Attitude determination and sensor alignment via weighted least squares affine transformations

Attitude determination and sensor alignment via weighted least squares affine transformation

Logarithmic gap costs decrease alignment accuracy

BACKGROUND: Studies on the distribution of indel sizes have consistently found that they obey a power law. This finding has lead several scientists to propose that logarithmic gap costs, G (k) = a + c ln k, are more biologically realistic than affine gap costs, G (k) = a + bk, for sequence alignment. Since quick and efficient affine costs are currently the most popular way to globally align sequences, the goal of this paper is to determine whether logarithmic gap costs improve alignment accuracy significantly enough the merit their use over the faster affine gap costs. RESULTS: A group of simulated sequences pairs were globally aligned using affine, logarithmic, and log-affine gap costs. Alignment accuracy was calculated by comparing resulting alignments to actual alignments of the sequence pairs. Gap costs were then compared based on average alignment accuracy. Log-affine gap costs had the best accuracy, followed closely by affine gap costs, while logarithmic gap costs performed poorly. Subsequently a model was developed to explain the results. CONCLUSION: In contrast to initial expectations, logarithmic gap costs produce poor alignments and are actually not implied by the power-law behavior of gap sizes, given typical match and mismatch costs. Furthermore, affine gap costs not only produce accurate alignments but are also good approximations to biologically realistic gap costs. This work provides added confidence for the biological relevance of existing alignment algorithms

Towards segmentation and spatial alignment of the human embryonic brain using deep learning for atlas-based registration

We propose an unsupervised deep learning method for atlas based registration to achieve segmentation and spatial alignment of the embryonic brain in a single framework. Our approach consists of two sequential networks with a specifically designed loss function to address the challenges in 3D first trimester ultrasound. The first part learns the affine transformation and the second part learns the voxelwise nonrigid deformation between the target image and the atlas. We trained this network end-to-end and validated it against a ground truth on synthetic datasets designed to resemble the challenges present in 3D first trimester ultrasound. The method was tested on a dataset of human embryonic ultrasound volumes acquired at 9 weeks gestational age, which showed alignment of the brain in some cases and gave insight in open challenges for the proposed method. We conclude that our method is a promising approach towards fully automated spatial alignment and segmentation of embryonic brains in 3D ultrasound

Optimal gap-affine alignment in O (s) space

Altres ajuts: DRAC project [001-P-001723]Pairwise sequence alignment remains a fundamental problem in computational biology and bioinformatics. Recent advances in genomics and sequencing technologies demand faster and scalable algorithms that can cope with the ever-increasing sequence lengths. Classical pairwise alignment algorithms based on dynamic programming are strongly limited by quadratic requirements in time and memory. The recently proposed wavefront alignment algorithm (WFA) introduced an efficient algorithm to perform exact gap-affine alignment in time, where s is the optimal score and n is the sequence length. Notwithstanding these bounds, WFA's memory requirements become computationally impractical for genome-scale alignments, leading to a need for further improvement. In this article, we present the bidirectional WFA algorithm, the first gap-affine algorithm capable of computing optimal alignments in memory while retaining WFA's time complexity of . As a result, this work improves the lowest known memory bound to compute gap-affine alignments. In practice, our implementation never requires more than a few hundred MBs aligning noisy Oxford Nanopore Technologies reads up to 1 Mbp long while maintaining competitive execution times. All code is publicly available at . Supplementary data are available at Bioinformatics online

Dynamic Gap Selector: A Smith Waterman Sequence Alignment Algorithm with Affine Gap Model Optimisation

Smith Waterman algorithm (S-W) is nowadays considered one of the best method to perform local alignments of biological sequences characterizing proteins, DNA and RNA molecules. Indeed, S-W is able to ensure better accuracy levels with respect to the heuristic alignment algorithms by extensively exploring all the possible alignment configurations between the sequences under examination. It has been proven that the first amino acid (AA) or nucleotide (NT) inserted/deleted (that identify a gap open) found during the alignment operations performed on sequences is more significant from a biological point of view than the subsequent ones (called gap extension), making the so called Affine Gap model a viable solution for biomolecules alignment. However, this version of S-W algorithm is expensive both in terms of computation as well as in terms of memory requirements with respect to others less demanding solutions such as the ones using a Linear Gap model. In order to overcome these drawbacks we have developed an optimised version of the S-Walgorithm based on Affine Gap model called Dynamic Gap Selector (DGS S-W). Differently from the standard S-W Affine Gap method, the proposed DGS S-W method reduces the memory requirements from 3*N*M to N*M where N and M represents the size of the compared sequences. In terms of computational costs, the proposed algorithm reduces by a factor of 2 the number of operations required by the standard Affine Gap model. DGS S-W method has been tested on two protein and one RNA sequences datasets, showing mapping scores very similar to those reached thanks to the classical S-W Affine Gap method and, at the same time, reduced computational costs and memory usag

Relative Affine Structure: Canonical Model for 3D from 2D Geometry and Applications

We propose an affine framework for perspective views, captured by a single extremely simple equation based on a viewer-centered invariant we call "relative affine structure". Via a number of corollaries of our main results we show that our framework unifies previous work --- including Euclidean, projective and affine --- in a natural and simple way, and introduces new, extremely simple, algorithms for the tasks of reconstruction from multiple views, recognition by alignment, and certain image coding applications

Inability of spatial transformations of CNN feature maps to support invariant recognition

A large number of deep learning architectures use spatial transformations of CNN feature maps or filters to better deal with variability in object appearance caused by natural image transformations. In this paper, we prove that spatial transformations of CNN feature maps cannot align the feature maps of a transformed image to match those of its original, for general affine transformations, unless the extracted features are themselves invariant. Our proof is based on elementary analysis for both the single- and multi-layer network case. The results imply that methods based on spatial transformations of CNN feature maps or filters cannot replace image alignment of the input and cannot enable invariant recognition for general affine transformations, specifically not for scaling transformations or shear transformations. For rotations and reflections, spatially transforming feature maps or filters can enable invariance but only for networks with learnt or hardcoded rotation- or reflection-invariant featuresComment: 22 pages, 3 figure