1 Introduction

Biometrics have been paid significant attention and gained a wide application area during the past decades due to their high discriminative performance in a number of fields such as surveillance, identification, human-computer interaction, etc. [14, 65]. Individuals pose biological characteristics also called metrics which separate them from the others [22]. Biometrics deals with these metrics that can be mainly categorized into two groups, physiological and behavioral [23]. Physiological characteristics are related to the shape of the body and most common ones are iris, retina, palm print, fingerprint, etc. Behavioral characteristics also sometimes called behaviometrics [38], i.e. voice, typing rhythm, gait, are related to the behaviors of the individuals. The face has come into prominence as a physiological identifier due to its high discriminative performance and facility of retrieval by remote devices without disturbing people [10, 21].

Face recognition continues to be a research topic that is still in the spotlight and on the agenda with regard to challenges it poses due to the presence of variations in illumination, pose, expression, etc. A great deal of attention has been focused on face recognition due to its challenging nature and wide application areas [27]. Face recognition has mainly based on the idea of classification of images with respect to some features that are specific to individuals. A vast majority of these studies have utilized texture analysis and classification. The texture is the repeating random or regular patterns throughout the image, which characterize the surface of an object or a region [30, 31]. Textures have been widely used as face descriptors to discriminate and retrieve images. Thus, finding high discriminative and low computationally complex descriptors have become a popular point of interest.

Descriptors are mainly categorized as either holistic or local. Methods such as GLCM [15, 16], PCA [25, 55], LDA [11], 2DPCA [59], LLE [50] and VDE [6] concern with the entire image for extracting holistic features, however, local descriptors, namely, LBP [1], LGBP [63], CS-LBP [17], GV-LBP [28], LDP [19], LJBPW [8], PLBP [44], LDGP [4], LPQ [58], LDNP [45, 47], HoG [7], LTP [53], Gabor [33, 60] exploits the local appearance features.

Local descriptors have gained remarkable attention due to their robustness against the prominent challenges of face recognition such as variations in illumination and facial expressions. It is identified that holistic descriptors are more influenced by the aforementioned challenges which as a result impairs their recognition performance. On the other hand, local descriptors pose remarkable recognition rates despite the challenges expressed.

Gabor wavelets, Radon transform [20], Texton learning [26, 56] and LBP are the most prominent methods that have inspired and pioneered many followers [9, 12, 13, 18, 37, 46, 62]. Among this approaches, LBP has remarkably come to the forefront due to its high performance and computationally low complexity [39, 40, 42]. LBP derives micro patterns by considering each pixel’s intensity difference relative to its contiguous pixels in its 3 × 3 neighborhood. Every contiguous pixel in the 3 × 3 neighborhood contributes as either a binary 1 or 0 to the new value of the reference pixel depending on its own and reference pixel intensity. After completion of the micro-pattern calculation, a histogram representing the distribution of these micro-patterns is created, which takes place as the discriminative feature vector during classification. LBP has found wide application area due to its flexibility to adapt. Thus, a number of successor studies have been proposed [41] to improve and extend the idea of LBP.

In this paper, a gradient-based local descriptor that is robust against the challenges of face recognition is proposed. In contrary to the ordinary methods, while calculating the gradient for each direction, an analysis is done by considering the predecessors of the corresponding pixel as well as the successors at that direction. Moreover, previous studies represent these local relationships by encoding them in binary because they consider only the positive and negative intensity changes. However, we propose an alternative way of representation that encodes the relationships between each pixel and its neighbors in a multi-valued logic manner. Our method does not only consider the variations but also uniformity. A threshold value is defined to identify whether an intensity variation is present in the specified direction. If the intensity change exceeds the threshold value, then it is evaluated as a variation either in positively or negatively depending on the direction of the change. Three states of the relationship between multiple pixels at each direction yield a more discriminative descriptor for face retrieval. Ternary logic is applied to express three states. Ternary values that are calculated at each direction are concatenated and the resulting compound ternary value is replaced with the reference pixel. By this way, a more discriminative face descriptor is achieved which is resistant to noise and challenges in unconstrained environments. Besides its favorable recognition performance, DLGBD also handles the effects of rotational variances and noise affects very successfully when compared to the state-of-the-art methods.

The rest of this paper is organized as follows. Section 2 briefly reviews the basic LBP and its extensions. Section 3 introduces the proposed local descriptor. Section 4 demonstrates the experimental results and Section 5 concludes the paper.

2 Preliminaries

LBP has gained significant popularity and attention due to its remarkable performance in terms of recognition rate and simplicity [34]. It has influenced many followers and has played a leading role as a source for them, such that, a great deal of research studies has been proposed as an extension of LBP. LBP was firstly produced for texture classification. However, when the high performance it provides was seen, it has been also applied to deduce the relationship between the pixels in the face images [2, 5]. Moreover, a diverse number of LBP variants have been proposed that address the problems in various fields, such as object detection [49, 54], motion and activity analysis [24, 64], biomedical image analysis [35, 36], visual inspection [51], etc.

The original LBP, characterizes the spatial structure of an image by expressing each pixel with a new gray-level value that is calculated relative to the neighboring pixels’ gray-level values in a 3 × 3 neighborhood. A local binary value is formed by concatenating the single-digit binary values that are calculated as the result of magnitude comparison of the reference pixel with each of its neighbors. This, simple, yet efficient local pattern description method, later evolved to a more sophisticated version, which led to multi-resolution analysis and rotation invariance. The successor LBP, operates on a circular neighborhood rather than the square pattern of the predecessor. The neighboring pixels that are settled equally apart from each other on a circle which is centered at the reference pixel (Fig. 1), are considered during pattern description. The coordinates of the neighboring pixel n are defined relative to the reference pixel as−r sin(2πn/p) r cos(2πn/p). Bilinear interpolation is used for regions where the circle does not pass through a certain pixel.

Fig. 1
figure 1

The p neighbors of the reference pixel Ic on the circle with radius r

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LBP of a reference pixel c, considering its P equally apart neighbors on a circle with radius R, is calculated as in the following:

$$ {LBP}_{P,R}(c)={\sum}_{P=0}^{P-1}s\left({I}_c-{I}_P\right){2}^p $$
(1)

where Ic and IP denote the intensity values of the reference pixel and the Pth neighboring pixel that is considered respectively. The function s(x) identifies the coefficient of the corresponding binary digit and defined as:

$$ s(x)=\left\{\begin{array}{cc}1,& if\ x\ge 0\\ {}0,& if\ x<0\end{array}\right. $$
(2)

LBP is invariant to monotonic gray-scale changes due to the invariance of the function s(x) against monotonic gray-scale changes [43]. An exemplary demonstration of the basic LBP is given in Fig. 2:

Fig. 2
figure 2

An exemplary calculation of the basic LBP

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2p possible different patterns can be calculated. Following the calculation of the LBP values for each pixel, the texture of the image (Imxn) is defined by considering the probability distributions of these LBP values on a histogram, as follows:

$$ H\left({LBP}_k\right)={\sum}_{i=1}^m{\sum}_{j=1}^n\delta \left\{k, LBP\left(i,j\right)\right\} $$
(3)

where δ{.} denotes the Kroneck product function [3].

The LBP value of each pixel changes when the image is rotated because each digit of the binary pattern corresponds to the result of the comparison of the intensity value of the reference pixel and the neighboring pixel at the specified direction. That is, when the image is rotated, the directional position of the specified neighbor also changes and so the corresponding position in the binary pattern. An extension of the basic LBP is proposed as a rotation invariant version. It has been identified that some of the calculated patterns more information than the others and describe the texture of the images better. Ojala et al. named this subset of 2p patterns as uniform patterns. An LBP is called uniform if it comprises at most two 0–1 or 1–0 transitions. LBPs such as 10,011,111, 00010000 are uniform, whereas 10,100,100 and 00110011 are non-uniform.

3 Proposed descriptor - DLGBD

This section presents the proposed local gradient-based descriptor in detail. The first part clarifies the determination of direction-dependent neighbors. The following section describes the nth order local gradient-based information encoding and the last section explains the calculation of the ultimate DLGBD texture descriptor of an image. The overall operational block diagram of DLGBD is illustrated in Fig. 4.

3.1 k-hop directional neighbor extraction

Let, Imxn be a grayscale image where row and col represent the number of rows and columns respectively. Ii,j denotes the intensity value of a pixel in row (i), column (j) where i ϵ [0,m) and j ϵ [0,n). The coordinates of the top-left-most pixel are (0,0). The column index j increases positively in the horizontal direction from left to right, and the row index i increases positively downside across the rows. Relations between the pixels are handled in four directions, namely, 0°, 45°, 90° and 135°. The local neighborhood that comprises the pixels at most k-hop away is represented by Nk. The population of the neighborhood |Nk| differs due to the value of k and is calculated as |Nk| = (2 k + 1)k-1. The neighbors of a reference pixel Ii,j are categorized according to their angular position relative to that pixel. Neighbors of a reference pixel Ii,j for k = 1 is described as given in Fig. 3:

Fig. 3
figure 3

Directional neighbors of reference pixel Ii,j for k = 1

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Fig. 4
figure 4

The block diagram of the complete process

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Fig. 5
figure 5

Directional neighbours of reference pixel Ii,j for k = 2

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Fig. 6
figure 6

Definition of neighbors I’i,j-2, I’i,j + 2 for α = 0° and I’i + 2,j, I’i-2,j for α = 90°

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Fig. 7
figure 7

a Identical LBP codes assigned to different patterns b The proposed descriptor overcomes the miss-assignment situation

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Fig. 8
figure 8

a Sample image matrix b\( {C}_{i,j}^{1,5}, \)1-hop pixcode for thr = 5c\( {C}_{i,j}^{1,7}, \)1-hop pixcode for thr = 7

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Fig. 9
figure 9

Examples of face images extracted from Face94, ORL, JAFFE, Yale and CAS-PEAL-R1 databases respectively

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Fig. 10
figure 10

Illustration of the robustness of DLGBD against rotational changes on a sample matrix

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Fig. 11
figure 11

Sample face images of an individual and his average face image

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$$ {N}_{0{}^{\circ}}^1=\left\{{I}_{i,j-1},{I}_{i,j+1}\right\}, $$
(4)
$$ {N}_{45{}^{\circ}}^1=\left\{{I}_{i+1,j-1},{I}_{i-1,j+1}\right\} $$
(5)
$$ {N}_{90{}^{\circ}}^1=\left\{{I}_{i+1,j},{I}_{i-1,j}\right\} $$
(6)
$$ {N}_{135{}^{\circ}}^1=\left\{{I}_{i+1,j+1},{I}_{i-1,j-1}\right\} $$
(7)
$$ {N}_{180{}^{\circ}}^1=\left\{{I}_{ij+1,j},{I}_{i,j-1}\right\} $$
(8)
$$ {N}_{225{}^{\circ}}^1=\left\{{I}_{i-1,j+1},{I}_{i+1,j-1}\right\} $$
(9)
$$ {N}_{270{}^{\circ}}^1=\left\{{I}_{i-1,j},{I}_{i+1,j}\right\} $$
(10)
$$ {N}_{315{}^{\circ}}^1=\left\{{I}_{i-1,j-1},{I}_{i+1,j+1}\right\} $$
(11)

where N10°, N145°, N190°, N1135°N1180°, N1225°, N1270°, N1315° denote the directional neighbor sets for α = 0°, 45°, 90°, 135°, 180°, 225°, 270° and 315° respectively. For k = 2, the neighbor sets are defined as in the following which is depicted in Fig. 5 as well.

$$ {N}_{0{}^{\circ}}^2=\left\{I{\hbox{'}}_{i,j-2},{I}_{i,j-1},{I}_{i,j+1},I{\prime}_{i,j+2}\right\}, $$
(12)

where

$$ I{\hbox{'}}_{i,j-2}= mean\left({I}_{i-1,j-2},{I}_{i,j-2},{I}_{i+1,j-2}\right), $$
(13)
$$ I{\hbox{'}}_{i,j+2}= mean\left({I}_{i-1,j+2},{I}_{i,j+2},{I}_{i+1,j+2}\right), $$
(14)
$$ {N}_{45{}^{\circ}}^2=\left\{{I}_{i+2,j-2},{I}_{i+1,j-1},{I}_{i-1,j+1,}{I}_{i-2,j+2}\right\} $$
(15)
$$ {N}_{90{}^{\circ}}^2=\left\{I{\hbox{'}}_{i+2,j},{I}_{i+1,j},{I}_{i-1,j},I{\hbox{'}}_{i-2,j}\right\}, $$
(16)

where

$$ I{\hbox{'}}_{i+2,j}= mean\left({I}_{i-1,j-2},{I}_{i,j-2},{I}_{i+1,j-2}\right), $$
(17)
$$ I{\hbox{'}}_{i-2,j}= mean\left({I}_{i-1,j+2},{I}_{i,j+2},{I}_{i+1,j+2}\right), $$
(18)
$$ {N}_{135{}^{\circ}}^2=\left\{{I}_{i+2,j+2},{I}_{i+1,j+1},{I}_{i-1,j-1},{I}_{i-2,j-2}\right\} $$
(19)
$$ {N}_{180{}^{\circ}}^2=\left\{I{\hbox{'}}_{i,j+2},{I}_{i,j+1},{I}_{i,j-1},I{\hbox{'}}_{i,j-2}\right\} $$
(20)
$$ {N}_{225{}^{\circ}}^2=\left\{{I}_{i-2,j+2},{I}_{i-1,j+1},{I}_{i+1,j-1},{I}_{i+2,j-2}\right\} $$
(21)
$$ {N}_{270{}^{\circ}}^2=\left\{I{\hbox{'}}_{i+2,j},{I}_{i+1,j},{I}_{i-1,j},I{\hbox{'}}_{i-2,j}\right\} $$
(22)
$$ {N}_{315{}^{\circ}}^2=\left\{{I}_{i-2,j-2},{I}_{i+1,j+1},{I}_{i-1,j-1},{I}_{i+2,j+2}\right\} $$
(23)

As clearly recognized from Eq. (13–14) and Eq. (17–18), when k > =2, mean pixel values I’i,j-2, I’i,j + 2 for α = 0° and I’i + 2,j, I’i-2,j for α = 90° are calculated by taking into account the predecessor and successor pixels in the specified direction (Fig. 6). Because, four main directions were identified angularly and these pixels were located on the search lines, thus, they had to be included in an angular pattern.

3.2 k-hop directional local information encoding

In this study, gradient (∇) is used to express the relationship among the pixels. Up to now, research studies have considered only two situations, increasing or decreasing relative pixel shifts. Thus, binary representation has been sufficient to express the two states. However, the situation that there is no intensity change between the two consecutive pixels should also be considered and taken into account during pattern calculation. In this study, besides the intensity changes, we also consider the steady state where ∇ = 0. Furthermore, a threshold value is defined to alleviate the effects of external factors such as noise. That is, intensity changes lower than the threshold value will be ignored and defined as the steady state. Besides, previously studies ordinarily consider the relationship between the reference pixel (Ii,j) and its successor (Ii,j + 1) or predecessor (Ii,j-1) (for α = 0°). However, a more discriminative descriptor is achieved by considering the relationship between the reference pixel and both its predecessor and successor pixels. Thus, nine alternative patterns emerge as a result of this multi-state relationship consideration. Multi-valued (ternary) representation is utilized to handle this large number of states. The applied encoding methodology for 1-hop neighborhood is as follows:

Let, In is the intensity value of the reference pixel, and \( {I}_{n-1}^{\alpha } \), \( {I}_{n+1}^{\alpha } \) denote the intensity values of the predecessor and successor pixels in the specified direction (α) respectively,

$$ {\nabla}_n^{s,\alpha }={I}_{n+1}^{\alpha }- In- thr $$
(24)
$$ {\nabla}_n^{p,\alpha }={I}_{n-1}^{\alpha }- In- thr $$
(25)

where \( {\nabla}_n^{s,\alpha } \) and \( {\nabla}_n^{p,\alpha } \) denote the gradient values through angle α respectively. The corresponding multi-valued pattern for the specified direction is defined according to Table 1:

Table 1 Multi-valued codes depending on the value of ∇
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where →, ↑, ↓ denote 0, positive and negative gradients respectively. Multi-valued codes (\( {C}_{i,j}^{\alpha } \)) for each direction, namely, α = 0°, 45°, 90°, 135°, 180°, 225°, 275° and 315° are calculated according to Table 1. Following this, the ultimate multi-valued pixel code (pixcode) \( {C}_{i,j}^{k, thr} \) is defined by addition of the eight distinct\( {C}_{i,j}^{\alpha } \) in radix 3.

$$ {C}_{i,j}^{k, thr}={C}_{i,j}^{0{}^{\circ}}\left(+\right)3\ {C}_{i,j}^{45{}^{\circ}}\ \left(+\right)3\kern0.50em {C}_{i,j}^{90{}^{\circ}}\ \left(+\right)3\ {C}_{i,j}^{135{}^{\circ}}\ \left(+\right)3\ {C}_{i,j}^{180{}^{\circ}}\ \left(+\right)3\ {C}_{i,j}^{225{}^{\circ}}\ \left(+\right)3\ {C}_{i,j}^{270{}^{\circ}}\ \left(+\right)3\ {C}_{i,j}^{315{}^{\circ}} $$
(26)

where (+)3 stands for the arithmetic addition operation in radix 3 and of which the truth table is given below:

X/Y

0

1

2

0

0

1

2

1

1

2

0

2

2

0

1

3.3 Back-to-binary conversion and scaling

The basic LBP and some of its variants do only consider the relationship between the reference pixel and its neighbors. However, the information concealed in the magnitude of the difference is being discarded in this way. Because of that, it is possible to arise the challenge of two pixels with different intensities having identical values in the new domain. The most proficient way of handling this situation is to take into account the value of the reference pixel by scaling the resulting decimal pixcode value by the intensity value of the reference pixel. Figure 7 illustrates the challenge of having the same binary patterns for pixels with different intensities and how our method handles this situation.

In DLGBD, the next step after calculation of pixcodes is the conversion and scaling of those multi-valued pixcodes to uint8 type values in order to maintain operations in the 8-bit gray-scale domain. The conversion of pixcodes back to the 8-bit grayscale domain is done as follows:

$$ {B}_{C_{i,j}^{k, thr}}=\left({\sum}_{l=0}^{l=D-1}{D}_l\times {r}^{l-1}\right)\times \left({I}_{i,j}\right)\times \left(255/2040\right) $$
(27)

where r denotes the radix. 255 is the maximum gray-level intensity value and 2040 is the maximum value that can be calculated as the result of multiplication of the maximum two-digit ternary number (22)3 and 255. These values are used to scale the result into the interval [0–255] and find the ultimate DGBLD(i,j).

Figure 8 illustrates the applied methodology on a sample sub-region of an image for 1-hop neighborhood:

4 Experimental results

Several experiments are conducted to evaluate and compare the performance of DLGBD with the against a number of state-of-the-art methods on the face recognition task using five benchmark databases, namely Face94 [29], ORL [48] JAFFE [32], Yale (http://vision.ucsd.edu/content/yale-face-database). Sample images retrieved from the mentioned databases are presented in Fig. 9.

Some preprocessing operations are applied to each image to provide the uniformity. Each image is firstly scaled to the size 64 × 64. Following the scaling stage, to eliminate the effect of redundant background and foreground factors, the face extraction is done by using the Viola Jones [57] algorithm.

The performance analysis of the proposed framework is performed in two folds. In the first step, the stability and resistance of the method against rotational, illumination changes and noise effects are clarified. Later, the recognition performance of the proposed method is analyzed and compared to the the-state-of-art methods such as LBP, LDP, LDNP (Local Directional Number Pattern), Gabor Features, HoG (Histogram of Gradients), LTP, LTetP (Local Tetra Pattern) [52] and LDrvP (Local Derivative Pattern) [61] by conducting extensive simulations. Experiments are executed on MATLAB 2017b running on the computer system with the specifications Intel CORE i7-5500 U 2.4 GHz processor and 8 GB RAM.

4.1 The stability analysis

As mentioned previously, rotational changes, variation of illumination and noise significantly affect the recognition performance. Thus, the proposed local descriptor and the overall architecture should not fail under challenging circumstances and keep robust in order to accomplish the recognition task satisfactorily. In advance, it is illustrated how the proposed local descriptor stands robustly against the rotational changes. Following this, the performance analysis is conducted to verify the resistance of DLGBD against illumination variations by extensive simulations. The last part in this section demonstrates the analysis results of the simulations done to see the behavior of DLGBD under varying noisy circumstances.

4.1.1 Rotation-variation resistance analysis

A robust texture descriptor should behave stable and produce similar features even the original image is rotated, because the content of the image does not change and it belongs to the same individual. Thus, it is important to show and verify the behavior of the proposed method when the image is suffered to rotational variations. Figure 10 depicts the stability performance of DLGBD. In Fig. 10, a sample matrix, which symbolizes a block of an image is demonstrated. As depicted in the figure, the local descriptor content that is extracted from the block does not change even the matrix is rotated 90° counter clockwise.

The rotation resistance performance analysis of DLGBD is done and compared to the other methods in two-folds. Firstly, without any training, similarity analysis is done by examining the chisq distances between the rotated image of an individual and the remaining images of the same individual. During the search stage, if the image, that has the minimum chisq distance with the rotated image, belongs to the same individual, then a true-positive situation occurs (a hit state). On the contrary, if labels of the matched image and the image being searched are not identical then a false-positive situation occurs (a miss state). Table 2 gives the results of matching rates belonging to DLGBD and other methods, on different databases. Obviously, DLGBD performs far better than any other method in terms of finding the right face without training.

Table 2 The matching rates by considering the similarities without any training (TP, FP refers to the TruePositive and FalsePositive respectively)
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In the second step, the face recognition performance analysis is done by committing training for each method on each database. During the training phase, half of the training data is rotated and given to the training algorithm. By this way, the system is being trained by both the rotated and non-rotated images of the individuals and intended to match a rotated test image with the correct individual. Table 3 clarifies the classification results of DLGBD and other methods as a result of supervised training. Again, DLGBD shows promising performance in terms of recognition accuracy even under the circumstance of rotational variation.

Table 3 The classification accuracy performances as the result of supervised training
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4.1.2 Noise resistance analysis

The second important factor that affects the recognition performance of a method is the noise. In order for a method to be considered as high performance in terms of face recognition accuracy, it must be able to react strongly to the noise factor and not be affected by noise. As have been done in previous studies that have been proposed thus far, the salt-pepper and Gaussian noise have been applied artificially on the images on each database. Following, the similarity analysis is done between the original and noisy images of an individual on each database. The similarity analysis is done by examining the correlation between feature sets of the salt-pepper noisy and non-noisy versions of the face images. Also, as a second step of salt-pepper noise effect analysis is done by investigating the correlation between the histograms of the feature sets belonging to the noisy and non-noisy images.

The second noise resistance analysis is made upon involving the Gaussian noise. The Gaussian noise with different variance (σ2) values are exposed to the images in each dataset. As in the salt-pepper noise effect analysis, the similarity and correlation values are measured between the images and their Gaussian noise suffered versions. As clearly expressed by Tables 4, 5, 6 and 7, the similarity between the histograms of the noisy-image-feature sets and non-noisy-image-feature sets that are produced by DLGBD are high when compared to the other methods. This proves the robustness of DLGBD against noise such as salt-pepper and Gaussian.

Table 4 The values of correlation between the feature sets of salt-pepper noisy and non-noisy images
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Table 5 The values of correlation between the histograms of the feature sets of salt-pepper noisy and non-noisy images
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Table 6 The MSE values between the feature set of a non-noisy image (CASPEALR1) and feature sets of its Gaussian noisy versions
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Table 7 The correlation values between the feature set of a non-noisy image (CASPEALR1) and feature sets of its Gaussian noisy versions
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4.2 The recognition performance analysis

In order to accurately measure and analyze the performance of the proposed framework and compare to the state-of-the-art methods in the area, the hold out testing is utilized. That is, if there are N images of an individual in a dataset, %80 of these and the average image of them are used for training. The rest are used for testing. While forming the average face image, the images of each individual are inherently aligned by considering the eyes of the individual. An exemplary average face calculation of an individual is given in Fig. 11:

The recognition performance analysis of DLGBD is done in two ways: 1- Training-based recognition performance analysis 2- Similarity-based recognition performance analysis.

4.2.1 Training-based recognition performance analysis

At this stage, the supervised learning method has been utilized while classifying. %80 of each individual in each dataset is used for training and the remaining images of the individuals are utilized for testing. Table 8 shows the performance results of DLGBD and the-state-of-the-art methods in terms of recognition accuracy. As it can be seen in Table 8, DLGBD performs promisingly well when compared to other methods in terms of classification accuracy analysis using supervised learning. DLGBD performs remarkably even on the challenging datasets CAS-PEAL-R1, JAFFE and ORL.

Table 8 The recognition performance results regarding supervised training
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4.2.2 Similarity-based recognition performance analysis

At this stage, recognition performance of DLGBD and the-state-of-the art methods are done by implementing similarity analysis between the feature sets of the images. That is, the feature set of the image that is being searched is calculated and then compared to the feature sets of each image in the dataset. If the tag of the most similar image found matches up with the tag of the image that is being searched, that shows a hit (true-positive), otherwise a miss (false-positive). Table 9 figures out the recognition accuracy performances of each method on each dataset. As clarified in the table, DLGBD competes with the other methods even on the challenging datasets without any training that is without any knowledge.

Table 9 The recognition performance results regarding similarity analysis
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5 Conclusion

In this paper, a novel Directional Local Gradient Based Descriptor (DLGBD) for image retrieval is presented. The proposed method extracts local gradient-based patterns in terms of direction-dependent neighbors. The relations between the pixels are handled in four directions. The local neighborhood comprises the pixels at most k-hop away. The population of the neighborhood differs due to the value of k. The neighbors of a reference pixel are categorized according to their angular position relative to that pixel. Since using larger number of threshold values increases the computational cost of the algorithm and at the same time it does not preserve the high recognition rates we used threshold value not more than five. The experimental results demonstrate that the proposed descriptor achieves promising scores and outperforms the state-of-art methods in terms of classification accuracy. Besides its favorable recognition performance, DLGBD also handles the effects of rotational variances and noise affects very successfully when compared to the state-of-the-art methods. As a future work, it is intended to examine how multi-spectral evaluation and dynamic neighborhood size depending on some criteria can contribute to the recognition performance of the method.