• quantum computing
• quantum
• edge detection
• computer vision

This Master's Degree thesis analyzes the application of the quantum computing paradigm in Computer Vision, comparing two different image representation techniques and proposing a new Edge Detection algorithm.
The implementation of classical CV algorithms in the quantum paradigm is motivated by the advantageous properties it offers. By exploiting qubits and superposition, an image can be represented with logarithmically fewer resources. Thanks to quantum parallelism, a property of quantum mechanics that offers the possibility of performing multiple calculations at the same time on a state in superposition, many operations computer vision algorithms perform, can be executed simultaneously achieving an exponential speedup.

Two different quantum encoding techniques are analyzed and compared: FRQI and NQER. The first method, given a "nxn" matrix, stores the image in 2logn +1 qubits. To do this this algorithm uses logn qubits to address the rows of the image, and the same quantity to address the columns. The remaining qubit is used to store in its amplitude the intensity value of the corresponding pixel. On the other hand, NEQR, while still using 2logn qubits to index the positions of the original image, uses 8 more extra qubits to store the intensity value in the base.

The proposed algorithm exploits the first method to perform edge detection. The encoding is performed once, but thanks to superposition many copies of the images are generated. The filter used for edge detection is Sobel. Instead of passing it over each pixel of the image, the copies of the image are shifted and then summed thanks to some properties of the superposition. This operation is performed once and thanks to quantum parallelism it is applied to all the states. The edge then is compared with a threshold value and its identification is stored in an extra qubit. The state is then measured and the resulting readout is an image with only the detected edges.