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Generated: 9/1/2022

GBT is Implementing Machine Learning Driven, Pattern Matching ...

This tutorial provides a summary of the issues faced by the industry before using machine learning to address its challenges of using the camera.

Introduction to Machine Learning for Camera Modeling

In order to build a general camera model, we used a dataset of 13,000 images and obtained 3,000 sets of images for testing. These sets of images are obtained to test the camera model built. The testing set is provided in this case to measure how well the model learned the images that it is supposed to learn.

Problem Statement

Camera models can be defined by formulating an optimization problem that consists of maximizing the log likelihood function.

Equation 1. This objective function can be formulated using log likelihood function as described below. The value of the log likelihood function is maximized to obtain the most suitable values of the parameters. Equation 1. Equation 1 is written as a linear model. This means that the model will learn a mapping from image pixels to the value of the parameters. If the mapping is linear, it is possible to learn this mapping using regression algorithms.

![](../assets/figures/1-1_Figure_1){width="100.00000%"}

In order to implement regression that can learn a non-linear regression model using machine learning with regression, the parameters that appear in Equation 1 need to be reinterpreted.

In case of regression, the parameters are the values of the independent variables and the dependent variables are the pixel values of an image obtained from a camera device in a single frame.

![](../assets/figures/1-1_Figure_1)(a)

The Independent variables are defined as parameters that are independent of each other. In the case of linear regression, there is a single independent variable. In case of non-linear regression, the number of independent variables used for modeling an image is more than 1. In linear regression, the independent variables are usually called the variables in a linear combination that can be denoted as shown in the figure.

![](../assets/figures/1-1_Figure_1)(b)

In non-linear regression, the independent variables can be represented by a set of variables in different parameters that are independent, but in a linear combination.

In this case Equation 2 is written for a single non-linear regression.

![](../assets/figures/1-1_Figure_1)(b)

This equation shows that if the parameters are multiplied by a single non-linear function, then a non-linear regression model can be formulated similar to a linear regression model. However, many non-linear functions can be used to construct the model. Each of those functions can be denoted as a different independent variable.

![](../assets/figures/1-1_Figure_1)(b)

However, we observed that in the application of this approach, it is not always necessary to include all the independent variables. In particular, we observed that it is not necessary to add the pixel values of the image as extra parameters that can be considered as the independent variables in the model. In our problem, there were about 600 image parameters required in addition to the independent variable. When all those model parameters are added to the image pixels as independent variables, the model loses its interpretability. To avoid this from happening, we used a model which did not include the image pixels as independent variables but as parameters and the independent variable was the mean of the image pixels.

![](../assets/figures/1-1_Figure_1)(b)

However, if, for example, there are N-images in the dataset that are used for training, there would be a different independent variable that are shared among all the images in that dataset. We observed this to be the case. However, we chose to use the mean of all the pixels in the images as the independent image variables to define the model.

Equation 2. This equation represents linear regression and is used to formulate a model without the pixel values of an image as the independent variables.

![](../assets/figures/1-1_Figure_1)(b)

In case of a single non-linear regression or non-linear regression equation, Equation 3 is the representation of a single non-linear regression model. This equation shows that if the parameters are multiplied by a non-linear function, then a non-linear non-linear regression model can be formulated similar to the linear case. In addition to the parameters of Equation 2, the parameters in Figure 1(c) need to be modeled. The independent variables are again the mean of all the pixels in the images. However, the dependent variables for non-linear regression need to be reinterpreted. This is because we are now modeling how the mean of all the pixels as the dependent variable.

![](../assets/figures/1-1_Figure_1)(b)

This equation shows that if the independent variables are multiplied by a non-linear function, then a non-linear non-linear regression model can be formulated similar to the linear regression model. However, many non-linear functions can be used to construct the model. Each of those functions can be denoted as a different independent variable.

Equation 3. This equation represents non-linear regression. The mean of the pixel values over all the training images is the dependent factor and all the variables of the image or set of images as independent factors including the pixel values. The parameter N in the equation is the number of training images used for training. In our use case, there were 13,000 images for training.

Learning Parameters of Camera Parameter Estimation

In this section, we explain the framework for the use of learning-based camera models to address the lack of robust camera parameters in the general image sensing and camera modeling industry.

The learning strategy for developing a non-linear non-linear model uses a data set having images with known camera parameters that represents an input of the learning algorithm. The objective is to predict the unknown parameters that are used to define new camera specifications. In this case the value of the unknown parameter is a single parameter that controls the non-linear mapping, in a set of three parameters. These were obtained from experiments that were carried out on the test set data. This is because the value of the mean of all the pixels in an image provides a sufficient measure of its robustness.

The problem domain for our use case is the following. The general camera parameter space is expressed as the linear model:

![](../assets/figures/1-1_Figure_1)(a)

In this domain, the unknown parameters of a camera model are modeled as a non-linear function of their values.

![](../assets/figures/1-1_Figure_1)(b)

After an initial investigation of literature search and expert opinion, we identified the following seven parameters that are used to describe the non-linear relationship that forms the mapping function for the camera. The number of parameters that are in the mapping function represent the number of independent variables over which the function is defined.

1. Gamma

2. Contrast

3. White Balance

4. Hue

5. Saturation

6. Brightness

7. JPEG Quality

To obtain the values of these parameters on a dataset for camera, we used the model of Non-linear non-linear regression defined at the start of this problem statement. The training set data comprises 13,000 images that were collected from various image datasets. The test data that evaluates the general camera model consists of the model parameters obtained from the training set as well as the test set values of image parameters obtained from the camera, using the camera model we just specified the values of camera parameters for the test set images, which are used in obtaining the general camera model using this optimization problem. The model in (b) defined with seven parameters for the non-linear function is used to solve the camera model optimization problem to obtain the new camera parameters. The general camera model obtained with the use of this optimization problem are then applied to the test images. The following equations show how the seven camera parameter are defined using the value of the test images. There are two unknown parameters as the input to the non-linear non-linear function.

![](../assets/figures/1-1_Figure_1)(b)

Concepts for Learning-Based Camera Models

For the non-linear non-linear mapping function, we define it in seven parameters as shown above. The mapping parameters are given as Equation 4. The parameters are the value of the individual factors that are added and multiplied to obtain the value of the final product. In this case the parameter A is used and we use seven values for the values of the parameters B to G because they represent the seven parameters of the camera. After obtaining values of the parameters from the dataset, we trained a model using machine learning techniques.

The model parameters are the values of the input parameters. The output is a value and that is the value of the input parameters that when multiplied give the output parameters.

![](..

This tutorial provides a summary of the issues faced by the industry before using machine learning to address its challenges of using the camera.

Introduction to Machine Learning for Camera Modeling

In order to build a general camera model, we used a dataset of 13,000 images and obtained 3,000 sets of images for testing. These sets of images are obtained to test the camera model built. The testing set is provided in this case to measure how well the model learned the images that it is supposed to learn.

Problem Statement

Camera models can be defined by formulating an optimization problem that consists of maximizing the log likelihood function.

Equation 1. This objective function can be formulated using log likelihood function as described below. The value of the log likelihood function is maximized to obtain the most suitable values of the parameters. Equation 1. Equation 1 is written as a linear model. This means that the model will learn a mapping from image pixels to the value of the parameters. If the mapping is linear, it is possible to learn this mapping using regression algorithms.

![](../assets/figures/1-1_Figure_1){width="100.00000%"}

In order to implement regression that can learn a non-linear regression model using machine learning with regression, the parameters that appear in Equation 1 need to be reinterpreted.

In case of regression, the parameters are the values of the independent variables and the dependent variables are the pixel values of an image obtained from a camera device in a single frame.

![](../assets/figures/1-1_Figure_1)(a)

The Independent variables are defined as parameters that are independent of each other. In the case of linear regression, there is a single independent variable. In case of non-linear regression, the number of independent variables used for modeling an image is more than 1. In linear regression, the independent variables are usually called the variables in a linear combination that can be denoted as shown in the figure.

![](../assets/figures/1-1_Figure_1)(b)

In non-linear regression, the independent variables can be represented by a set of variables in different parameters that are independent, but in a linear combination.

In this case Equation 2 is written for a single non-linear regression.

![](../assets/figures/1-1_Figure_1)(b)

This equation shows that if the parameters are multiplied by a single non-linear function, then a non-linear regression model can be formulated similar to a linear regression model. However, many non-linear functions can be used to construct the model. Each of those functions can be denoted as a different independent variable.

![](../assets/figures/1-1_Figure_1)(b)

However, we observed that in the application of this approach, it is not always necessary to include all the independent variables. In particular, we observed that it is not necessary to add the pixel values of the image as extra parameters that can be considered as the independent variables in the model. In our problem, there were about 600 image parameters required in addition to the independent variable. When all those model parameters are added to the image pixels as independent variables, the model loses its interpretability. To avoid this from happening, we used a model which did not include the image pixels as independent variables but as parameters and the independent variable was the mean of the image pixels.

![](../assets/figures/1-1_Figure_1)(b)

However, if, for example, there are N-images in the dataset that are used for training, there would be a different independent variable that are shared among all the images in that dataset. We observed this to be the case. However, we chose to use the mean of all the pixels in the images as the independent image variables to define the model.

Equation 2. This equation represents linear regression and is used to formulate a model without the pixel values of an image as the independent variables.

![](../assets/figures/1-1_Figure_1)(b)

In case of a single non-linear regression or non-linear regression equation, Equation 3 is the representation of a single non-linear regression model. This equation shows that if the parameters are multiplied by a non-linear function, then a non-linear non-linear regression model can be formulated similar to the linear case. In addition to the parameters of Equation 2, the parameters in Figure 1(c) need to be modeled. The independent variables are again the mean of all the pixels in the images. However, the dependent variables for non-linear regression need to be reinterpreted. This is because we are now modeling how the mean of all the pixels as the dependent variable.

![](../assets/figures/1-1_Figure_1)(b)

This equation shows that if the independent variables are multiplied by a non-linear function, then a non-linear non-linear regression model can be formulated similar to the linear regression model. However, many non-linear functions can be used to construct the model. Each of those functions can be denoted as a different independent variable.

Equation 3. This equation represents non-linear regression. The mean of the pixel values over all the training images is the dependent factor and all the variables of the image or set of images as independent factors including the pixel values. The parameter N in the equation is the number of training images used for training. In our use case, there were 13,000 images for training.

Learning Parameters of Camera Parameter Estimation

In this section, we explain the framework for the use of learning-based camera models to address the lack of robust camera parameters in the general image sensing and camera modeling industry.

The learning strategy for developing a non-linear non-linear model uses a data set having images with known camera parameters that represents an input of the learning algorithm. The objective is to predict the unknown parameters that are used to define new camera specifications. In this case the value of the unknown parameter is a single parameter that controls the non-linear mapping, in a set of three parameters. These were obtained from experiments that were carried out on the test set data. This is because the value of the mean of all the pixels in an image provides a sufficient measure of its robustness.

The problem domain for our use case is the following. The general camera parameter space is expressed as the linear model:

![](../assets/figures/1-1_Figure_1)(a)

In this domain, the unknown parameters of a camera model are modeled as a non-linear function of their values.

![](../assets/figures/1-1_Figure_1)(b)

After an initial investigation of literature search and expert opinion, we identified the following seven parameters that are used to describe the non-linear relationship that forms the mapping function for the camera. The number of parameters that are in the mapping function represent the number of independent variables over which the function is defined.

1. Gamma

2. Contrast

3. White Balance

4. Hue

5. Saturation

6. Brightness

7. JPEG Quality

To obtain the values of these parameters on a dataset for camera, we used the model of Non-linear non-linear regression defined at the start of this problem statement. The training set data comprises 13,000 images that were collected from various image datasets. The test data that evaluates the general camera model consists of the model parameters obtained from the training set as well as the test set values of image parameters obtained from the camera, using the camera model we just specified the values of camera parameters for the test set images, which are used in obtaining the general camera model using this optimization problem. The model in (b) defined with seven parameters for the non-linear function is used to solve the camera model optimization problem to obtain the new camera parameters. The general camera model obtained with the use of this optimization problem are then applied to the test images. The following equations show how the seven camera parameter are defined using the value of the test images. There are two unknown parameters as the input to the non-linear non-linear function.

![](../assets/figures/1-1_Figure_1)(b)

Concepts for Learning-Based Camera Models

For the non-linear non-linear mapping function, we define it in seven parameters as shown above. The mapping parameters are given as Equation 4. The parameters are the value of the individual factors that are added and multiplied to obtain the value of the final product. In this case the parameter A is used and we use seven values for the values of the parameters B to G because they represent the seven parameters of the camera. After obtaining values of the parameters from the dataset, we trained a model using machine learning techniques.

The model parameters are the values of the input parameters. The output is a value and that is the value of the input parameters that when multiplied give the output parameters.

![](..