## 3 Analysis of the System
### Integration of Multiple Classifiers into a Siamese Network  
The second proposed procedure allows using Siamese networks to solve the one-shot learning problem. In an OSL problem, a single image is available for each category. An approach to solving this problem consists of training the model with some classes of the dataset and to validate it with a different group of classes. The test is finally carried out with a third group of classes. Figure 2 shows the category split that has been made. There are 50 classes for training, 18 for validation and 13 for test (81 totals). Three approaches based on Siamese nets have been evaluated: a traditional Siamese net with a CNN, a Siamese net using a LOMO descriptor [2] and a Siamese net integrating a CNN and a LOMO descriptor. In the first approach to solving the problem, a Siamese net with a ResNeXt-101-32x8d [4] has been used. A Siamese net compares the feature layer of two CNNs to infer whether two images belong to the same class or not. Each of the two input images of the network is channeled through one of the convolutional sisters, which share models and weights. Figure 3 shows the scheme of this architecture. Each of the sister subnets shares the same ResNeXt-101 model with the same parameters. The model receives two images as input. The convolutional part of the ResNeXt-101 produces a feature vector in the last layer (\(u_{1},u_{2},\dots,u_{64}\)). In a classification problem, this vector is connected to the Full-Connected (FC) layer with a \(Softmax\) activation. However, in this case, this vector is  
Figure 1: Cascade classifier based on ResNeXt-101-32x8d. transformed into a single dimension (_Flatten_) and compared by Euclidean distance with the vector produced for another image \((v_{1},v_{2},\dots,v_{64})\). In Figure 3, \(d_{E}(u,v)\) represents the Euclidean distance. The distance is then connected to another layer with a single neuron and sigmoidal activation, responsible for inferring whether the two images belong to the same category \"1\" or whether they belong to a different category \"0\". In the second approach, a descriptor integrated within the Siamese net has been used (see Figure 4). In this case, the descriptor has no trainable parameters, but the rest of the model does. The LOMO descriptor was initially defined by [PERSON] et al. [2] for the ReID problem (Re-identification of people). This descriptor first processes the images  
Figure 3: First approach: Siamese net with ResNeXt-101-32x8d. Figure 2: Category split to test the OSL problem. with Retinex [35], with the aim of adjusting both the color constancy and dynamic range compression automatically, achieving a good approximation to human visual perception. From the images obtained with Retinex images, LOMO uses the HSV color histogram to extract color features. In addition, the Scale Invariant Local Ternary Pattern (SILTP) descriptor [36] is used for the description of the lighting invariant texture. SILTP is an improved operator of the well-known Local Binary Pattern (LBP) [37]. While LBP is invariant relative to certain transformations, it is not robust relative to noise. SILTP improves LBP by introducing a scale-invariant local comparison tolerance, achieving invariance relative to intensity scale changes and robustness relative to image noise. LOMO works with 10 \(\times\) 10 sliding windows, with an overlap of five pixels, to process local blocks in 128 \(\times\) 48 images. Within each window, two SILTP histogram scales (\(SILTP_{4,3}^{0.3}\) and \(SILTP_{4,5}^{0.3}\)) and a joint HSV histogram of 8 \(\times\) 8 \(\times\) 8 cells are extracted. \(SILTP_{N,R}^{\tau}(x_{c},y_{c})\) is equal to the concatenation of \(N\) binary strings, obtained for \(N\) neighborhood pixels equally spaced on a circle of radius \(R\) with respect to the pixel \((x_{c},y_{c})\). The binary strings are calculated by using the \(\tau\) scale factor. From \(k=0\) to \(k=N-1\), the binary string is \"01\" when \(I_{k}>I_{c}\cdot(1+\tau)\), \"10\" when \(I_{k}<I_{c}\cdot(1-\tau)\) and \"00\" otherwise.