2.8 Evaluation criteria for similarity of image features
HOT SPOT
The calculation of image feature similarity plays a crucial role in the accuracy of subsequent image retrieval. Different similarity measurement functions can yield diverse image retrieval results. In this work, the following similarity measurement function is utilized:(1) Euclidean Distance: Euclidean Distance is a widely used distance metric for comparing two points in three or more dimensions of space [In Eq ((2) Cosine Similarity: Cosine similarity utilizes the cosine value of the angle between two vectors in the vector space to quantify their dissimilarity [In football players’ joint point detection, a CNN is used to convolve the input images and generate confidence maps, also known as hot spot maps, for detecting the joint points. Multi-stage learning is employed, where each stage refines the learning and detection results of the previous stage, aiming to bring the final results closer to the target values. Let After detecting the joint points, it is necessary to connect them to form a complete human body model. However, if the connection is solely based on the confidence of the detection points, errors may occur when multiple points are involved. A local affinity domain method incorporates limb direction information into the predictions to address this issue, generating a two-dimensional (2D) vector code. Typically, the human body model can be represented as a simple connection of multiple joint points. After polynomial fitting of the body joint points in the x-axis and y-axis directions, the coefficients of the polynomial fitting are used as features for data analysis. PCA is then applied to perform data dimension reduction. PCA aims to reduce the dimensionality of the data by utilizing the eigenvectors of the sample covariance matrix. It constructs an orthogonal transformation that minimizes the mean square error (MSE). Through this transformation, the characteristics of the samples are decomposed into orthogonal components, revealing the fundamental components of the data information.In the data training phase, several steps are followed to prepare the data for classification using Support Vector Machines (SVMs). First, the average of the training data samples is calculated, and this average is subtracted from each training data point. Next, the covariance matrix and eigenvalues are computed. The dimension of the matrix is then reduced based on the contribution rate of the calculated eigenvectors. This reduction helps to eliminate redundant or less informative dimensions. Finally, the final training data is obtained by multiplying the difference between each training sample and the average data by the dimensionality reduction matrix. During the data testing phase, a similar process is applied. The average of the training data is subtracted from each testing data point, and the resulting difference is multiplied by the dimensionality reduction matrix.Once the data is prepared, it is fed into SVMs for classification and action recognition. SVMs are capable of handling nonlinear problems by using a kernel function to map the data into a higher-dimensional feature space (Hilbert space) where the problem becomes linearly separable. In this case, the Gaussian kernel function is typically used to transform the feature space, allowing the SVM training model to successfully recognize different actions.