Deck Pose Estimation Algorithm

In this section, we describe a feature based approach to deck pose estimation. Our approach is sparse feature based matching using nested descriptors, a least median of squares robust homogra- phy estimation [180] with preconditioning [181], bagging [182] and nested shape reprojection error.

Algorithm 1:Deck Pose Estimation

Input:K,I,R,p,q,H_DR,qb,k

Output: ˆt

(pi,qi) 8iargminj||XI(pi) XR(qj)||2 // Greedy nested shape assignment

leastMedian •

fori 1tomaxiterdo

(p˜,q˜) qb(p,q,k) // Bagged sample

HI

R fdlt(K 1p˜,K 1q˜) // Linear Homography

z ||XI(KHRIK 1q) XR(q)||2F // Nested shape reprojection error (6.13)

ifmedian(z)<leastMedianthen

leastMedian=median(z) // Least median of squares

ˆ

t=⇥(KH_RIK 1)H_DR⇤₍₃₎ // Position of deck origin in camera frame (6.3)

The novel contribution is the use of the nested shape descriptors during reprojection for increased accuracy to compensate for uncertain correspondence given circular deck markings.

The algorithm for deck pose estimation which uses the nested shape descriptors and robust homography estimation is summarized in algorithm1. This algorithm assumes as input

• K: a calibrated intrinsic calibration matrix determined from an offline calibration procedure to determine focal length, principal point, and lens distortion [184].

• I: an input grayscale image of sizeM⇥N

• R: a reference image of size M0_⇥N0_{. This reference template is determined offline from} reference drawings of the deck. An example reference template is the black and white circle shown in figure6.1. This is the standard deck marking for shipboard landing for the Firescout UAS on air capable ships.

• p:ninterest points inI, as determined from Canny edge positions. • q:minterest points inRas determined from Canny edge positions.

• HDR: a presurveyed homography from the deck to reference template determined from a man-

ual correspondence between the corners of reference template and a manually metric survey of the deck, and these correspondences are input to the DLT algorithm in section6.1.4. • qb: a bagged sample function with sample regions defined to capture the unique structures in

the template, such as the center circle and the upper and lower corners.

• maxiter: The maximum number of iterations of the least median of squares randomized ho- mography search.

Algorithm 1 proceeds as follows. First, we compute an initial correspondence using greedy assignment of nested descriptors. XI(p)is the nested descriptor computed from imageIat interest

pointsp, andXR(q)is the nested descriptor from reference templateRat interest pointsq. For each

descriptor in the observed image using the minimum pairwise Euclidean distance to all nested shape descriptors in the template. This provides a list ofninitial correspondences(pˆ,qˆ).

Next, we perform bagged sampling [182]. The bagged sample functionqbis a function that se-

lectskcorrespondences at random from the initial correspondence list, such that samples are chosen in a round robin selection phase from one ofb sample bags. A sample bag is a regions of interest in the reference template, such that a correspondence(p,q)drawn from bag jguarantees that pointq

is in sample region j. In this application, the bagged sample function defines five sampling regions from the template that capture the circle corners and lines as groups. k samples are chosen round robin from each of these bags in order. The bagged sampling function provides efficiency in the random sample so that non-degenerate and unambiguous correspondences are chosen. For exam- ple, if all samples are drawn from only bags 1 and 2 there exists a rotational symmetry in the outer circle that will results in an incorrect alignment. Similarly, if all of the samples are chosen from bag 5, then since the samples are closely spaced, the resulting homography is likely to be numerically unstable. By performing round-robin random sampling from each bag in order, we maintain well separated non-degenerate and non-ambiguous correspondences for use in homography estimation.

Next, we perform robust homography estimation using a least median of squares approach [180]. We randomly selectkcorrespondences using the bagged sampling, then we compute the DLT ho- mography from this random sample. The points are first preconditioned for improved numerical stability [181]. The nested covariance is important to provide an uncertainty of the correspondences since the majority of points on a deck template are ambiguous, such as points on the inner line or the outer circle. Next, we compute the nested shape reprojection error (6.13) for the remaining points, and compute the median of this reprojection error. If the median is less than the least median so far, we update the best solution and iterate. The algorithm terminates aftermaxiteriterations.

from the homography decomposition (6.3). This uses the transitivity property of homographies HI

D=HTIHDT, such that a homography from deck to image (HDI) is given by the product of presur-

veyed homography from deck to reference template (HR

D) and estimated homography from template

to image (DI R).