## 2 Materials and Methods  
The imaging studies used in this work were performed in the tomography laboratory at the Independent Public Clinical Hospital No. 4 in Lublin. The research results used were collected retrospectively from the database of the hospital. They were conducted on a 32-slice GE tomography scanner using a standard spine protocol, covering the lumbar and sacral vertebrae. The examination was carried out in spiral acquisition and assessed using multiplanar and three-dimensional reconstructions. The exposure parameters during the examination included an X-ray tube current ranging from 180 mA to 300 mA and a tube voltage of 120 kV or 140 kV. The reconstruction layer thicknesses for soft tissue and bone were 2.5 mm and 1.25 mm, respectively. The CT images were obtained from 100 patients, with fifty in the control group (without diagnoses of osteoporosis or osteopenia) and an equal number in the group diagnosed with osteoporosis. The control group consisted of 26 women and 24 men aged from 53 to 77 years without symptoms of osteoporosis or osteopenia. The patient group included 33 women and 17 men aged from 44 to 95 years with diagnosed osteoporosis. The qualification of patients to both groups was based on the diagnosis of qualified radiologists and additionally on the measurement of radiological density of the spongy tissue of the first lumbar verteb (L1). According to the literature [1], the threshold value of density was set at 120 Hounsfield units (HU). Patients with densities above this threshold, in whom the radiologist did not suggest changes in the structure of spongy tissue, were classified into the control group (as healthy). The analyses used images from soft tissue reconstruction, even though bone reconstruction is usually used to assess the condition of bone tissue. This decision was justified by the author's previous studies, which showed that, in texture analysis, images from soft tissue reconstruction achieve higher classification accuracy (ACC = 95%) compared to bone reconstruction (ACC = 92%) [31]. Moreover, due to the atypical nature of the examined tissue, characterized by lower mineral density than compact bone, images from soft tissue reconstruction better reflect the range of values associated with texture features. Sample cross-sections from the series of images were selected, showing the interior of the verteb along with the cancellous bone. From each patient's series of scans, four cross sectional images of the L1 vertebra were selected. These images represented cross-sections closest to the midpoint of the vertebra's height to ensure that the largest possible area of cancellous bone was visible (Figure 1). From each selected cross-sectional image, a single sample of the examined tissue image was obtained. The size of the selected samples was chosen to maximize the use of the texture area containing potential information from the cross-sectional image of the vertebra. As a result, four hundred samples, each measuring 50 \(\times\) 50 pixels, were obtained. Example images of tissue from healthy patients and patients with osteoporosis are shown below (Figure 2). One of the commonly used actions during image preparation for further classification is the histogram normalization process. In previous studies conducted by the author, it was shown that this operation leads to a decrease in classification accuracy, ranging from 4% for the TPR coefficient to 14% for ACC [32]. The first stage of this study involved performing a texture analysis of the images using the MaZda program (version 4.6) [33]. This program enables the analysis of grayscale images and the determination of numerical values for various image features.