p-norms of histogram of oriented gradients for X-ray images

Lebesgue spaces (Lp over Rn) play a significant role in mathematical analysis. They are widely used in machine learning and artificial intelligence to maximize performance or minimize error. The well-known histogram of oriented gradients (HOG) algorithm applies the 2-norm (Euclidean distance) to detect features in images. In this paper, we apply different p-norm values to identify the impact that changing these norms has on the original algorithm. The aim of this modification is to achieve better performance in classifying X-ray medical images related to of COVID-19 patients. The efficiency of the p-HOG algorithm is compared with the original HOG descriptor using a support vector machine implemented in Python. The results of the comparisons are promising, and the p-HOG algorithm shows greater efficiency in most cases

Notes on *-finite operators class

Let ${ \mathcal H }$ be a separable infinite-dimensional complex Hilbert space and ${ \mathcal B }({ \mathcal H })$ denotes the algebra of all bounded linear operators on ${ \mathcal H }$. An $A \in { \mathcal B }({ \mathcal H })$ is said to be *-finite operator if $0 \in \overline{W}(TA-AT^*)$ for each $T \in { \mathcal B }({ \mathcal H })$. In this paper, we present some properties of *-finite operators and prove that a paranormal operator under certain scalar perturbation is *-finite operator. However, we give an example of paranormal operators which is not *-finite operators