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Face Alignment with Landmarks

HardCV

Implement a face alignment system using facial landmarks to normalize face images, enhancing recognition accuracy. This process involves computing a similarity transform to adjust the face image based on detected landmarks such as eyes, nose, and mouth.

The goal is to align the face image so that the eye centers are horizontally aligned, the inter-eye distance is fixed, and the image is cropped to a standard size, which can be achieved through a combination of translation, rotation, and scaling. These transformations can be represented using affine matrices, which describe linear transformations in 2D space.

To achieve this, the following steps are necessary:

  1. Calculate the centers of the eyes from the detected landmarks.
  2. Determine the angle of rotation required to align the eyes horizontally.
  3. Compute the scale factor needed to achieve a fixed inter-eye distance.
  4. Apply the calculated transformations to the face image.
(x′y′)=(cos⁡(θ)−sin⁡(θ)sin⁡(θ)cos⁡(θ))(xy)+(txty)\begin{pmatrix} x' \\ y' \end{pmatrix} = \begin{pmatrix} \cos(\theta) & -\sin(\theta) \\ \sin(\theta) & \cos(\theta) \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix} + \begin{pmatrix} t_x \\ t_y \end{pmatrix}

This technique is widely used in face recognition systems to improve the accuracy of facial feature matching.

Example:

Input:
Face image and landmarks
Output:
Aligned face
Reasoning:

Compute transform from landmarks to canonical positions

Constraints:

  • Input parameters: image (3D numpy array, RGB, shape=(height, width, 3)), landmarks (2D numpy array, shape=(n_landmarks, 2)) where n_landmarks is at least 4 (two eyes, nose, mouth)
  • Valid ranges: pixel values in [0, 255], landmark coordinates within image boundaries
  • Output format: aligned face image as 3D numpy array (RGB, shape=(height, width, 3)), uint8 precision
  • Special conditions: assume at least two eye landmarks are provided, and the inter-eye distance is fixed at 60 pixels after transformation
  • Assumptions: input image is not empty, and landmarks are detected with sufficient accuracy for alignment purposes
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