Class implements both functionalities for detection of lines and computation of their binary descriptor

Class' interface is mainly based on the ones of classical detectors and extractors, such as Feature2d's Feature Detection and Description and Descriptor Matchers. Retrieved information about lines is stored in KeyLine objects.

Introduction

One of the most challenging activities in computer vision is the extraction of useful information from a given image. Such information, usually comes in the form of points that preserve some kind of property (for instance, they are scale-invariant) and are actually representative of input image.

The goal of this module is seeking a new kind of representative information inside an image and providing the functionalities for its extraction and representation. In particular, differently from previous methods for detection of relevant elements inside an image, lines are extracted in place of points; a new class is defined ad hoc to summarize a line's properties, for reuse and plotting purposes.

Computation of binary descriptors

To obtatin a binary descriptor representing a certain line detected from a certain octave of an image, we first compute a non-binary descriptor as described in [LBD]. Such algorithm works on lines extracted using EDLine detector, as explained in [EDL]. Given a line, we consider a rectangular region centered at it and called line support region (LSR). Such region is divided into a set of bands {B_1, B_2, ..., B_m}, whose length equals the one of line.

If we indicate with d_L the direction of line, the orthogonal and clockwise direction to line d_perp can be determined; these two directions, are used to construct a reference frame centered in the middle point of line. The gradients of pixels g' inside LSR can be projected to the newly determined frame, obtaining their local equivalent g' = (g^T * d_perp, g^T * d_L)^T <=> (g'_{d_perp}, g'_{d_L})^T.

Later on, a Gaussian function is applied to all LSR's pixels along d_perp direction; first, we assign a global weighting coefficient f_g(i) = (1/sqrt(2*pi)*sigma_g)*exp(-d_i^2/2*sigma_g^2) to i-th row in LSR, where d_i is the distance of i-th row from the center row in LSR, sigma_g = 0.5(m * w - 1) and w is the width of bands (the same for every band). Secondly, considering a band B_j and its neighbor bands B_{j-1}, B_{j+1}, we assign a local weighting F_l(k) = (1/sqrt(2*pi)*sigma_l)*exp(-d_k'^2/2*sigma_l^2), where d_k' is the distance of k-th row from the center row in B_j and sigma_l = w. Using the global and local weights, we obtain, at the same time, the reduction of role played by gradients far from line and of boundary effect, respectively.

Each band B_j in LSR has an associated band descriptor(BD) which is computed considering previous and next band (top and bottom bands are ignored when computing descriptor for first and last band). Once each band has been assignen its BD, the LBD descriptor of line is simply given by:

LBD = (BD_1^T, BD_2^T, ... , BD_m^T)^T

To compute a band descriptor B_j, each k-th row in it is considered and the gradients in such row are accumulated:

V1_j^k = lambda * sum[g'_{d_perp} > 0] (  g'_{d_perp} )
V2_j^k = lambda * sum[g'_{d_perp} < 0] ( -g'_{d_perp} )
V3_j^k = lambda * sum[g'_{d_L}    > 0] (  g'_{d_L}    )
V4_j^k = lambda * sum[g'_{d_L}    < 0] ( -g'_{d_L}    )

with \lambda = f_g(k) * f_l(k)

By stacking previous results, we obtain the band description matrix (BDM)

BDM_j = [V1_j^1, V1_j^2, ..., V1_j^n ;
         V2_j^1, V2_j^2, ..., V2_j^n ;
         V3_j^1, V3_j^2, ..., V3_j^n ;
         V4_j^1, V4_j^2, ..., V4_j^n ] in R^(4xn)

with n the number of rows in band B_j:

n = {2w, j = 1||m;
    {3w, else.

Each BD_j can be obtained using the standard deviation vector S_j and mean vector M_j of BDM_J. Thus, finally:

LBD = (M_1^T, S_1^T, M_2^T, S_2^T, ..., M_m^T, S_m^T)^T in R^(8m)

Once the LBD has been obtained, it must be converted into a binary form. For such purpose, we consider 32 possible pairs of BD inside it; each couple of BD is compared bit by bit and comparison generates an 8 bit string. Concatenating 32 comparison strings, we get the 256-bit final binary representation of a single LBD.

References

[LBD]:

HK Yuen, John Princen, John Illingworth, and Josef Kittler. "Comparative study of hough transform methods for circle finding". Image and Vision Computing, 8(1):71-77, 1990.

[EDL]:

R Grompone Von Gioi, Jeremie Jakubowicz, Jean-Michel Morel, and Gregory Randall. "LSD: A fast line segment detector with a false detection control". IEEE Transactions on Pattern Analysis and Machine Intelligence, 32(4):722-732, 2010.