## Revolutionize Your Image Analysis with HSA Kit

**Detect Regions and Objects in Any Image, Big or Small**

HSA Kit can detect various regions and objects in different kinds of images of various sizes, including huge whole slide images. This process, known as project analysis, results in a comprehensive table with customizable data for the detected regions.

## Unmatched Flexibility and Efficiency

**Scalable Project Management**

**Unlimited Projects and Files**: Prepare as many projects with as many files as you need.**Automated Analysis**: Run analyses autonomously, producing millions of result polygons.

**Comprehensive Data Reduction**

**Custom Result Tables**: Automatically reduce complex analysis data into a detailed result table for each project.**Modular Customization**: Our modules provide tailored results. If a desired module doesn’t exist, we can create it for you.

## Result Table Customization

HSA Kit allows you to create custom result tables with a variety of columns to suit your analysis needs. Here are a few examples:

**Count**: The number of polygons in a structure.**Area**: The total area of all polygons within a structure.**StdDev**: The standard deviation of the polygon areas within a structure.

## Results Details

### Area results

**Total Area**

The sum of all polygon areas.

$$\text{Total Area} = \sum_{i=1}^{n} \text{Area}_i$$

**Percentage Area of Base ROI**

The percentage of the total area of polygons relative to the base ROI.

$$\text{Percentage Area} = \left( \frac{\text{Total Area}}{\text{Base ROI Area}} \right) \times 100 \%$$

**Minimum Area**

The smallest polygon area.

$$\text{Minimum Area} = \min(\text{Area}_1, \text{Area}_2, \ldots, \text{Area}_n)$$

**Maximum Area**

The largest polygon area.

$$\text{Maximum Area} = \max(\text{Area}_1, \text{Area}_2, \ldots, \text{Area}_n)$$

**Average Area**

The mean area of all polygons.

$$\text{Average Area} = \frac{\sum_{i=1}^{n} \text{Area}_i}{n}$$$ββ$

**Median Area**

The median area of all polygons.

$$\text{Median} =

\begin{cases}

\text{Area}_{\left(\frac{n+1}{2}\right)} & \text{if } n \text{ is odd} \\

\frac{\text{Area}_{\left(\frac{n}{2}\right)} + \text{Area}_{\left(\frac{n}{2} + 1\right)}}{2} & \text{if } n \text{ is even}

\end{cases}$$ββ

**Mode Area**

The most frequently occurring area value.

$$\text{Mode Area} = \text{The value that appears most frequently in the dataset}$$

**Standard Deviation (StdDev) Area**

The measure of dispersion of polygon areas.

$$\text{StdDev} = \sqrt{\frac{1}{n} \sum_{i=1}^{n} (\text{Area}_i – \text{Average Area})^2}$$$β$

**Variance of Area**

The square of the standard deviation.

$$\text{Variance} = \frac{1}{n} \sum_{i=1}^{n} (\text{Area}_i – \text{Average Area})^2$$

**Mean Absolute Deviation of Area**

The average of the absolute deviations from the mean.

$$\text{MAD} = \frac{1}{n} \sum_{i=1}^{n} |\text{Area}_i – \text{Average Area}|$$

**Skewness**

The measure of the asymmetry of the distribution of area values.

$$$\text{Skewness} = \frac{\sum_{i=1}^{n} (\text{Area}_i – \text{Average Area})^3}{n \cdot \text{StdDev}^3}$$$

**Kurtosis**

The measure of the “tailedness” of the distribution of area values.

$$$\text{Kurtosis} = \frac{\sum_{i=1}^{n} (\text{Area}_i – \text{Average Area})^4}{n \cdot \text{StdDev}^4}$$$

**Object Size Quartiles (1st, 2nd, 3rd)**

The quartile values of polygon areas.

$$$\text{Q1} = \text{Area}_{\left(\frac{n+1}{4}\right)}$$$$$$\text{Q3} = \text{Area}_{\left(\frac{2(n+1)}{4}\right)}$$$$$$\text{Q3} = \text{Area}_{\left(\frac{3(n+1)}{4}\right)}$$$$β$

**Interquartile Range (1st – 3rd)**

The range between the first and third quartile.

$$\text{IQR} = \text{Q3} – \text{Q1}$$

**Decile Sizes (1st to 9th)**

Values that divide the dataset into ten equal parts.

$$\text{D1} = \text{Area}_{\left(\frac{n+1}{10}\right)}$$

$$\text{D2} = \text{Area}_{\left(\frac{2(n+1)}{10}\right)}$$

$$\text{D3} = \text{Area}_{\left(\frac{3(n+1)}{10}\right)}$$

$$\text{D4} = \text{Area}_{\left(\frac{4(n+1)}{10}\right)}$$

$$\text{D5} = \text{Area}_{\left(\frac{5(n+1)}{10}\right)}$$

$$\text{D6} = \text{Area}_{\left(\frac{6(n+1)}{10}\right)}$$

$$\text{D7} = \text{Area}_{\left(\frac{7(n+1)}{10}\right)}$$

$$\text{D8} = \text{Area}_{\left(\frac{8(n+1)}{10}\right)}$$

$$\text{D9} = \text{Area}_{\left(\frac{9(n+1)}{10}\right)}$$

**Confidence Intervals of Area**

The range within which the true mean of the population lies with a certain confidence level.

$$\text{CI} = \text{Average Area} \pm (z \times \frac{\text{StdDev}}{\sqrt{n}})$$

**Shape Factor**

A measure of the compactness of the shape.

$$$\text{Shape Factor} = \frac{4\pi \times \text{Area}}{\text{Perimeter}^2}$$β$

**Area to Perimeter Ratio**

The ratio of area to perimeter.

$$$\text{Ratio} = \frac{\text{Area}}{\text{Perimeter}}$$β$

**Eccentricity**

The ratio of the distance between the foci of the ellipse and its major axis length.

$$\text{Eccentricity} = \sqrt{1 – \frac{b^2}{a^2}}$$

### Other results

**Object count**

The number of polygons

**Object density**

The number of polygons per unit area.

$$\text{Object Density} = \frac{\text{Number of Polygons}}{\text{Total Area}}$$

**Disperion index**

A measure of how polygons are dispersed over the area.

$$\text{Dispersion Index} = \frac{\text{Variance of Polygons per Unit Area}}{\text{Mean Polygons per Unit Area}}$$

**Clustering analysis**

A measure of how polygons are clustered together.

$$\text{Clustering Index} = \frac{\text{Variance of Polygons in Sub-regions}}{\text{Mean Polygons in Sub-regions}}$$

**Maximum perimeter**

The largest perimeter of the polygons.

$$\text{Maximum Perimeter} = \max(\text{Perimeter}_1, \text{Perimeter}_2, \ldots, \text{Perimeter}_n)$$

**Average perimeter**

The mean perimeter of all polygons.

$$\text{Average Perimeter} = \frac{\sum_{i=1}^{n} \text{Perimeter}_i}{n}$$

**Median perimeter**

The median perimeter of all polygons.

$$\text{Median Perimeter} =

\begin{cases}

\text{Perimeter}_{\left(\frac{n+1}{2}\right)} & \text{if } n \text{ is odd} \\

\frac{\text{Perimeter}_{\left(\frac{n}{2}\right)} + \text{Perimeter}_{\left(\frac{n}{2} + 1\right)}}{2} & \text{if } n \text{ is even}

\end{cases}$$**stdev perimeter**

The measure of dispersion of the perimeters of the polygons.

$$\text{StdDev Perimeter} = \sqrt{\frac{1}{n} \sum_{i=1}^{n} (\text{Perimeter}_i – \text{Average Perimeter})^2}$$

**Variance of perimeter**

The square of the standard deviation of the perimeters.

$$\text{Variance of Perimeter} = \frac{1}{n} \sum_{i=1}^{n} (\text{Perimeter}_i – \text{Average Perimeter})^2$$

## Custom Solutions for Your Unique Needs

Whether you need to analyze small images or large whole slide images, HSA Kit provides robust tools and customizable modules to meet your specific requirements. If our existing modules donβt meet your needs, we can create new ones tailored for you.