Filter membrane and3MTest strips are increasingly being used for microbial detection in fields such as biology, medicine, food, and environment. Many filter membranes or test strips have a characteristic of having grid lines of different colors and sizes on their surface. These grids are helpful for manual observation and counting, but they pose difficulties for the increasing use of automated colony counters. Because the color of the grid is often very dark, traditional methods often detect grids instead of colonies. the figure below1、2、3Three commonly used filter membranes are displayed separately3MTest pieces and segmentation results using traditional image segmentation methods.

Among them, the figure1-aThis is the original image of the Sedolis filter membrane, with black grids on the surface and light yellow bacterial colonies growing. image1-bThe segmentation effect is achieved using traditional threshold segmentation method. image1-cThe segmentation effect is achieved using the color gradient method. Due to the fact that the grid color of the filter membrane is darker than that of the colonies, traditional image processing methods segment the grid instead of the colonies.

image1. Sedolis filter membrane

image2-ayes3MStaphylococcus aureus test strip, with yellow grids and purple colonies on the surface. image1-bThe segmentation effect is achieved using traditional threshold segmentation method. image1-cThe segmentation effect is achieved using the color gradient method. These two segmentation methods not only segment the colonies, but also divide the grid, making it impossible to count the colonies.

image2. 3MStaphylococcus aureus test strip

image3-ayes3MThe E. coli test strip has a red grid, red colonies, and a red background on the surface. This situation is the most complex, regardless of using traditional threshold segmentation methods (Figure)3-b）Or is it the color gradient segmentation method (Figure)3-c）It is impossible to achieve ideal results.

image3. 3MEscherichia coli test strip

It has been proven that traditional image processing techniques are no longer able to solve the above-mentioned filter membranes or3MThe colony detection of test strips requires the development of new detection methods.Quick numbers_technology teamAfter two years of research and development, based on the current level set activity contour model, combined with filter membrane and3MThe characteristics of the test piece form a suitable filter membrane or3MThe new segmentation algorithm for the test piece has successfully solved the above problems.

1Level set active contour model based on morphological constraints

The principle of image segmentation based on the level set active contour model is to continuously approach the segmentation target by minimizing the energy functional. If constraints based on prior knowledge are introduced in the energy functional to induce the active contour to approach the target specified by the constraints, the desired target can be segmented. The two main ideas proposed earlier are as follows.

one isCremersThe proposed model based on prior knowledge constraints. The shape determined by prior knowledge is represented by a level setF₀The active contour model based on shape prior knowledge adds a shape constrained energy term to the energy functional to guide the curve to converge to this shape:

In the equation,LDefined the scope within which prior knowledge of shape takes effect,L=-1The area is excluded from the integral. This method strictly specifies the position and size of shape information, which is limited in practical applications.

Another one isTony ChanThe proposed active contour model based on shape prior knowledge allows for shape translation, scaling, and rotation. If the level setF₂It is based on the level setF₁After translation, rotation, and scaling, let the translation coordinates bea,bThe scaling factor isrThe rotation angle isθThe relationship expression between the two level sets is:

If ψ0It is a level set function of a fixed shape, which is obtained by solving the sign distance function. ψ is the level set function corresponding to the original shape after translation, rotation, or scaling. So the energy function of the level set model based on shape prior knowledge is:

The numerical solution of the above two methods involves gradient descent flow solution of multiple variables in the energy function, and multiple variables need to be updated for each curve iteration. Therefore, the approximation speed of the active contour model is very slow and cannot be practically adopted.
For grid filter membranes or3MFor test pieces, the colonies that need to be detected are usually circular, so the prior knowledge of the shape of the horizontal set can be set as circular. For a circle, the translation and scaling in its geometric transformation will only cause shape changes, while rotation will not affect the shape of the circle. Therefore, the level set model based on a circle only requires three additional variables（a,b,r）The energy functional of the level set active contour model based on circular constraints can be simplified as:

In the formula, the second term is the constraint term, which acts to promote the convergence of the final contour line into a circle. In this model, in addition to calculating the gradient descent flow of the level set function, only（a,b,r）Three variables are updated, greatly reducing the number of iterations and improving segmentation speed.

To achieve synchronous detection of multiple colonies on a petri dish, it is necessary to further introduce a multi-phase level set active contour model; At the same time, in order to further improve the detection speed, a fast solution method using the level set active contour model is needed. In both aspects, the research team of Xunshu Technology has achieved important results and practical applications, which can be referred to in the "Colony Counting" published by Xunshu Technology Co., Ltd_innovative technology（one）Level Set Activity Contour Model.

2Detection effect on surface wrinkles and blurry edges of bacterial colonies

The level set active contour model based on morphological constraints retains the features of the level set active contour modelIt has the advantages of strong noise resistance, smooth and continuous segmentation boundaries, and can handle complex surface structures, while also being able to approach circular targets very well. Especially for colonies or cells with blurred contours and severe surface wrinkles, it exhibits extremely effective segmentation.

image4Displayed the detection effect on a protoplast cell with blurred edges. Among them, the figure4-aIt is the original image of protoplast cells; image4-bThe general level set active contour model is used, and due to the lack of circular constraints, a non circle is detected; image4-cThe algorithm used is the "Shape Constrained Level Set Active Contour Model" developed by Xunshu Technology. Due to the circular constraint, the final approximation is inevitably a circle, which effectively restores the original state of the cell.

image4. edge blurThe detection effect of protoplast cells

image5Displayed the detection effect on a protoplast cell with severe surface wrinkles. Among them, the figure4-aIt is the original image of protoplast cells; image4-bThe general level set active contour model is used, which detects a pile of fragments due to the lack of circular constraints; image4-cThe algorithm used is the "Shape Constrained Level Set Active Contour Model" developed by Xunshu Technology. Due to the circular constraint, the final approximation is a complete protoplast cell.

image5. Surface wrinklesThe detection effect of protoplast cells

3Regarding the filter membrane and3MThe detection effect of the test piece

image6Showcased the "Shape Constrained Level Set Active Contour Model" developed using Xunshu Technology, which applies to grid filter membranes and3MThe detection effect of the test piece. Among them, the figure6-aThe6-bThe6-cThey are Sedolis filter membrane3MStaphylococcus aureus test strip3MOriginal image of Escherichia coli test strip. image6-dThe6-eThe6-fIt is the segmentation effect after adopting the "level set active contour model based on morphological constraints". Due to its circular constraint, the active contour avoids approaching the grid and ultimately detects all circular colonies.

image6. Effect of Level Set Active Contour Model Based on Morphological Constraints

4Outlook

Image segmentation method based on level set active contour model,It has the advantages of strong noise resistance, good numerical stability, smooth and continuous segmentation boundaries, and the ability to handle complex topological structures, making it one of the most cutting-edge image segmentation technologies currently available.

After more than two years of research and development, the R&D team of Xunshu Technology has not only mastered this advanced technology, but also creatively researched and developed fast active contour models, multi-phase active contour models, and level set active contour models based on morphological constraints that are suitable for complex colony segmentation and counting, based on the characteristics of microbial colonies. These models not only achieve accurate and effective statistics of complex colonies and high difficulty petri dishes, but also are suitable for the detection of cells and other substances.

Hangzhou Xunshu Technology Co., Ltd R&D Department