In this article, we will explore the fascinating world of statistical shape models. We will walk you through the necessary steps to create such a model, using a simple example to illustrate the process. If you’re eager to learn more about statistical shape models, you can find additional information in our slides here.
Contents
The Three Relevant Classes
To begin, let’s examine the three relevant classes that we will be importing. First, we have the general Procrustes analysis, which is responsible for scaling and translating the shapes and creating the mean shape. Next, the principal component analysis (PCA) is employed to extract the principal modes of variation. Finally, the active shape model utilizes the mean shape and principal modes of variation to build a statistical shape model.
Understanding the Code
Now, let’s delve into the code. At the beginning, you need to define the parameters. In practice, the number of training samples would be much higher, but for our example, we will use only two shapes. Additionally, we define the number of sampling points for the shape, the dimension spacing, shift to the center of the images, and two parameters to generate two different shapes. With these parameters, we create two grids.
Generating the Mean Shape
The first step in creating the model is to generate the mean shape. To do this, we create a Generalized Procrustes Analysis (GPA) object and add the two shapes. Running the code, we obtain the mean shape as a matrix. We then create a grid from this mean shape matrix.
Principal Component Analysis
Next, we perform the principal component analysis (PCA) to calculate the modes of variation. The PCA object contains not only the mean shape but also the scaled and shifted points, which are required for this analysis. By creating a data matrix from the GPA, we can then create a PCA object using this data matrix as a parameter. Running the PCA, we obtain the eigenvalues, allowing us to determine the number of principal components.
Creating the Statistical Shape Model
Finally, we create the statistical shape model by generating an Active Shape Model (ASM) object with the PCA as a parameter. This model includes the mean shape and the principal components as modes of variation. By assigning weights to these components, we can generate new shapes that lie in the directions of the principal components.
Experimenting with Weights
To observe the impact of different weights on the shape generation, we can play around with the weights ourselves. Starting with the weights 1 and 0, a new shape is created and converted to a grid. Similarly, we can try different weight combinations, such as 0 and 2 and 0 and 0, which should generate the mean shape. By running the code, we can visualize these different shapes.
FAQs
Q: What are statistical shape models?
A: Statistical shape models are mathematical representations that capture the variations and patterns in a set of shapes. They are widely used in fields such as computer vision, medical imaging, and computer graphics.
Q: How are statistical shape models created?
A: Statistical shape models are created by performing various steps, including scaling and translating the shapes, extracting the principal modes of variation, and building a model using the mean shape and principal components.
Q: What are the applications of statistical shape models?
A: Statistical shape models have diverse applications, ranging from medical image analysis, object recognition, and animation to anthropometry and industrial design.
Conclusion
In this article, we have explored the concept of statistical shape models and walked through the process of creating one using a simple example. Statistical shape models have immense potential in various domains, enabling us to analyze and generate shapes with precision. By experimenting with different weights, you can further explore the versatility of these models. Embrace the power of statistical shape models and unlock a new dimension of possibilities!
Techal
