A Teacher-Learning-Based Optimization Approach for Blur Detection in Defocused Images

Abstract

Defocus blur is often encountered in images taken with optical imaging equipment. It might be unwanted, but it might also be a deliberate artistic effect, which means it might help how we see the scenario in an image. In specific applications like image restoration or object detection, there may be a need to divide a partially blurred image into its blurred and sharp regions. The effectiveness of blur detection is influenced by how features are combined. In this paper, we propose a parameter-free metaheuristic optimization strategy known as teacher-learning-based optimization (TLBO) to find an optimal weight vector for the combination of blur maps. First, we compute multi-scale blur maps, i.e., features using an LBP-based blur metric. Then, we apply a regularization scheme to refine the initial blur maps. This results in a smooth, edge-preserving blur map that leverages structural information for improved segmentation. Lastly, TLBO is used to find the optimal weight vectors of each refined blur map for the linear feature combination. The proposed model is validated through extensive experiments on two benchmark datasets, and its performance is comparable against five state-of-the-art methods.

1. Introduction

In the domain of image analysis and computer vision, defocus blur is a significant challenge that can greatly impact the quality and practical applications of captured images. This type of blur is principally generated by the limitations of optical imaging systems, where the camera lens fails to bring all elements of a scene into focus. The result is a loss of image sharpness, particularly evident in regions that should ideally be delineated. Defocus blur not only compromises image aesthetics but also undermines subsequent computational tasks, such as semantic segmentation [1], object recognition [2], and object tracking [3]. The ongoing research in defocus blur detection and correction aims to improve the robustness and accuracy of digital imaging systems, thereby expanding their applicability in various domains including medical imaging [4], autonomous vehicles [5], and augmented reality [6]. In digital photography, large-aperture lenses are used to create defocus blur, which helps to soften the background and emphasize the primary subject. Nevertheless, this blurring effect can inhibit computational image analysis by hiding useful background details important for interpreting the scene. Therefore, it may be crucial to segregate the image into blurred and sharp areas. This enables us to selectively apply post-processing or restoration methods without affecting the in-focus regions, while also ensuring that image features are only gathered from distinctly delineated regions.

The majority of current image deblurring techniques assume that the blur is spatially invariant [7,8,9,10]. These methods usually estimate a single blur kernel to reconstruct the original image, exploiting various image priors through maximum posteriori estimation. However, some approaches consider that blur can vary spatially; these typically deblur small sections of the image, treating the blur as uniform within each section, and then combine these deblurred patches. Accurate identification of blurred and non-blurred areas has several useful applications, such as (1) preventing unnecessary computational work on areas that are already sharp; (2) enhancing artistic effects like bokeh in computational photography, especially for smartphones with high-depth-of-field cameras; and (3) aiding in object recognition tasks, especially when not all parts of the object are in-focus, by either assisting in the accurate extraction of image features or serving as an additional cue to locate the object within the frame.

In the domain of defocus blur detection, features play a pivotal role. For the last few years, numerous local and global features of blur have been proposed [11,12,13,14,15,16]. Features may be integrated in either a linear or nonlinear way to construct an effective blur map. There are many ways to combine features linearly by adjusting their relative significance of learning optimal weights. Metaheuristic algorithms, namely, constrained particle swarm optimization [17] and biogeography-based optimization [18], have been applied for feature combination. The drawbacks of these optimization algorithms include parameter tuning and being computationally expensive. The algorithm’s performance lacks robustness across diverse image sets because the parameters are optimized based on a training set that may not be representative of different types of images. The secondary challenge revolves around the construction of the fitness or cost function, which is defined on the basis of the desirable characteristics of a blur map such as the uniformity and compactness of defocus blur at different scales, ranging from local patches to more global regions.

In order to address the concern specified above, we proposed a novel blur detection method that used a meta-heuristic algorithm called teaching-learning-based optimization (TLBO). It is parameter-free and exhibits a high degree of efficacy in identifying the optimal weight vector through a linear combination of diverse image features, with the aim of improving blur detection [19]. In the proposed scheme, first, multi-scale blur maps (BM) of an input image are assessed using a blur measure operator. In our case, we used the local binary pattern-based operator [20] for computing the initial blur maps. In the second phase, regularization is applied to refine the blur maps. In the third phase, the refined blur maps are combined using the TLBO scheme. The blur map is then segmented to separate the blur and non-blur regions of the input images.

The subsequent sections of this paper are structured as follows. Section 2 offers a concise overview of cutting-edge defocus blur detection techniques. The model we propose is delineated in Section 3. Section 4 delves into the experimental setup; analysis; and comparative analysis of results with other state-of-the-art methods. Finally, Section 5 brings the paper to a close with conclusions and directions for future research.

2. Related Work

In the literature, we studied hand-crafted approaches for defocus blur detection. To handle defocus blur analysis, many frequency- and gradient-based methods have been proposed [21,22,23]. Initially, a technique for local blur estimation was introduced by Elder [24] using information from the first and second-order derivatives. Later, several other approaches were suggested for identifying and estimating defocus blur. Pan [25,26] utilized a gradient-based method that depended on the fact that blurring inherently diminishes the intensity of image gradients. As a result, the gradient distribution in an unblurred area is more likely to have elements with extreme values, also known as heavy-tail components. The blur metric designed by Su et al. [27] is based on a singular-value feature for each pixel and also integrates an alpha channel gradient distribution pattern for blur detection.

Frequency-based defocus blur detection methods leverage the principle that an image in focus contains a higher proportion of high-frequency elements compared to an image that is out of focus. Therefore, the number of high-frequency components in a specific section of an image can serve as an indicator of its sharpness. Ali et al. [28] introduce a method for detecting varying levels of blur across different areas of an image. Their approach utilizes a fusion of high-frequency multi-scale elements along with a sort transform applied to gradient magnitudes, allowing them to assess the degree of blur at individual locations within the image. Shi [29] addresses representations of blur features in gradient local filters, image gradients, and Fourier domains to perform blur detection in images. Moreover, Tang [30] obtains a coarse blur map by using a blur metric that is based on the log-averaged spectrum residual. Couzinie [31] introduces a framework for minimizing multi-label energy in order to represent local blur estimators and their associated smoothness. Shi [32] utilizes sparse representation and image decomposition to directly link sparse edge representation with the estimation of blur intensity. Yi [20] presents a sharpness metric for defocus blur segmentation relying on the uniform distribution of local binary patterns in an in-focus and out-of-focus region in an image. In spite of the effectiveness of hand-crafted approaches in some situations, these methods fall short of providing reliable results in more complex scenes. Recently proposed non-deep/machine learning based methods are summarized in [33,34]. In a more recent method [35], the idea of indirectly reflecting the local sharpness of the lens is used according to the image blur detection, and an image blur assessment method is developed based on intensity and derivative (IDD). In [36], a method is presented based on singular value decomposition (SVD) features, and the defocus blur map is constructed from the sparse defocus blur map by the Matting Laplace algorithm. In [37], a model-independent method is presented for local blur-scale estimation. Various statistical test criteria involving maximal likelihood functions are used to test the hypothesis is that based on Gaussian distribution.

Owing to their advanced feature extraction and learning capabilities, deep CNN-based methods have set new benchmarks in numerous computer vision tasks [38,39,40,41] and defocus blur detection [42,43]. A CNN-based model [42] is employed to extract high-dimensional deep features. These features are then combined with traditional handcrafted features, and the combined set is input into a fully connected neural network classifier to determine the degree of defocus. In [44], a robust 6-layer CNN for blur detection is introduced, which optimizes its efficiency through null filter removal and feature sampling. Purohit et al. [45] suggest training two distinct sub-networks to capture global context and local features. The combined pixel-level probabilities from both networks are then integrated into an MRF framework for segmenting blur regions. Zhang et al. [46] employs a dilated FCNN, complemented by pyramid pooling and boundary layers, to create blur maps. Understanding the scale-dependent nature of defocus blur, Zhao et al. [43] developed BTBNet, a multi-stream convolutional network that fuses together low-level indicators with broader semantic data. Its dual-stream structure intensifies computational demands during training and testing, yet some low-contrast regions remain elusive. In a recent method [47], a pair of reversible defocused homogeneous regions from mutual guidance networks (MGMs) were generated, and then the depth information and RGB features were used to learn the defocus blur homogeneous regions. In another recent method [48], an adaptive multi-supervised network comprising a feature extraction module, a feature fusion network (FFN), and a Multi-scale Channel Attention Module (MCAM) were proposed to improve the blur detection in the de-focused images. Li, Huaguang et al. [49] proposed a multi-interactive scheme that could gradually learn the characteristics of degraded input defocus blur, and then feature interactive modules were introduced to achieve the information interaction between different features. In another work [50], a mutual-referenced attack framework is designed based on a divide-and-conquer perturbation image generation model, where the focus region attack image and defocus area attack image are generated. A mutual-referenced feature transfer (MRFT) model is used for feature integration and improving attack performance.

3. Proposed Method

The steps in the proposed method are illustrated in Figure 1. First, we compute multi-scale blur maps (BM) of an input image by using a blur measure operator. In the second step, regularization is applied on each map to refine the blur maps. In the third step, a teaching-learning-based optimization (TLBO) scheme is used to obtain the resultant blur map by combining the blur maps linearly. Finally, the resultant blur map is segmented to split the regions characterized by blurriness and sharpness.

3.1. Multi-Scale Blur Maps

Let $I\left(\mathit{z}\right)$ be a defocused blur image, where $\mathit{z}=(z_1,z_2)$ represents the pixel coordinates. We compute multi-scale blur maps using a sharpness metric based on local binary patterns proposed in [20]. The LBP codes for a pixel $I_c$ are defined as:

$$\begin{array}{cc}\hfill {\mathrm{LBP}}_{Q,R}\left(I_c\right)& =\sum _{q=0}^{Q-1}S(I_q-I_c)·2^q\hfill \end{array}$$

(1)

$$\begin{array}{cc}\hfill S\left(a\right)& =\left\{\begin{array}{cc}1\hfill & \mathrm{if}\left|a\right|\ge \tau \hfill \\ 0\hfill & \mathrm{if}\left|a\right|<\tau ,\hfill \end{array}\right.\hfill \end{array}$$

(2)

where $Ic$ is the intensity of the central pixel; $I_q$ corresponds to the intensities of the Q pixels located on a circle of radius R centered at $I_c$; and $\tau$ is a small, positive threshold. For the $3\times 3$ neighborhood, $Q=8$ and $R=1$. For computing the sharpness metric, only uniform patterns are utilized. A pattern is uniform if the circular sequence of bits contains no more than two transitions from one to zero, or zero to one. Thus, the multi-scale blur maps ${\eta }_s\left(\mathit{z}\right)$ are computed as,

$${\eta }_s\left(\mathit{z}\right)=m_{\mathrm{LBP}}^{\left(s\right)}\left(I\left(\mathit{z}\right)\right)={\displaystyle \frac{1}{s}}\sum _{i=6}^{9}I\left({\mathrm{LBP}}_{8,1}^{\mathrm{riu}2}\left(i\right)\right),$$

(3)

where $I\left({\mathrm{LBP}}_{8,1}^{\mathrm{riu}2}\left(i\right)\right)$ is the number of rotation invariant uniform 8-bit LBP patterns of type i, and $s\in \{s:s=2l+1\times 2l+1\},l\in \{5,6,...n\}$ represents the scale, i.e., the total number of pixels in the selected local region.

3.2. Regularization

The initial blur maps may contain inconsistencies with respect to the level of sharpness or blurriness. In [20], authors use the alpha matting algorithm to enhance the initial blur maps. As alpha matting is computationally expensive method, instead, we propose a regularization approach to enhance the initial blur maps and reduce the blur inconsistencies. For this, we adopted the regularization scheme presented in [51]. A regularized blur map ${\widehat{\eta }}_s\left(\mathit{z}\right)$ for the initial blur map ${\eta }_s\left(\mathit{z}\right)$ can be obtained by iteratively solving the following linear system:

$$\widehat{{\mathsf{\eta }}_s}={\left(\mathit{I}+{\lambda }_s{\mathit{L}}_s\right)}^{-1}{\mathsf{\eta }}_s,$$

(4)

where $\mathit{I}$ denotes an identity matrix of dimensions $v\times v$, i.e., v is the total number of pixels in the map; ${\mathit{L}}_s$ represents a sparse, spatially varying matrix; and ${\lambda }_s$ is the default parameter. Both $\widehat{\mathsf{\eta }}$ and $\mathsf{\eta }$ are column vectors of dimensions $v\times 1$ representing the regularized ${\widehat{\eta }}_s\left(\mathit{z}\right)$ and the initial blur map ${\eta }_s\left(\mathit{z}\right)$. For optimization, we have used the default parameters for all maps as mentioned in paper [51].

3.3. Teaching-Learning-Based Optimization

Once we have multi-scale regularized blur maps ${\widehat{\eta }}_s\left(\mathit{z}\right)$, then the problem is how to combine them to obtain an optimal map for further processing. The regularized blur maps can be considered as features; our goal is to find the optimal weight vector $y_1^{*},y_2^{*},\dots ,y_n^{*}$ for each pixel in blur maps, and it must satisfy the constraint ${\sum }_{i=1}^n{y}_i^{*}=1$, where n is the number of weights (dimension of the weight vector), to combine the features. For this purpose, we propose the use of teaching-learning-based optimization (TLBO) [19]. It is a metaheuristic population-based optimization algorithm. The algorithm operates independently of any specific tunable parameters, preventing the need for parameter adjustments during its implementation. The hyperparameters such as population size p and variables n are predefined, which can affect the accuracy and complexity of the TLBO scheme. The algorithm starts by generating an initial random population $\mathit{Y}=\{{\mathit{y}}_1,{\mathit{y}}_2,\dots ,{\mathit{y}}_P\}$, where each individual ${\mathit{y}}_m=\{y_1,y_2,\dots ,y_n\}$ is a real-valued vector representing a feasible solution to the problem at hand. To obtain an optimal weight vector for combining the blur maps, the fitness value is maximized; thus, the optimization problem is defined as follows:

$${\mathit{y}}^{*}=\underset{\mathit{y}}{max}\mathrm{fitness}\left(\mathit{Y}\right),$$

(5)

where the fitness of the whole population $\mathit{Y}$ is evaluated for the optimal weight vector. The algorithm employs two phases to update the individuals: the Teacher Phase and the Learner Phase. The best-performing individual in the current population is designated as ${\mathit{y}}_t$. The mean vector $\overline{\mathit{y}}$ of the current population is calculated. Each individual is updated by moving its position towards the teacher based on the difference between the teacher and the mean vector $\overline{\mathit{y}}$. A teaching factor $t_f$ (randomly chosen; either 1 or 2) and a random number in the range $r(0,1)$ are also utilized during this update. If the updated position ${\mathit{y}}_w$ yields a better fitness score, it replaces the current individual’s position. In the Learner Phase, each individual ${\mathit{y}}_m$ is compared with a randomly selected other individual ${\mathit{y}}_j$. If ${\mathit{y}}_j$ is better, ${\mathit{y}}_m$ moves towards it; otherwise, it moves away from it. The new position ${\mathit{y}}_k$ is accepted only if it has a better fitness score than the original ${\mathit{y}}_m$. The algorithm proceeds through these iterations until it reaches a maximum number of iterations $itr$. For handling constraints, the algorithm employs the heuristic [52] constrained handling method, where the constraints are added in the data fidelity term to formulate the objective function. In our case, the objective function $F(\mathit{y},{\widehat{\eta }}_s\left(\mathit{z}\right))$ that takes a weight vector and the input features (regularized blur maps) is defined as,

$$F(\mathit{y},{\widehat{\eta }}_s\left(\mathit{z}\right))=f(\mathit{y},{\widehat{\eta }}_s\left(\mathit{z}\right))+p(\mathit{y},{\widehat{\eta }}_s\left(\mathit{z}\right))$$

(6)

where $f(\mathit{y},{\widehat{\eta }}_s\left(\mathit{z}\right))$ refers to the data fidelity term, and $\mathit{y},{\widehat{\eta }}_s\left(\mathit{z}\right)$ serves as the penalty function or constraints.

The data fidelity term provides a good guess of the blur map, and it is computed by applying the weight vector ${\mathit{y}}_m$ on the input features. In other words, the data fidelity term is simply a weighted sum of all the blur maps and can be defined as,

$$f(\mathit{y},{\widehat{\eta }}_s\left(\mathit{z}\right))=\sum _{i=1}^n{y}_i\times {\widehat{\eta }}_i\left(\mathit{z}\right).$$

(7)

In a good blur map, regions with a significant amount of blur should exhibit minimal values, whereas sharply focused areas should register maximum values. Moreover, the blur detection map should uniformly highlight the areas with a certain level of blur and delineate them clearly from sharply focused regions. In order to maintain all the aforementioned attributes of a quality blur map, we have formulated the constraints as described below:

$$\begin{array}{cc}\hfill p(\mathit{y},{\widehat{\eta }}_s\left(\mathit{z}\right))& =g(\mathit{y},{\widehat{\eta }}_s\left(\mathit{z}\right))+h(\mathit{y},{\widehat{\eta }}_s\left(\mathit{z}\right))\hfill \end{array}$$

(8)

$$\begin{array}{cc}\hfill g(\mathit{y},{\widehat{\eta }}_s\left(\mathit{z}\right))& =\sqrt{{\left({\displaystyle \frac{\partial \mathit{f}(\mathit{y},{\widehat{\eta }}_s\left(\mathit{z}\right))}{\partial z_1}}\right)}^2+{\left({\displaystyle \frac{\partial \mathit{f}(\mathit{y},{\widehat{\eta }}_s\left(\mathit{z}\right))}{\partial z_2}}\right)}^2}\hfill \end{array}$$

(9)

$$\begin{array}{cc}\hfill h(\mathit{y},{\widehat{\eta }}_s\left(\mathit{z}\right))& ={\left|{\displaystyle \frac{{\partial }^2\mathit{f}(\mathit{y},{\widehat{\eta }}_s\left(\mathit{z}\right))}{\partial z_1^2}}+{\displaystyle \frac{{\partial }^2\mathit{f}(\mathit{y},{\widehat{\eta }}_s\left(\mathit{z}\right))}{\partial z_2^2}}\right|}^2\hfill \end{array}$$

(10)

where function $g(\mathit{y},{\widehat{\eta }}_s\left(\mathit{z}\right))$ computes the gradient magnitude for each pixel in the combined blur map (data fidelity term) and the function $h(\mathit{y},{\widehat{\eta }}_s\left(\mathit{z}\right))$ computes the high-frequency energy of the combined blur map by using the Laplacian operator. The fitness score $fitness\left(\mathit{y}\right)$ for the individual (weight vector) is computed by collecting all of the values from the data fidelity term and the constraints.

$$\begin{array}{c}\hfill fitness\left(\mathit{y}\right)=\sum _{z_1}\sum _{z_2}f(\mathit{y},{\widehat{\eta }}_s\left(\mathit{z}\right))+\sum _{z_1}\sum _{z_2}g(\mathit{y},{\widehat{\eta }}_s\left(\mathit{z}\right))+\sum _{z_1}\sum _{z_2}h(\mathit{y},{\widehat{\eta }}_s\left(\mathit{z}\right)).\end{array}$$

(11)

In this context, the goal is to find the optimal $\mathit{y}*$ weight vector that maximizes the fitness value of a potential solution. The procedure and steps for the TLBO scheme for combining blur maps are illustrated in Algorithm 1.

Algorithm 1: Pseudo-code for the teaching-learning-based optimization scheme for optimal weight vector for combining multi-scale blur maps.

1: Initialize the population size: $P=50$, iteration: $itr=50$, variable size: $n=8$, bounds of variables: $U_B=1$, $L_B=0$, blur maps: ${\widehat{\eta }}_s\left(\mathit{z}\right)$  2: $\mathit{Y}\leftarrow$ generate population $(P,n)$  3: Compute fitness ($\mathit{Y}$) based on fitness score  4: $r\leftarrow rand(0,1)$  5: while iter $=1:itr$ do  6:     Teacher Phase  7:     for $\mathrm{m}=1:P$ do  8:         $t_f=round[1+rand(0,1)\{2-1\}]$  9:         ${\mathit{y}}_w={\mathit{y}}_m+r·({\mathit{y}}_t-(t_f·\overline{\mathit{y}}))$ 10:         Compute (${\mathit{y}}_w$) based on fitness score 11:         if $fitness\left({\mathit{y}}_w\right)<fitness\left({\mathit{y}}_m\right)$ then 12:            ${\mathit{y}}_m={\mathit{y}}_w$ 13:         end if 14:         Learner Phase 15:         $j\leftarrow random\left(p\right)\{m\ne j\}$ 16:         if $fitness\left({\mathit{y}}_m\right)<fitness\left({\mathit{y}}_j\right)$ then 17:            ${\mathit{y}}_k={\mathit{y}}_m+r·({\mathit{y}}_m-{\mathit{y}}_j)$ 18:         else 19:            ${\mathit{y}}_k={\mathit{y}}_m+r·({\mathit{y}}_j-{\mathit{y}}_m)$ 20:         end if 21:         Compute(${\mathit{y}}_k$) based on fitness score 22:         if $fitness\left({\mathit{y}}_k\right)<fitness\left({\mathit{y}}_m\right)$ then 23:            ${\mathit{y}}_m={\mathit{y}}_k$ 24:         end if 25:     end for 26: end while 27: return best_individual(${\mathit{y}}^{*}$); so far

3.4. Blur Map

Lastly, an improved blur map is derived from the linear combination of regularized blur maps. Utilizing the TLBO optimization algorithm, the proposed approach obtains an optimal weight vector ${\mathit{y}}^{*}=\{y_1^{*},y_2^{*},\dots ,y_n^{*}\}$. Thus, the final blur map $\tilde{\eta }\left(\mathit{z}\right)$ is calculated as follows:

$$\tilde{\eta }\left(\mathit{z}\right)=\sum _{i=1}^n{y}_i^{*}\times {\widehat{\mathsf{\eta }}}_i.$$

(12)

Finally, the improved and the resultant blur map is segmented into blurred and sharp areas using a threshold,

$$\left\{\begin{array}{cc}0,\hfill & \mathrm{if}\tilde{\eta }\left(\mathit{z}\right)<{\tau }_2\hfill \\ 1,\hfill & otherwise\hfill \end{array}\right.$$

(13)

where ${\tau }_2$ is the threshold computed by applying Otsu’s method [53]. This method finds a threshold value that lies between two peaks of histograms of the final blur map.

4. Results

4.1. Experimental Setup

The effectiveness of the suggested approach is evaluated using two standard datasets, namely, CUHK [29] and DUT [54]. CUHK contains 704 images, each labelled for ground truth blurry regions, spanning a variety of real-world scenes. The DUT-DBD dataset includes 500 images, each annotated at the pixel level, accompanied by their corresponding ground truth data. These images include both blurred and sharp regions, varying in resolution and sourced from the internet. The images present in these datasets include various elements such as people, vehicles, artificial structures, and other living entities. The images in the DUT dataset are more challenging as many of the images contain uniformly blurred regions, complex backgrounds, and low contrast levels. The image dimensions in the CUHK dataset vary, ranging from sizes of $640\times 640$ down to $640\times 295$ pixels, and the dimensions of images in the DUT dataset are $320\times 320$ for most of the images. The performance of the suggested methodology can be assessed through qualitative and quantitative evaluations of to these images. The quantitative measures of precision, recall, and F-measure are calculated after applying segmentation. The precision and recall can be defined as,

$$\mathrm{Precision}={\displaystyle \frac{R\cap R_{gt}}{R}}$$

(14)

$$\mathrm{Recall}={\displaystyle \frac{R\cap R_{gt}}{R_{gt}}}$$

(15)

where R represents the pixel set in the segmented blurred region and $R_{gt}$ is the pixel set in the ground truth blurred region. Similarly, the weighted harmonic mean [55], or F-measure, of precision and recall was computed for comparison of the results. The definition of F-measure is as follows:

$$\mathrm{F}\text{-}\mathrm{measure}={\displaystyle \frac{(1+{\beta }^2)\times \mathrm{precision}\times \mathrm{recall}}{{\beta }^2\times \mathrm{precision}+\mathrm{recall}}}$$

(16)

where $\beta$ is the weight.

4.2. Ablation Study

In order to analyze the performance of our optimization algorithm, we performed the ablation study. In the first experiment, blur maps for the selected images from the CUHK dataset are computed and the results for the intermediate stages for computing the blur maps are analyzed. First, the initial blur maps are computed; then, these maps are refined through alpha matting [56], guided filter [57], robust regularizer [51], and the proposed method. The results are shown in Figure 2. It can be observed that the proposed method has provided more improvement compared to the other comparative methods. In our approach, blur maps are linearly combined using a parameter-free metaheuristic teaching-learning-based optimization (TLBO) algorithm [19]. We evaluated the blur map with the ground truth map and note several key observations: (i) the emphasis on sharp object areas, (ii) consistent highlight across regions, and (iii) distinctive quality between blurred and sharp areas. Our model outperforms in all qualitative evaluations, producing a superior blur map on a range of challenging natural images compared to other techniques. Notably, our approach yields a blur map that consistently highlights sharp regions, effectively suppresses the blurred regions, and distinctly differentiates between the sharp and blur, more so than two comparable meta-heuristic strategies C-PSO [17] and BBO [18]. Our learning-based algorithm produces different final blur maps with $m_{\mathit{LBP}}$, alpha matting, guided filter, and robust regularization. Yi’s metric has difficulty in differentiating between sharp smooth regions and blurred smooth areas because it only takes into account a limited local neighborhood size. When the source of blurriness is defocused, the LBP-based sharpness metric is only capable of detecting defocus blur. We have another type of blurriness like that caused by substandard camera lenses, in-scene motion, out-of-focus blur, or depth of field. The alpha matting algorithm ends up producing a matte that fails to separate the foreground and background elements at their edges. This can manifest as rough or jagged boundaries, misplaced pixels that should belong to either the foreground or background but are incorrectly categorized. The guided filter does not perform well when the edges are not well-defined or are too intricate, which results in smudged or unclear edges. Our proposed method not only maintains a smooth texture but also effectively preserves most of the defined structural edges.

Similarly, in the second experiment, blur maps for the selected images from the DUT dataset are computed and the results for the intermediate stages of computing the blur maps are analyzed. First, initial blur maps are computed, and then these maps are refined through alpha matting [56], guided filter [57], robust regularizer [51], and the proposed method. The resultant maps are shown in Figure 3. The proposed method is more effective compared to others, and similar conclusions can also be drawn here.

In addition, we have also conducted a quantitative evaluation in terms of precision, recall, and F-measure scores, as illustrated in Figure 4. In this experiment, methods are applied on all the images in the CUHK and DUT datasets. First, initial blur maps are computed; then, these maps are refined through alpha matting [56], guided filter [57], robust regularizer [51], and the proposed method. From the resultant maps, metrics for precision, recall, and F-measure are computed for each image. Finally, the average scores are taken for each method for comparison. It can be observed that the performance of the proposed method is better compared to other methods. Our approach demonstrates a notable gain in recall and F-measure against Yi’s LBP blur metric, alpha matting, and guided filter. However, our method has demonstrated comparable efficacy to the guided filter and alpha matting on defocus blur detection datasets CUHK and DUT, respectively, as measured by precision. The precision score in both datasets is slightly lower in Figure 4 due to uncertainty in detecting sharp regions during the refinement of the blur maps.

4.3. Comparative Analysis

To investigate the effectiveness of the proposed method, we compared the outputs obtained from the proposed method with five state-of-the-art methods. For instance, Yi [20] proposed a sharpness metric by using rotation-invariant uniform local binary patterns and a defocus blur segmentation algorithm to distinguish between sharp and blurred areas. Shi [32] formed a sparse feature representation of an image segment by utilizing a pre-trained dictionary, aiming to detect subtle yet noticeable blur. Vu [58] combined spectral and spatial based sharpness map by using a weighted geometric mean. A spatially varying blur is computed with the fusion of multi-scale Discrete Cosine Transform (DCT) by Ali [28] to exploit the difference in the frequency domain for sharp and blurred image regions. Chen [59] generated a defocus map by using SLIC [60] over-segmentation to produce superpixels and for calculating the similarity between these superpixels.

In the first experiment, blurred segmented results for the selected images from the CUHK dataset are computed by using Yi [3], Ali [51], Shi [29], Chen [59], Vu [58], and the proposed method. The visual results are shown in Figure 5. The outputs from these methods are grayscale images, with higher pixel intensity signifying increased sharpness. To analyze the qualitative performance, the final segmented maps computed by each method are shown in Figure 5. It can be observed that the segmented maps in row 4, row 6, and row 7 computed through the methods of Ali [51], Chen [59] and Vu [58], respectively, are far from the ground truth and of poor quality. Almost all of the comparative methods failed to obtain a reasonable segmented map for the image in the last column, whereas the proposed method has obtained a segmented map closer to the ground truth. It can also be observed that our optimized blur maps are adequately smooth and the majority of the sharp, structural edges are effectively maintained. Consequently, the refinement in the quality of blur maps yields a notable elevation in performance metrics at the segmentation stage. Hence, the proposed method is more effective at detecting and segmenting the blur compared to other methods.

In the second experiment, blurred segmented results for the selected images from the DUT dataset are computed by using Yi [3], Ali [51], Shi [29], Chen [59], Vu [58], and the proposed method. The visual results are shown in Figure 6. The outputs from these methods are grayscale images, with higher pixel intensity signifying increased sharpness. To analyze the qualitative performance, the final segmented maps computed by each method are shown in Figure 6. It can be observed that the method of Chen [59] has provided the worst results. The methods of Ali [51] and Vu [58] have also provided segmented maps of lower quality. The method of Yi [3] has provided reasonable segmented maps; however, on boundaries, discrepancies are visible. The visual results provided by the proposed method are adequately smooth, and the majority of the sharp, structural edges are effectively maintained. Consequently, the refinement in the quality of blur maps yields a notable elevation in performance metrics at the segmentation stage. Hence, it can be concluded that the proposed method is more effective at detecting and segmenting the blur compared to other methods.

In addition to the qualitative results, an experiment is also performed for quantitative comparison in terms of precision, recall, and F-measure. In this experiment, methods Yi [3], Ali [51], Shi [29], Chen [59], Vu [58], and the proposed method are applied on each image of the CUHK and DUT datasets. The resultant segmented maps are compared with the ground truths, and three quantitative measures precision, recall, and F-measure are computed. The average values of these quantitative measures are shown in Figure 7. Our method achieves comparative performance across all metrics on both datasets. The performance of our algorithm on CUHK in terms of precision, recall, and F-measure achieves better performance than other comparable methods. However, the performance of our method is close to Yi on the DUT dataset in terms of precision, as indicated in Figure 7, while the recall score is higher than other methods on the DUT dataset. This validates the efficiency of the proposed approach when dealing with images that are complex and pose significant challenges.

4.4. Computational Cost Analysis

In order to estimate the time taken by different phases of the proposed method, we use the system with the specifications such as X64 bit-based PC, 12th generation Intel Core i9-11900K processor, and having 32 GB RAM. The proposed method consists of three phases. In the first phase, multi-scale initial blur maps are generated. For this purpose, we use the LBP-based operator for the input images of size $300\times 400$. For a multi-scale map, the window-size varies from $11\times 11$ to $25\times 25$ and the time taken is increased by increasing the window size. We computed times $0.34,0.36,0.39,0.42,0.45,0.53,0.58,0.62$ in seconds for window sizes $11\times 11,13\times 13,15\times 15,17\times 17,19\times 19,21\times 21,23\times 23,25\times 25$, respectively. For the second phase, regularization is applied, and for this the average time is computed as 0.28 s, which is much less than the Alpha Matting algorithm [20], which is $0.87$ s. For the third phase, TLBO is applied to combine the maps to obtain a single improved map.

The time taken by the TLBO algorithm depends on the values for hyper-parameters such as the number of iterations and the population size. In the

Table 1. Time taken in (seconds) by teacher-learning-based optimization (TLBO) for different numbers of iterations and population sizes.

Population			Iterations
Size	1	20	50	100	150
50	0.2	1.8	4.2	8.2	11.9
100	0.3	2.5	8.3	16.2	24.1
150	0.5	5.2	12.4	24.1	36.1

, the time taken for various scenarios are provided. It can be observed that the time taken by the TLBO algorithm increases as the number of iterations and the population sizes are increased. To obtain reasonable results for different images, the average time taken for the population size 50 with 50 iterations to merge 8 maps is $4.2$ s, which is better than the Multi-Scale Inference [20] method, which takes $8.7$ s for merging 3 maps. It can be concluded that the computational complexity of the proposed method is comparable to existing methods.

5. Conclusions

In this paper, we propose an efficient, parameter-less meta-heuristic feature combination algorithm called teaching-learning-based optimization (TLBO) for combining blur maps. First, multi-scale blur maps are generated using a specific blur metric, and these maps are then refined. A fitness function is formulated to compute the optimal weight vector for combining these refined blur maps. These optimal weight vectors are subsequently used to linearly combine the maps. To evaluate the efficacy of our proposed approach, we conducted comprehensive tests on two standard datasets. We compared our method’s performance against that of five state-of-the-art blur detection techniques. Our experimental findings indicate that our model either outperforms or is comparable to other methods. In the future, we will explore additional effective optimization algorithms and efficient fitness functions capable of managing the combination of features in complex images. Additionally, we intend to investigate robust feature selection strategies that can enhance the performance of defocus blur detection.