title: Ð¡Ð¾Ð²ÐµÑÑÐµÐ½ÑÑÐ²Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð¼ÐµÑÐ¾Ð´Ð° ÑÐµÐ³Ð¼ÐµÐ½ÑÐ°ÑÐ¸Ð¸ Ð¸Ð·Ð¾Ð±ÑÐ°Ð¶ÐµÐ½Ð¸Ð¹ Ð±Ð¸Ð¾Ð»Ð¾Ð³Ð¸ÑÐµÑÐºÐ¸Ñ Ð¾Ð±ÑÐµÐºÑÐ¾Ð² Ñ ÑÐµÐ»ÑÑ Ð¾Ð¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ñ ÑÑÑÑÐºÑÑÑÑ ÐºÐ»ÐµÑÐ¾Ðº Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ Ð³ÑÐ°Ð´Ð¸ÐµÐ½ÑÐ½Ð¾-Ð²Ð·Ð²ÐµÑÐµÐ½Ð½Ð¾Ð³Ð¾ ÑÐ°ÑÑÑÐ¾ÑÐ½Ð¸Ñ
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: Improvement of image segmentation method for biological objects with the aim of determining cell structure using grey-weighted distance transform
Creators: name: ÐÐ¾Ð»ÑÑÐ°ÐºÐ¾Ð²Ð°, ÐÐ½Ð½Ð°
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2023
Subjects: Ð¼ÐµÐ´Ð¸ÑÐ¸Ð½ÑÐºÐ¸Ðµ Ð¸Ð·Ð¾Ð±ÑÐ°Ð¶ÐµÐ½Ð¸Ñ
ÑÐµÐ³Ð¼ÐµÐ½ÑÐ°ÑÐ¸Ñ Ð¸Ð·Ð¾Ð±ÑÐ°Ð¶ÐµÐ½Ð¸Ð¹
Ð°Ð²ÑÐ¾Ð¼Ð°ÑÐ¸ÑÐµÑÐºÐ°Ñ ÑÐµÐ³Ð¼ÐµÐ½ÑÐ°ÑÐ¸Ñ
ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ðµ ÑÐ¹ÐºÐ¾Ð½Ð°Ð»Ð°
GWDT
medical imaging
image segmentation
automatic segmentation
eikonal equation

description: ÐÐ°Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° Ð¸Ð·ÑÑÐµÐ½Ð¸Ñ Ð¼ÐµÑÐ¾Ð´Ð¾Ð² Ð²ÑÑÐ¸ÑÐ»ÐµÐ½Ð¸Ñ ÑÐµÑÐ¾-Ð²Ð·Ð²ÐµÑÐµÐ½Ð½Ð¾Ð¹ ÐºÐ°ÑÑÑ ÑÐ°ÑÑÑÐ¾ÑÐ½Ð¸Ñ (Ð°Ð½Ð³Ð». Grey-weighted distance transform, GWDT), Ð° ÑÐ°ÐºÐ¶Ðµ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ ÐµÐ³Ð¾ Ð¿Ð¾ÑÐ»ÐµÐ´ÑÑÑÐµÐ³Ð¾ Ð¿ÑÐ¸Ð¼ÐµÐ½ÐµÐ½Ð¸Ñ Ð² ÑÑÐµÐ¼Ðµ ÑÐµÐ³Ð¼ÐµÐ½ÑÐ°ÑÐ¸Ð¸ Ð¾Ð±ÑÐµÐºÑÐ¾Ð² Ð½Ð° Ð¼ÐµÐ´Ð¸ÑÐ¸Ð½ÑÐºÐ¸Ñ Ð¸Ð·Ð¾Ð±ÑÐ°Ð¶ÐµÐ½Ð¸ÑÑ. ÐÐ°Ð´Ð°ÑÐ¸, ÐºÐ¾ÑÐ¾ÑÑÐµ ÑÐµÑÐ°Ð»Ð¸ÑÑ Ð² ÑÐ¾Ð´Ðµ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ: 1. ÐÑÑÐ»ÐµÐ´Ð¾Ð²Ð°ÑÑ Ð²ÑÑÐ¸ÑÐ»ÐµÐ½Ð¸Ðµ Ð¿ÑÐµÐ¾Ð±ÑÐ°Ð·Ð¾Ð²Ð°Ð½Ð¸Ñ Ð²Ð·Ð²ÐµÑÐµÐ½Ð½Ð¾Ð³Ð¾ ÑÐ°ÑÑÑÐ¾ÑÐ½Ð¸Ñ Ð´Ð»Ñ Ð¸Ð·Ð¾Ð±ÑÐ°Ð¶ÐµÐ½Ð¸Ñ Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ ÑÐµÑÐµÐ½Ð¸Ñ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ ÑÐ¹ÐºÐ¾Ð½Ð°Ð»Ð°, 2. ÐÐºÐ»ÑÑÐ¸ÑÑ Ð¿ÑÐµÐ¾Ð±ÑÐ°Ð·Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð²Ð·Ð²ÐµÑÐµÐ½Ð½Ð¾Ð³Ð¾ ÑÐ°ÑÑÑÐ¾ÑÐ½Ð¸Ñ Ð² ÑÑÐµÐ½Ð°ÑÐ¸Ð¹ ÑÐµÐ³Ð¼ÐµÐ½ÑÐ°ÑÐ¸Ð¸ ÐºÐ»ÐµÑÐ¾Ðº Ð´Ð»Ñ ÑÐ»ÑÑÑÐµÐ½Ð¸Ñ ÑÐ°Ð·Ð´ÐµÐ»ÐµÐ½Ð¸Ñ ÑÐ»Ð¸Ð²ÑÐ¸ÑÑÑ Ð¾Ð±ÑÐµÐºÑÐ¾Ð² 3. ÐÑÐ¸Ð¼ÐµÐ½Ð¸ÑÑ ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐ°Ð½Ð½ÑÐ¹ ÑÑÐµÐ½Ð°ÑÐ¸Ð¹ Ðº ÑÐºÑÐ¿ÐµÑÐ¸Ð¼ÐµÐ½ÑÐ°Ð»ÑÐ½ÑÐ¼ Ð¸Ð·Ð¾Ð±ÑÐ°Ð¶ÐµÐ½Ð¸ÑÐ¼ ÐºÐ»ÐµÑÐ¾Ðº. Ð ÑÐ¾Ð´Ðµ ÑÐ°Ð±Ð¾ÑÑ Ð±ÑÐ» Ð¿ÑÐ¾Ð²ÐµÐ´ÐµÐ½ Ð¾Ð±Ð·Ð¾Ñ ÑÐ¸ÑÐ»ÐµÐ½Ð½ÑÐ¼ Ð¼ÐµÑÐ¾Ð´Ð¾Ð² Ð²ÑÑÐ¸ÑÐ»ÐµÐ½Ð¸Ñ GWDT, Ð²ÑÐ±ÑÐ°Ð½ Ð¾Ð¿ÑÐ¸Ð¼Ð°Ð»ÑÐ½ÑÐ¹ ÑÐ¿Ð¾ÑÐ¾Ð± Ð´Ð»Ñ Ð¿Ð¾ÑÐ»ÐµÐ´ÑÑÑÐµÐ¹ ÑÐµÐ°Ð»Ð¸Ð·Ð°ÑÐ¸Ð¸,ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐ°Ð½Ð° ÑÑÐµÐ¼Ð° ÑÐµÐ³Ð¼ÐµÐ½ÑÐ°ÑÐ¸Ð¸ â Ð¿Ð¾ÑÐ»ÐµÐ´Ð¾Ð²Ð°ÑÐµÐ»ÑÐ½Ð¾ÑÑÑ Ð²ÑÐ¿Ð¾Ð»Ð½ÐµÐ½Ð¸Ñ Ð¼ÐµÑÐ¾Ð´Ð¾Ð² Ð´Ð»Ñ Ð¿Ð¾Ð»ÑÑÐµÐ½Ð¸Ñ ÐºÐ¾Ð½ÑÑÑÐ¾Ð² Ð¾Ð±ÑÐµÐºÑÐ¾Ð² Ð½Ð° Ð¸Ð·Ð¾Ð±ÑÐ°Ð¶ÐµÐ½Ð¸Ð¸. Ð ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐµ ÑÐ°Ð±Ð¾ÑÑ Ð±ÑÐ»Ð° ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐ°Ð½Ð° ÑÑÐµÐ¼Ð° ÑÐµÐ³Ð¼ÐµÐ½ÑÐ°ÑÐ¸Ð¸ Ð½Ð° ÑÐ·ÑÐºÐµ Python, Ð¸ÑÐ¿Ð¾Ð»ÑÐ·ÑÑÑÐ°Ñ Ð´Ð¸ÑÐºÑÐµÑÐ½ÑÐ¹ Ð¼ÐµÑÐ¾Ð´ Ð²ÑÑÐ¸ÑÐ»ÐµÐ½Ð¸Ñ GWDT Ñ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸ÐµÐ¼ chamferâ Ð¼ÐµÑÑÐ¸ÐºÐ¸ Ñ ÑÐ¾ÑÐµÐ´ÑÑÐ²Ð¾Ð¼ (3Ã3). ÐÑÐ» ÑÐ´ÐµÐ»Ð°Ð½ Ð²ÑÐ²Ð¾Ð´, ÑÑÐ¾ Ð¼Ð¾Ð¶Ð½Ð¾ Ð¾Ð¿ÑÐµÐ´ÐµÐ»Ð¸ÑÑ ÐºÐ¾Ð½ÑÑÑÑ Ð¾Ð±ÑÐµÐºÑÐ¾Ð² Ð½Ð° Ð¸Ð·Ð¾Ð±ÑÐ°Ð¶ÐµÐ½Ð¸Ð¸ Ð¿Ð¾ ÐµÐ³Ð¾ GWDT Ñ Ð²ÑÑÐ¾ÐºÐ¾Ð¹ ÑÐ¾ÑÐ½Ð¾ÑÑÑÑ. ÐÑÐµÐ´Ð»Ð¾Ð¶ÐµÐ½Ð½ÑÐ¹ Ð² ÑÐ°Ð±Ð¾ÑÐµ Ð¿Ð¾Ð´ÑÐ¾Ð´ Ð¼Ð¾Ð¶ÐµÑ ÑÐ¾Ð²ÐµÑÑÐµÐ½ÑÑÐ²Ð¾Ð²Ð°ÑÑÑÑ Ð¸ Ð±ÑÑÑ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½ Ð² Ð¿ÑÐ¾Ð²ÐµÐ´ÐµÐ½Ð¸Ð¸ Ð½Ð°ÑÑÐ½ÑÑ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ð¹ Ð´Ð»Ñ Ð¿ÑÐµÐ´ÑÑÐ°Ð²Ð»ÐµÐ½Ð¸Ñ Ð¾ ÑÐ°ÑÐ¿Ð¾Ð»Ð¾Ð¶ÐµÐ½Ð¸Ð¸ Ð¸ ÑÐ¸ÑÐ»Ðµ Ð¾Ð±ÑÐµÐºÑÐ¾Ð² Ð½Ð° Ð¸Ð·Ð¾Ð±ÑÐ°Ð¶ÐµÐ½Ð¸ÑÑ Ð² Ð³ÑÐ°Ð´Ð°ÑÐ¸ÑÑ ÑÐµÑÐ¾Ð³Ð¾.
description: This work is devoted to studying the methods of calculating the grey-weighted distance transform (GWDT), as well as to investigating its subsequent application in the scheme of object segmentation in medical images. The tasks that were solved during the research are: 1. Study the calculation of the weighted distance transform for an image using the eikonal equation solution, 2. Include the weighted distance transform in the cell segmentation scenario to improve the separation of merged objects, 3. Apply the developed scenario to experimental cell images. During the work, a review of numerical methods for calculating GWDT was carried out, and the stages of subsequent automatic segmentation were developed. As a result of the work, a segmentation scheme was developed using a discrete method for calculating GWDT with the use of a 3Ã3 Chamfer metric neighborhood. It was concluded that object contours on an image can be accurately determined based on its GWDT. The approach proposed in the work can be further improved and used in scientific research to represent the location and number of objects on grayscale images.