier was based on LibSVM proposed by Chang and Lin (2011), which is comparable to that used by Marini et al. (2013), and implemented using a radial basis function kernel, with the gamma and cost parameters optimised using a 5-fold grid search. In the case of the Random Tree classifier, K randomly chosen attributes at each node were considered, in this case K = int(log2(# f eatures) + 1), and the maximum depth of the tree was set to be

unlimited. Twenty trees were used for the Random Forest classifier, as this results in a convergence of the out of bag errors (other parameters for this classifier are the same as for the RT).

The three broad methods that can be applied to compare the statistical significance of the results of two classifiers over k-folds cross-validation are the paired t-test, Wilcoxon’s signed-rank test and the sign test. These methods can be applied to the results of either the k-fold cross-validation directly or r-times k-fold cross-validation. We compare the statistical significance of the results of two classifiers using the Wilcoxon’s signed-rank

test applied on the r-times k-fold cross-validation results, as in Fay (2007). The results of the r.k experiments performed with both learning algorithms are used as input to this statistical significance tests. In all experiments involving statistical significance of clas- sifiers, r = 10 and k = 5 were used. The Wilcoxon’s signed-rank test was chosen as it is a non-parametric alternative to the paired t-test, more powerful than the signed test (Fay, 2007) and is not substantially affected by the presence of outliers Demšar (2006).

For all statistical significance test performed, the null hypothesis H0 is that there is

no significant difference between the two classifiers being compared while the alternative hypothesis H1is that, there is a significant difference. All tests are carried out as a two-

sided test with a 49 degree of freedom and α = 0.05 significance level. This corresponds to a critical value of 415. The decision rule is that H0 is rejected if the test statistic W is

less than 415. W is defined as the smaller of W+ and W−, where W+ is the sums of the positive ranks and W−, the negative ranks.

4.4

Results

This section presents results of the experiments using the appearance features with the four classifiers: Naive Bayes (NB), Random Forest (RF), Random Tree (RT) and Support Vector Machine (SVM). In particular, an evaluation of the performance of the appearance features against that of Marini et al. (2013), on the three datasets (dataset #1, #2 and Caltech-UCSD Birds-200-2011) were presented.