Comparison between Thermal and Visible Facial Features on a Verification Approach - Biomedical Engineering Systems and Technologies - page 278

Following (Lowe, 2004), scale-space in the Difference-of-Gaussian function (DoG)
convolved with the image, ,, can be computed as a difference of two nearby
scales separated by a constant factor k:
( )

(3)
From [16], it is stated that the maxima and minima of the scale-normalised Laplacian
of Gaussian (LGN),

D ( x , y , σ ) = G ( x , y , k σ ) − G ( x , y , σ ) ∗ I ( x , y ) = L ( x , y , k σ ) − L ( x , y , σ )

produce the most stable image features in comparison
with other functions, such as the gradient or Hessian. The relationship between D and
2

2 2

σ ∇ G

is:

2
∇ σ

2 2

G ( x , y , k σ ) − G ( x , y , σ ) ≈ ( k − 1 σ ∇ G

(4)

The factor 1 is a constant over all scales and does not influence strong location.
A significant difference in scales has been chosen,

= k , which has almost no im-
pact on the stability and the initial value of 1.6 provides close to optimal repeat-
ability according to [15].
After having located accurate keypoints and removed strong edge responses of the
DoG function, orientation is assigned. There are two important parameters for varying
the complexity of the descriptor: the number of orientations and the number of the
array of orientation histograms. Throughout this paper a 4x4 array of histograms with
8 orientations is used, resulting in characteristic vectors with 128 dimensions. The
results in [15] support the use of these parameters for object recognition purposes
since larger descriptors have been found more sensitive to distortion.

2

2.3 Classifier Based on Vocabulary Tree

The verification scheme used in this paper is based on [11]. Once the SIFT descriptors
are extracted from the image database, it's time for organizing them in a vocabulary
tree. A hierarchically verification scheme allows to search selectively for a specific
node in the vocabulary tree, decreasing search time and computational effort.

Fig. 3. Two levels of a vocabulary tree with branch factor 3

The k-means algorithm is used in the initial point cloud of descriptors for finding
centroids through the minimum distance estimation so that a centroid represents a
cluster of points.