Scale-Free Registrations in 3D: 7 Degrees of Freedom with Fourier Mellin SOFT Transforms

Bülow, Heiko; Birk, Andreas

doi:10.1007/s11263-018-1067-5

Cited by 19 publications

(18 citation statements)

References 55 publications

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“…Phase correlation of the resulting structures yields unique Dirac peaks indicating all parameters of the underlying transformation. For more details, see [ 19 ]. Once this step is successful, which can be verified by a unique signal/noise ratio of the Dirac maximum, the registration is precise within the rendered pixel/voxel resolution.…”

Section: The Fms Algorithmmentioning

confidence: 99%

“…Other examples of non-rigid registration in the context of medical applications can, for example, be found in [ 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 ]. While feature based methods are well established and have proven their usefulness, they also have known limitations with respect to robustness, especially when the quality of the data is not optimal, for example, due to sensor noise, limitations in the resolution, or interfering structures [ 19 ].…”

Section: Introductionmentioning

confidence: 99%

“…Here, Fourier-Mellin-SOFT (FMS) is extented for use with MRT data sequences. FMS determines 7 degrees of freedom (dof) in subsequent dependent steps [ 19 ]. It is based on decoupling all single dof by processing spectral structural information.…”

Section: Introductionmentioning

confidence: 99%

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Registration of Magnetic Resonance Tomography (MRT) Data with a Low Frequency Adaption of Fourier-Mellin-SOFT (LF-FMS)

Bülow

Birk

2021

Sensors

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Fourier-Mellin-SOFT (FMS) is a rigid 3D registration method, which allows the robust registration of 3 degrees-of-freedom (dof) rotation, 1-dof scale, and 3-dof translation between scans on discrete grids. FMS is based on a spectral decomposition of these 7-dof. This complete spectral representation of the input data enables an adaption to certain frequency ranges. This special property is used here to focus on relevant mutual 3D information between bone structures with a Low Frequency adaptation of FMS (LF-FMS), that is, it is utilized for matching and concurrently determining corresponding transformation parameters. This process is applied on a set of Magnetic Resonance Tomography (MRT) data representing the hand region, in particular the carpal bone area, in a sequence of different hand positions. This data set is available for different probands, which allows a comparison of resulting parameter plots and furthermore matching in between bone structures.

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Section: The Fms Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Registration of Magnetic Resonance Tomography (MRT) Data with a Low Frequency Adaption of Fourier-Mellin-SOFT (LF-FMS)

Bülow

Birk

2021

Sensors

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“…The idea of using registration of multiple scans from different unknown sensor positions is based on our previous work on registration of noisy data with partial overlap including especially sonar [ 19 , 20 , 21 ]. This includes especially spectral registration methods [ 38 , 39 ], which are capable of matching scans as an entire unit without a dependency on features within the scan representation.…”

Section: Pixel Based Scan Registrationmentioning

confidence: 99%

Synthetic Aperture Sonar (SAS) without Navigation: Scan Registration as Basis for Near Field Synthetic Imaging in 2D

Bülow

Birk

2020

Sensors

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Sonars are essential for underwater sensing as they can operate over extended ranges and in poor visibility conditions. The use of a synthetic aperture is a popular approach to increase the resolution of sonars, i.e., the sonar with its N transducers is positioned at k places to generate a virtual sensor with kN transducers. The state of the art for synthetic aperture sonar (SAS) is strongly coupled to constraints, especially with respect to the trajectory of the placements and the need for good navigation data. In this article, we introduce an approach to SAS using registration of scans from single arrays, i.e., at individual poses of arbitrary trajectories, hence avoiding the need for navigation data of conventional SAS systems. The approach is introduced here for the near field using the coherent phase information of sonar scans. A Delay and Sum (D&S) beamformer (BF) is used, which directly operates on pixel/voxel form on a Cartesian grid supporting the registration. It is shown that this pixel/voxel-based registration and the coherent processing of several scans forming a synthetic aperture yields substantial improvements of the image resolution. The experimental evaluation is done with an advanced simulation tool generating realistic 2D sonar array data, i.e., with simulations of a linear 1D antenna reconstructing 2D images. For the image registration of the raw sonar scans, a robust implementation of a spectral method is presented. Furthermore, analyses with respect to the trajectories of the sensor locations are provided to remedy possible grating lobes due to the gaping positions of the transmitter devices.

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“…Due to FMT's robustness and high accuracy, it has been successfully applied in multiple applications, such as image registration [11,24,25], fingerprint image hashing [26], visual homing [27], point cloud registration [28], 3D modeling [29], remote sensing [12,30], and localization and mapping [31,32]. However, it requires that the capture device doesn't roll or pitch and that the environment is planar and parallel to the imaging plane.…”

Section: Introductionmentioning

confidence: 99%

Rethinking the Fourier-Mellin Transform: Multiple Depths in the Camera’s View

Kuang

Kneip

et al. 2021

Remote Sensing

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Remote sensing and robotics often rely on visual odometry (VO) for localization. Many standard approaches for VO use feature detection. However, these methods will meet challenges if the environments are feature-deprived or highly repetitive. Fourier-Mellin Transform (FMT) is an alternative VO approach that has been shown to show superior performance in these scenarios and is often used in remote sensing. One limitation of FMT is that it requires an environment that is equidistant to the camera, i.e., single-depth. To extend the applications of FMT to multi-depth environments, this paper presents the extended Fourier-Mellin Transform (eFMT), which maintains the advantages of FMT with respect to feature-deprived scenarios. To show the robustness and accuracy of eFMT, we implement an eFMT-based visual odometry framework and test it in toy examples and a large-scale drone dataset. All these experiments are performed on data collected in challenging scenarios, such as, trees, wooden boards and featureless roofs. The results show that eFMT performs better than FMT in the multi-depth settings. Moreover, eFMT also outperforms state-of-the-art VO algorithms, such as ORB-SLAM3, SVO and DSO, in our experiments.

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Scale-Free Registrations in 3D: 7 Degrees of Freedom with Fourier Mellin SOFT Transforms

Cited by 19 publications

References 55 publications

Registration of Magnetic Resonance Tomography (MRT) Data with a Low Frequency Adaption of Fourier-Mellin-SOFT (LF-FMS)

Registration of Magnetic Resonance Tomography (MRT) Data with a Low Frequency Adaption of Fourier-Mellin-SOFT (LF-FMS)

Synthetic Aperture Sonar (SAS) without Navigation: Scan Registration as Basis for Near Field Synthetic Imaging in 2D

Rethinking the Fourier-Mellin Transform: Multiple Depths in the Camera’s View

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