The algorithms that go into your luggage screening at airports

That’s Maths: Baggage scanners use X-ray tomography similar to CT scans

When you check in your baggage for a flight, it must be screened before it is allowed on the plane. Baggage screening detects threats within luggage and personal belongings by X-ray analysis as they pass along a conveyor belt. Hold-baggage and passenger screening systems are capable of detecting contraband materials, narcotics, explosives and weapons.

Millions of bags, boxes and parcels pass through airport security every year. Baggage screening needs to be highly efficient and reliable to avoid delays. Hazard-detection systems have to comply with strict standards, without impacting throughput. Hold-baggage screening devices are capable of inspecting thousands of bags per hour.

The image can be viewed by an operator from any desired angle, and automated image recognition software can detect suspicious or hazardous contents

Increasing security threats have led to higher needs for detection and for increased efficiencies. From next year, airport screening systems for hand baggage must have detection levels similar to medical CT (computed tomography) scans.

CT scanners in hospitals have X-ray machines that scan through 360 degrees, generating images from every angle. In hospital CT scanners, the X-ray apparatus rotates on a heavy gantry. In real-time tomography systems used for baggage scanning, this is too slow, so multiple X-ray sources are switched electronically.

A CT baggage scanner is a large hollow tube with a conveyor belt passing through it, carrying the baggage. The X-ray apparatus scans the baggage from every angle. Software uses this data to create a very detailed tomogram or 3-D image of the bag. The image can be viewed by an operator from any desired angle, and automated image recognition software can detect suspicious or hazardous contents. If dangerous material is identified, the CT scanner alerts the operator for further checking.

The new regulations require all hold-baggage screening to be equipped with European Civil Aviation Conference (ECAC) Standard 3 approved explosives detection systems. Standard 3 requires the use of advanced systems using CT technology.

Mathematical algorithms

X-rays are absorbed to differing degrees by objects of varying optical density. The total attenuation is expressed as a "line integral": the sum of the absorptions along the path of the X-ray beam. Construction of a 3-D image from the absorption pattern is possible thanks to a discovery made in 1917 by an Austrian mathematician, Johann Radon. He developed the operation now known as the Radon transform.

Reconstruction techniques have grown in sophistication, but are still founded on Radon’s work. More accurate algorithms have been developed in recent years, and research in this area is continuing. For detectors spanning a set called the Tam-Danielson window, an exact reconstruction is possible.

A digital image is made up of elements called pixels (picture cells), and if we know the value (colour or intensity) of each pixel, the image can be reconstructed. In a similar way, a three-dimensional volume can be discretised into voxels (volume cells).

Each voxel represents a location on a regular grid in three-dimensional space. The analysis of the data in a real-time tomography system involves the solution of a large system of linear equations for the values of each voxel. The algebraic systems are generally too large for a direct assault, so approximate methods such as the conjugate gradient algorithm are used.

If you find airport security stressful – as most of us do – just reflect on the ingenious combination of engineering technology and mathematical algorithms that is keeping you safe.

Peter Lynch is emeritus professor at UCD School of Mathematics & Statistics. He blogs at