#Permutation matrix how to
#Permutation matrix full
#Permutation matrix registration
#Permutation matrix code

If a constructor option is provided in both the calling sequence directly and in an outputoptions option, the latter takes precedence (regardless of the order). These options may also be provided in the form outputoptions=, where represents a Maple list. The constructor options provide additional information (readonly, shape, storage, order, datatype, and attributes) to the Matrix or Vector constructor that builds the result. For example, the pivot vector Vector(3, ) is equivalent to the pivot vector Vector(6, ). This allows the shortened form of a pivot vector used by NAG when the number of rows of an LU factorizable Matrix A is larger than the number of its columns.

This value must be greater than or equal to the dimension of the input Vector V. If the optional nonnegative integer parameter d is provided then the dimension(s) of the output object have the value d. The default datatype of a returned permutation Matrix is integer. A (i.e., no pivoting is required to compute the decomposition of M. Premultiplying A by M permutes A to a Matrix whose factorization would require no row swapping in order to use the same choices of pivot values. Ī returned permutation Matrix M has all entries with value 1 or 0. The default datatype of a returned permutation Vector is integer. n, then no swapping would be required to do the factorization with the exact same choices of pivot rows. Prior to performing the i th pivot, row i and row V of the partially row-reduced Matrix are swapped.Ī returned permutation Vector U has as its i th entry the ordinal of the row of A such that, if all U th rows of A were permuted to the i th row, i = 1. Its i th element is the ordinal of the row of the partially row-reduced Matrix which is selected as the i th choice of pivoting row.

By default, the resulting object is a Vector of rectangular storage and integer datatype or a Matrix of sparse storage and integer datatype.Ī pivot vector V in NAG form, returned for example by an LU decomposition of a Matrix A, has all integer entries. The CreatePermutation(V) function constructs a permutation Vector or Matrix from a NAG pivot vector. (optional) constructor options for the result object (optional) equation of the form output = obj where obj is one of 'Vector' or 'Matrix', or a list containing one of these names selects format of the output object (optional) nonnegative integer dimension(s) of output

#Permutation matrix code

The code will be made public.Convert a NAG pivot vector to a permutation Vector or Matrix Extensive experiments have validated our method, which creates a new state-of-the-art performance for robust 3D point cloud registration.

#Permutation matrix registration

Our S2H matching procedure can be easily integrated with existing registration frameworks, which has been verified in representative frameworks including DCP, RPMNet, and DGR. Moreover, to guarantee end-to-end learning, we supervise the learned partial permutation matrix but propagate the gradient to the soft matrix instead. Specifically, we augment the profit matrix before the hard assignment to solve an augmented permutation matrix, which is cropped to achieve the final partial permutation matrix. In response, we design a dedicated soft-to-hard (S2H) matching procedure within the registration pipeline consisting of two steps: solving the soft matching matrix (S-step) and projecting this soft matrix to the partial permutation matrix (H-step).

#Permutation matrix full

However, this proposal poses two new problems, i.e., existing hard assignment algorithms can only solve a full rank permutation matrix rather than a partial permutation matrix, and this desired matrix is defined in the discrete space, which is non-differentiable. To address the above challenges, we propose to learn a partial permutation matching matrix, which does not assign corresponding points to outliers, and implements hard assignment to prevent ambiguity. However, in this paper, we prove that these methods have an inherent ambiguity causing many deceptive correspondences. Alternatively, the soft matching-based methods have been proposed to learn the matching probability rather than hard assignment.

#Permutation matrix how to

Even though considerable progress has been made in deep learning-based 3D point cloud processing, how to obtain accurate correspondences for robust registration remains a major challenge because existing hard assignment methods cannot deal with outliers naturally.