Question

Motion-based user interaction Write a program to compute a low-resolution motion field in order to interactively control a simple application (Cutler and Turk 1998). For example: 1\. Downsample each image using a pyramid and compute the optical flow (spline-based or pixel-based) from the previous frame. 2\. Segment each training video sequence into different "actions" (e.g., hand moving inwards, moving up, no motion) and "learn" the velocity fields associated with each one. (You can simply find the mean and variance for each motion field or use something more sophisticated, such as a support vector machine (SVM).) 3\. Write a recognizer that finds successive actions of approximately the right duration and hook it up to an interactive application (e.g., a sound generator or a computer game). 4\. Ask your friends to test it out.

Short answer

This problem is solved by first downscaling images and calculating optical flow. Then video is segmented into specific actions with corresponding velocity fields learned. Next a recognizer is created that can detect these actions and interact with an application. The solution is then tested.

Step-by-step solution

Image Downsampling and Optical Flow Calculation

To achieve this, use an image pyramid scheme where images are progressively reduced in size. Downsample each image and compute the optical flow from the previous frame. Optical flow is the pattern of apparent motion of image objects between two consecutive frames caused by the movemement of object or camera. It is computed based on pixel intensity patterns.

Segment Video Sequence and Learn Velocity Fields

Segment each training video sequence into different actions i.e., hand moving inwards, moving up, no motion and 'learn' the velocity fields for each one. This essentially means understanding what sort of motion field corresponds to each action. This could be done by finding the mean and variance for each motion field or could use a more complex method such as a support vector machine (SVM).

Write a Recognizer

A recognizer needs to be written to detect the successive actions of the right duration and then connect it to an interactive application such as a sound generator or a computer game. This recognizer will use the data prepared in the previous step to understand what action is being taken.

Testing

After you’ve completed your recognizer, have it tested. Ask friends to interact with the application through motions and observe if the recognizer is correctly identifying the actions and if the application reacts correctly.

Key concepts

Optical Flow

Optical flow is a key concept in computer vision, particularly when analyzing motion. It refers to the pattern of apparent motion observed in objects and surfaces within a series of images. By observing how pixels change position across successive frames, we are able to infer movement.
This motion is either due to the movement of objects or camera motion itself.
To compute optical flow, pixel intensity values are compared across frames. The goal is to map every pixel in one frame with its corresponding pixel in the next frame. Two common methods are used for computing optical flow:

• Spline-based methods, which fit continuous curves to pixel displacement, making them effective for smooth and clear motion detection.
• Pixel-based methods, which calculate motion at an individual pixel level, providing higher resolution motion data but at increased computational cost.

Overall, optical flow helps in accurately tracking and predicting object paths in video sequences, essential for applications like animation, robotics, and user interface design.

Image Downsampling

Image downsampling is the process of reducing the size or resolution of an image. This is accomplished through image pyramid schemes, where images are progressively scaled down.
The main objective of downsampling is to ease computational load and enhance processing speed, especially when dealing with large volumes of data.
During downsampling:

• The original image is scaled down by a factor, often halving the width and height.
• Critical data points are preserved to ensure representation remains accurate after size decrease.

In motion-related tasks, downsampling allows for quicker analysis while maintaining essential features for accurate optical flow calculation. By working with smaller images, algorithms can run faster, making real-time applications feasible. Additionally, smaller data sizes facilitate smoother motion tracking and improved interactive experience in applications.

Motion Field Segmentation

Motion field segmentation is the process of dividing a video sequence into distinct parts based on movement patterns. In the context of computer vision, it helps in isolating specific actions or behaviors within video frames.
By segmenting a motion field, different actions, such as a hand moving inwards or upwards, can be distinctly categorized.
This segmentation involves:

• Analyzing pixel movements to identify common velocity patterns.
• Clustering these patterns to form coherent segments which represent specific motions.

Once the segments are defined, they can be used to "learn" action-specific motion fields. This learning phase involves calculating the average movement (mean) and how much it varies (variance).
Such detailed data aids in building more nuanced recognizers which accurately correlate motion fields with specific actions inside interactive systems.

Support Vector Machine (SVM)

A Support Vector Machine (SVM) is a supervised machine learning algorithm commonly applied in classification tasks within computer vision, including interpreting motion data. Using SVMs in motion field analysis involves:

• Transforming motion data into a feature space where significant patterns are distinguishable.
• Creating a hyperplane, an ideal boundary that separates different categories of motion.
• Optimizing this boundary to maximize distance between different classifications, ensuring accuracy and reliability in predictions.

SVMs are particularly powerful in scenarios where there's a need to distinguish between subtle differences in motion. Their ability to handle high-dimensional data makes them versatile in configuring complex patterns within a motion field. Thus, SVMs are extensively used in applications like gesture recognition, where precise identification of different movements is crucial for interactive control systems.