## 4 Results  
The PCA algorithm requires two databases, the training database and the testing database. In the first database, each gesture of the training database is represented as a column vector, that is, the values of each column that forms a matrix represent the pixels of the gesture image. Subsequently, the algorithm calculates the average of this matrix to normalize the gesture vectors. Then, the Eigen vectors of a covariance matrix is obtained. Finally, each gesture is projected to the corresponding gesture space when the Eigen vector matrix is multiplied by each of the gesture vectors. At the testing database, a gesture of a subject (which is a test gesture) in the same way is represented as a column vector that is subsequently normalized with respect to the average gesture. Then, the algorithm projects the test gesture into the gesture space using the Eigen vector matrix. Next, the Euclidean distance is calculated between this projection and each of the known projections of the database in the training stage, so that the algorithm selects the minimum value of these comparisons. This indicates that the  
Figure 1: Example of the KNN Classifier with manual gestures. The test image can be a rectangle, a diamond or a triangle depending on the value of \(k\). If \(k=1\) (solid line circle), this is assigned to the rectangle; if \(k=5\) (dashed line circle), this is determined to the diamond; and, if \(k=10\) (solid dashed line circle), it belongs to the triangle. The algorithm only considers the object (rectangle, a diamond or a triangle) nearest to the image test of \(k=1\). Figure 2: Block diagram of the hand recognition proposal. algorithm recognizes a gesture from the training database with respect to the test gesture. It should be noted that at this stage the testing database is used. Training and testing data are sets of manual gesture images. The training database is for the PCA algorithm training, while the testing database is for testing the flexibility and adaptability of the proposed gesture recognition algorithm. Another difference of both databases is that the images in each database are different, i.e. the set of gestures in the training database belong to some test subjects while the gestural images of the testing database are acquired from other test subjects who are different from those who participated for the training database. Therefore, there are no images from the training and testing database belonging to the same person as each image in both databases belongs to different people. Training database: This database contains images of gestures performed by 20 people (there are 10 female subjects and 10 male subjects) and each person develops five gestures. Therefore, there are a total of 100 images of manual gestures for each hand posture. The images are captured using a PC camera. The database consists of three hand postures: index, V sign and fist under a uniform background (see Figure 3). These last two gestures are attached to experience the testing database of other studies [34; 35] with the algorithm of this work. [PERSON] [34] used a neural network model to recognize six hand postures where an analysis of face location and body anthropometry is used through space discretization. On the other hand, [PERSON] [35] presented a human computer interface to control an application by executing manual gestures using a binary Support Vector Machine classifier and Local Binary Patterns as feature vectors. Testing database: The database of the V sign and fist hand posture was obtained from [34; 35] with different lighting conditions. The database of [PERSON] [34] contains thousands of various images with both uniform and complex backgrounds; in this case, the images with a uniform background were used. In [35], the database contains 30 video sequences performed by six different individuals.