Fréchet inception distance (FID)

Fréchet Inception Distance (FID) is a metric used to evaluate the quality of images produced by generative models, particularly Generative Adversarial Networks (GANs). Unlike previous metrics such as the Inception Score (IS), FID compares the distribution of generated images to the distribution of real images, providing a more holistic measure of image quality and diversity.

Definition of Fréchet Inception Distance (FID)

Combining Fréchet Distance and Inception Model

The term “Fréchet Inception Distance” combines two key concepts:

1. Fréchet Distance: Introduced by Maurice Fréchet in 1906, this metric quantifies the similarity between two curves. It can be thought of as the minimum “leash length” required to connect a dog and its walker, each walking along separate paths. The Fréchet Distance has applications in various fields such as handwriting recognition, robotics, and geographic information systems.

2. Inception Model: Developed by Google, the Inception-v3 model is a convolutional neural network architecture that transforms raw images into a latent space, where the mathematical properties of images are represented. This model is particularly useful for analyzing features at multiple scales and locations within an image.

How FID is Measured

FID is calculated using the following steps:

1. Preprocess the Images: Resize and normalize the images to ensure compatibility.
2. Extract Feature Representations: Use the Inception-v3 model to convert images into numerical vectors representing different features.
3. Calculate Statistics: Compute the mean and covariance matrix for the features of both real and generated images.
4. Compute the Fréchet Distance: Compare the means and covariance matrices to calculate the distance.
5. Obtain the FID: The final FID score is obtained by comparing the Fréchet Distance between the real and generated images. Lower scores indicate higher similarity.

Purpose of Fréchet Inception Distance (FID)

Assessing Image Quality and Diversity

FID is primarily used to assess the visual quality and diversity of images generated by GANs. It serves multiple purposes:

• Realism: Ensures that generated images look like real images.
• Diversity: Evaluates whether the generated images are sufficiently different from each other and from the training data.

Applications

• Model Evaluation: FID is used to compare different generative models and their variations.
• Quality Control: Helps identify and filter out unrealistic images, such as those with anatomical anomalies in generated human faces.

FID vs. Inception Score (IS)

Historical Context

The Inception Score (IS) was one of the first metrics introduced to evaluate GANs, focusing on individual image quality and diversity. However, it has some limitations, such as sensitivity to image size and lack of alignment with human judgment.

Advantages of FID

Introduced in 2017, FID addresses these limitations by comparing the statistical properties of generated images to those of real images. It has become the standard metric for evaluating GANs due to its ability to capture the similarity between real and generated images more effectively.

Limitations of FID

While FID is a robust and widely used metric, it has its limitations:

• Domain Specificity: FID works well for images but may not be as effective for other types of generative models, such as those generating text or audio.
• Computationally Intensive: Calculating FID can be resource-intensive, requiring significant computational power.