IEEE Geoscience and Remote Sensing Magazine - March 2021 - 147

local region contributes to the histogram, depending on the
location, gradient orientation, and magnitude.
The image gradients computed around every keypoint
are integrated into the 3D histogram, resulting in 2 # 2 # 2
bins, each of which is incremented by the gradient magnitude multiplied by a weight inversely related to the distance
between the location and keypoint. The faster the distance,
the less the weight. The peak value of the histogram and the
ones larger than 80% of the peak are defined as the dominant orientation. A square neighborhood around each point
is cropped. It is inversely rotated by the dominant orientation. To ensure scale invariance, image gradients are calculated at the same scale to which the keypoint belongs. The local feature is obtained by concatenating the histograms. The
generation of the local feature is shown in Figure 10.
GLOH
GLOH generates the local patch as a log-polar grid with
three bins in the radial direction and eight bins along the
angular direction [91]. The radius for the outer circles is set
according to the task at hand. The central circle is handled
as a single bin, while the outer circular regions are divided
into eight bins equally distributed along the angular direction. The gradient orientation weighted by magnitude is
quantized into eight levels. The histogram can be generated
similarly. The local descriptor is obtained by concatenating
the histograms across all sectors. Compared to SIFT, GLOH
refines the division of location.
ADAPTIVE BINNING
The previous local descriptor divides the neighborhood
around the keypoint into fixed cells-16 grids for SIFT
(Figure 11) and 17 sectors for GLOH (Figure 12)-in each
of which the gradient orientation is quantized at fixed levels. Differently, Sedaghat and Ebadi divide the inner circle
and outer circular regions into different radial sectors [92].
The gradient orientations within each sector are quantized
into different levels. The neighborhood around the detected keypoint is divided into n nonoverlapping circular

Orientation

rings, R 1, R 2, f, R n, each of which is further divided into
N i cells equally distributed along the angular direction
{R i ( j)} Nj =i 1. The gradient orientations in R i ( j) are then
quantized into k i levels of the histogram. The level of
quantization is different from cell to cell. The local feature
is obtained by combining the histograms, producing a descriptor with the dimension of R i N i k i.
DAISY
Tola et al. present a new gradient calculation [93], [94].
They compute the weighted sums of gradient norms by
convolving the gradients with Gaussian filters in specific
directions. For image I (x, y), a set of orientation maps is
defined, O i (x, y) = (2I/2i) +, where i is the quantized direction and ($) + = max {$ , 0}. They are convolved with the
Gaussian kernel parameterized by v to generate local regions in different sizes, O vi (x, y) = O i (x, y) ) G v (x, y). The
local descriptor is defined as the coefficients resulting
from the convolved orientation maps located on concentric circles:
h v (x, y) = [O v1 (x, y), O v2 (x, y), f, O vN (x, y)].
Considering M circular cells, the representation is obtained
by concatenating the normalized vectors

Θ

(x)

Spatial
(y)

Keypoint

FIGURE 10. The generation of the SIFT descriptor.

SIFT

GLOH

FIGURE 11. A square grid for SIFT and a log-polar sector for GLOH.
MARCH 2021

IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE

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IEEE Geoscience and Remote Sensing Magazine - March 2021

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