7.3.2 Invariant Feature Recognition
A way to further improve alignment of tilt series is to optimize the detection of
corresponding points in images of the tilt series. For this purpose, new approaches
in object detection or panoramic stitching, based on the concept of Scale Invariant
Feature Transform (SIFT), introduced by Lowe [27], have been proposed for
alignment in electron tomography [28].
Feature-based alignment methods require several steps which are performed by
separate algorithms. Here we will describe these steps which correspond to the
common strategy used for image alignment using SIFT. Additionally to the
emergence of this method many other algorithms appeared, providing alternatives
for the different steps.
• Detection of points of interest
First step is the detection of points of interest. To this purpose the algorithm has
to choose points in the image which will be easy to locate in other images of the
same sample. These points of interest are determined where the algorithm is able to
recognize a feature which is based on mathematical properties, such as local
extrema, and may not match physical features of the sample. This feature detection
step is performed independently on all images of a series and leads to the creation of
unique descriptors for each point of interest.
• Creation of a unique descriptor for each point of interest
With a set of point of interest on each image, alignment requires that they
correspond to the same physical location on the feature to be matched. One way to
achieve that is to rely on distinctive features. Most algorithms attach a single
descriptor to each interest point for that purpose.
• Comparison of interest points between two or more images
The next step is to identify the matches in the sets of points of interest by
comparing their descriptors. Once the point of interest, associated to the same
feature, are grouped together they can be used to deduce the space transformation
which occurred during the tilt-series acquisition.
7.3.2.1 Methods to Detect the Points of Interest
Different mathematical methods can be used to perform the detection step which
yields various shape of interest on the image: point, curve or area. The methods
proposed in detection algorithms are essentially based on contours detection, i.e. the
detection of variation of intensity levels on the area near the location of interest. In
the case of the SIFT detection algorithm, each point of interest is identified by its
location on the image (coordinates x, y), its gradient orientation, the scale factor and
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197
A way to further improve alignment of tilt series is to optimize the detection of
corresponding points in images of the tilt series. For this purpose, new approaches
in object detection or panoramic stitching, based on the concept of Scale Invariant
Feature Transform (SIFT), introduced by Lowe [27], have been proposed for
alignment in electron tomography [28].
Feature-based alignment methods require several steps which are performed by
separate algorithms. Here we will describe these steps which correspond to the
common strategy used for image alignment using SIFT. Additionally to the
emergence of this method many other algorithms appeared, providing alternatives
for the different steps.
• Detection of points of interest
First step is the detection of points of interest. To this purpose the algorithm has
to choose points in the image which will be easy to locate in other images of the
same sample. These points of interest are determined where the algorithm is able to
recognize a feature which is based on mathematical properties, such as local
extrema, and may not match physical features of the sample. This feature detection
step is performed independently on all images of a series and leads to the creation of
unique descriptors for each point of interest.
• Creation of a unique descriptor for each point of interest
With a set of point of interest on each image, alignment requires that they
correspond to the same physical location on the feature to be matched. One way to
achieve that is to rely on distinctive features. Most algorithms attach a single
descriptor to each interest point for that purpose.
• Comparison of interest points between two or more images
The next step is to identify the matches in the sets of points of interest by
comparing their descriptors. Once the point of interest, associated to the same
feature, are grouped together they can be used to deduce the space transformation
which occurred during the tilt-series acquisition.
7.3.2.1 Methods to Detect the Points of Interest
Different mathematical methods can be used to perform the detection step which
yields various shape of interest on the image: point, curve or area. The methods
proposed in detection algorithms are essentially based on contours detection, i.e. the
detection of variation of intensity levels on the area near the location of interest. In
the case of the SIFT detection algorithm, each point of interest is identified by its
location on the image (coordinates x, y), its gradient orientation, the scale factor and
7 Alignment of Tilt Series
197