Statistical Model for the Quality of Panoramic Images of 2D Artifacts

Abstract

The field of digital imaging emphasizes the quality of 2D artifact images, often facing challenges when capturing large images due to their wide field of view. A successful technique for addressing this is panoramic image creation, which involves merging overlapping segments from a larger image. Research in this domain focuses on understanding the visual quality aspects of panoramic images. This study aims to achieve two main objectives: firstly, to identify the key visual quality attributes associated with panoramic images, and secondly, to propose predictor variables for a statistical model that assesses the quality of 2D artifact panoramic images. To accomplish this, the researchers conducted a case study centered on generating panoramic images of mural paintings found in Sri Lankan temples. Through their investigation, they pinpointed color balance and noise & distortion as the most significant factors influencing the overall quality of these images. The researchers employed three methods to create the panoramas: an innovative technique, alongside two established methods—Photoshop and Hugin. Experts in Visual Arts evaluated the resulting images using a four-point Likert scale. Color balance and noise & distortion were used as predictor variables, while overall quality was the response variable. The gathered data underwent analysis using ordinal logistic regression within the Minitab statistical package. The outcomes underscored the pivotal roles of color balance and noise & distortion in determining the quality of panoramic images. Moreover, the findings showcased the model’s high accuracy in fitting the data, reinforcing its effectiveness in assessing panoramic image quality.

1. Introduction

It was identified that there are less amount of research works in Sri Lanka in the area of digitization of 2D artifacts for conservation. It was able to find out a report written by Schmid [1]. It talks about the main points such as the mission background & the objectives, identification of issues and draft strategy for conservation. According to the report, it had been mentioned that Central Cultural Fund (CCF) and Department of Archeology (DOA) requested international expert in conservation for the evaluation of the condition of Sigiriya Paintings in Sri Lanka. The report presents about the discussion of main issues of Sigiriya paintings such as lack of documentation, need for monitoring, creation of a permanent record through 3D laser-scanning, Protection against rainwater, preliminary scientific investigation and documentation, emergency stabilization, construction of new visitors’ platforms and reduction of number of visitors to the painting pocket. It is proposed some actions and precautions to rectify above issues. Digitization of all existing written and visual documentation and creation of simple computer repository of the existing documentation were proposed as some of the actions for above issues in the area of digital technology [1]. Quality aspect of the digitization process is an important research area. There were different notions related to image quality in the past. In response to the lack of a unified view on image quality, considerable effort was dedicated to imposing structure on the existing concepts. This led to the development of image quality theory, which was first introduced in 1988 [2]. Originally conceived as a four-way approach, this theory has evolved into what is now known as the “image quality circle.” This robust framework effectively organizes the diverse range of ideas that contribute to the understanding of image quality. As a result, it serves as a valuable process model, streamlining and directing research, product development, marketing, and technology-related endeavors. The image quality circle can be diagrammatically shown as shown in the Figure 1.

Figure 1.

Image quality circle.

There are four major components in this circle and those components are linked via one another by three links called, System/Image Models, Visual Algorithms and Image Quality Models. Technology Variables encompass the fundamental elements that can be controlled by imaging designers to alter the existing quality of an image. These variables encompass factors such as paper parameters, toner size, dots per inch (resolution) and other relevant aspects. Physical Image Parameters are quantitative and it can be any measurable aspect of an image. Further, Physical image parameters are called objective measures of image quality. One approach is applying the process of image quality metrics to measure the quality of the image with reference to the full or partial reference of the original image. Structural similarity index matrix (SSIM) and peak signal-to-noise ratio (PSNR) are two examples for quality matrix. There is no limit for this physical image parameters except that they need to be physical and measurable. Customer perceptions are derived with a set of perceptual attributes of image quality, mostly visual, that form the basis of the quality preference or judgment by the customer. Some of the examples are darkness, sharpness, and graininess. Quality Ratings to the images given by customers refers to the comprehensive evaluation of image quality provided by them based on their judgment. This rating is represented on an interval scale, allowing for the expression of overall image quality as either a numerical value or a qualitative descriptor, such as “excellent”, “good” or “bad”. The authors conducted a research in which they generated panoramic images using three different methods: a novel method and two other existing methods. Experts in the field of Visual Arts assessed the visual quality of the created images. Subsequently, statistical models were developed using the ordinal logistic regression technique in the Minitab statistical package. The predictor variables and response variables from the collected data set were utilized in the creation of these models for the three methods. The results clearly indicate that the statistical model derived from the novel method outperformed the other two methods in terms of accuracy. These findings demonstrate that two crucial attributes significantly influence the quality of panoramic images, as supported by the highly accurate model. As a result, the proposed statistical model can be employed in any application that involves the generation of digital images with 2D artifacts.

2. Research problem

In the background exploration, it has been identified the importance of conservation of two-dimensional artifacts in the Asian countries [3]. There are two notions in this field of research as preservation and conservation of valuable artifacts. Preservation involves safeguarding cultural property by implementing measures that effectively minimize physical and chemical decline of the damage [4]. Through such proactive actions, the loss of informational content can be effectively averted [5]. The UNESCO [6] definition says.

“In the domain of cultural property, the aim of conservation is to maintain the physical and cultural characteristics of the object to ensure that its value is not diminished and that it will outlive our limited time span”. The term “digital preservation” encompasses a range of methods aimed at ensuring the longevity of digital materials well into the future, as stated by the Council on Library and Information Resources [7]. This concept focuses on the sustainable management and accessibility of digital resources over time.

According to this definition, digital preservation is the management and maintenance of digital objects such as manuscripts, maps, rare books and other significant cultural materials. These digital objects can be accessed and used by future requirements. Further, it is required to study the theory and philosophy of conservation and explore the basis and framework of conservation, restoration, preservation theory and practice in the globalized world [8]. Therefore, conservation represents a more expansive domain, constituting a dedicated profession aimed at safeguarding cultural property for the benefit of future generations. The scope of conservation activities encompasses several important aspects such as examination, documentation, treatment, and preventive care, all of which are bolstered by extensive research and education efforts [5]. This comprehensive approach ensures the enduring preservation and appreciation of valuable cultural assets.

It is a known fact that there are several types of valuable artworks in Sri Lanka which are needed to be conserved for the archeological aspect of next generation. It has been observed that various techniques are used for conservation of those artifacts in most of the places like Colombo museum, some historical temples in Sri Lanka such as Bellanwila Rajamaha viharaya, Kelani Rajamaha Viharaya and Sapugaskanda Rajamaha Viharaya. At the analysis of the methods applied for the conservation of valuable artifacts in those places, it can be understood that maintaining the quality of artifacts is a critical factor. In this context, identification of techniques to study the quality will be an important research area. Accordingly, Authors have identified that the problem of this research is “Statistical Model for the Quality of Panoramic Images of 2D Artifacts”.

3. Literature review

3.1 Literature review on the creation of panoramic images of 2D artifacts

Author was able to critically review several researches done in different countries by analyzing the techniques used by them such as panoramic image creation. At the analysis, it was found that panoramic image creation is an application of image stitching technology [9, 10, 11, 12]. Authors have identified that image stitching as the main technique of 2D image digitization [13, 14]. Sruthi et al. explain the idea of panorama image creation. There are two main techniques for image stitching as direct method and feature based method. Further, it talks about the approach and a specific method, called scale invariant feature transform (SIFT) for detecting local features in an image. After finding local features, overlapping areas are identified. Using dynamic programming method, a minimal cost path is selected to stitch images. Here, seven steps were used for the process of developing a panoramic image. By cutting at the overlapping places, images are merged together to form the final panorama image [15]. This research uses a scientific method for creation of a panorama image. Kokate et al. present the idea of image mosaicing based on feature extraction. It explains the idea of panoramic image production. Two approaches, direct and feature based techniques are discussed in this paper. Further, the difference between those two approaches are discussed. Components of image stitching are discussed as calibration, registration and blending. Steps of feature-based image stitching are discussed in detail. This paper talks about two concepts called local feature descriptor and feature detector. Accordingly, two techniques for describing local feature descriptor such as SIFT and speeded up robust features (SURF) are discussed in this paper by analyzing the individual pixels of the images. Harris corner detector is described as a feature detector with the technical details. RANSAC algorithm is used as the Homography detection algorithm in that research [12]. This research supports to understand the idea of local feature descriptor and the techniques for feature detection. It talks about two approaches with the comparison of the suitability rather than just applying a particular technique. Ultimately, better approach is selected for image stitching. This comparison helps Authors to analyze the suitability of a particular technique rather than using one technique directly in the stitching process within the research. Wu et al. discuss about the applications of SIFT in different fields, such as machine vision, image retrieval and image stitching. This paper systematically analyzes SIFT and its variants [16]. Parallax is a displacement or difference in the apparent position of an object along two different views. Lens distortion is the appearance of straight lines as curved lines inward or outward to the center of the object. Scene motion is the visible lines of moving objects in a photograph. Exposure is the amount of light per unit area reaching to a frame of a photographic film. Ebtsam et al. present the idea of panoramic image creation. It talks about a different aspect, called field of view and how it affects for panoramic image creation. As there is a difference of the field of view between the human visual system and a typical camera, a requirement arises to get several pictures from a camera and stitch them to form a composite image with a much larger field of view. This paper aims to provide a comprehensive survey of feature-based image stitching. It covers the primary components involved in image stitching and presents a framework for a complete image stitching system based on feature-based approaches. By exploring these key aspects, this study seeks to offer valuable insights into the field of image stitching and its applications.

According to this research, there are many feature descriptors such as SIFT, SURF, Histogram of oriented gradients (HOG), Gradient Location and Orientation Histogram (GLOH), Principal Component Analysis SIFT (PCA-SIFT), Pyramidal HOG (PHOG), and Pyramidal Histogram of Visual Words (PHOW). Some of them are described in detail. Finally, the current challenges of image stitching process have also been discussed in this paper [17]. This paper uses a methodical approach. Actually, it elaborates the concept of feature-based techniques with more details. Levin and Weiss introduce the idea of having a quality panorama image by the evaluation of the techniques used for image stitching. Then, it explains how to measure the quality of image stitching. The focus of this study lies in two main areas: first, evaluating the similarity of the stitched image to each of the input images, and second, assessing the visibility of the seam between the stitched images. To achieve these objectives, an approach must be adopted that ensures the stitched image is as similar as possible to the input images both geometrically and photometrically, while simultaneously ensuring the seam between the stitched images remains imperceptible. This dual aspect approach aims to enhance the overall quality and seamlessness of the final stitched image.

It had been presented several cost functions for these requirements and define the mosaic image as their optimum [18]. Mikolajczyk and Schmid proposed a method to compare the performance of descriptors for local interested regions. It was calculated for different image transformations such as rotation, scale change, view point change, image blur, JPEG compression and illumination change. Further, experiment was done for the interest region descriptors in the presence of real geometric and photometric transformations. At the experiment, GLOW (Gradient Location and Orientation Histogram) obtains the best results followed by SIFT [19]. Balntas et al. have identified and demonstrated that the existing dataset and evaluation protocols regarding the benchmark have led to the inconsistency in results in the literature. So they have proposed a new public benchmark for local descriptors. They have mentioned that the new benchmark would enable the community to gain new insights since it is more significantly large than any existing dataset in the field [20]. Maponga presents that the image stitching has a lot of researches in area of medical imaging, computer vision, satellite imaging and video conferencing. It talks about two main approaches: direct method and feature-based method. Direct approach utilizes all the pixels of the image but it has disadvantages such as quite inflexible and greatly affected by exposure differences of the same object in different images to be stitched. Furthermore, it is undesirable for real time applications as it performs slowly. Feature-based technique performs better depending on what exactly feature-based technique was implemented. Several techniques such as SIFT, SURF and PHOW were discussed. Advantages and Disadvantages were discussed [21]. Khan et al. Present that the concept of Image Mosaicing is currently a vibrant and dynamic research area within the realms of computer vision and computer graphics. It encompasses a wide array of diverse algorithms focused on detecting and describing features in images. These algorithms play a crucial role in the development and advancement of Image Mosaicing techniques, contributing to the exploration of new possibilities in visual representation and synthesis.

In this paper, it is studied image stitching technique called SIFT algorithm which is rotation, scale invariant as well as more effective in presence of noise. However, it needs high computational time. Additionally, the paper examines the SURF algorithm, which demonstrates robustness in terms of execution time and illumination invariance. Another algorithm explored is ORB, which exhibits rotation and scale invariance and boasts improved execution time. However, its performance tends to degrade in the presence of noise [22]. Patil and Gohatre present various techniques for the process of image stitching under various light conditions. Results obtained show that for the day light condition SIFT works better and for night light condition it is shown that Harris /Hessian detector performs better than SIFT detector [23]. There are different application areas of image stitching such as remote sensing which are applied for the domains of agriculture and natural disaster. Further, the application of remote sensing images becomes much widespread with the development of satellite technology [24].

Williams et al. discuss about post-processing solutions for creating quality digital images by combining captured portions of objects. Further, some alternative approaches such as robotic systems and some linear array scanners that are moved through the large images by stitching image components were also discussed. Even though they are high accurate, they are high expensive systems. This paper talks about digitization environment which affects the post-processing for the stitching procedure. Furthermore, it elaborates basic operations for image stitching and some software tools that can be used for panorama creation [9]. This paper is more important in terms of getting idea for alternative approaches for image stitching. It is really important to consider the digitization environment and the software tools which can be used for panorama creation in this research. Sarlin et al. have presented a new way to think about the feature matching problem. In most of the above applications, methods have been used by using local feature detecting and matching for stitching technique. But, in this paper, idea has been changed to use novel neural network architecture to learn the matching process from pre-existing local features [25].

3.2 Literature review on statistical data analysis: categorical data analysis

Statistics can be used for the analysis of data in the nature of quantitative and qualitative. Statistical methods are used by researchers to analyze data, present the results and interpret them in the particular domain [26]. Statistical analysis is a crucial process behind how we make discoveries in the areas such as science, social science. Further, it will lay the foundation to make decisions based on the results, and make predictions. This allows us to understand a subject area much more deeply. It was researched to identify a suitable method to develop a quality model for the panoramic images. Accordingly, regression model in statistics [27] was identified as one of the suitable models. A categorical variable is characterized by a measurement scale that comprises a defined set of categories. In this type of variable, data points are grouped into distinct, non-numeric categories rather than continuous numerical values.

Accordingly data type that can be applied as categorical variable is defined as the categorical data [28, 29]. Ordinal variable is one of categorical data type which has a natural ordering. Some of the examples are: level of a course (high, medium and low), overall quality of an art work (excellent, good, average and poor). Categorical data can be analyzed using regression model in statistics. It was researched to identify a suitable method to develop a quality model for the panoramic images. Logistic regression was identified as a suitable method to find the significance of independent and dependent variables of the statistical model [30].

4. Research methodology

This research methodology covers technical details related to five key areas. It includes a research of the essential attributes of panoramic images for visual quality, the process of capturing mural paintings and creating panoramic images from them, the implications of testing panoramic image creations using existing methods, the proposal of a new method for panoramic image development, and the subjective evaluation of the quality of the created panoramic images. These areas are thoroughly discussed within this study.

4.1 Research on quality attributes of panoramic images

Figure 2 illustrates how to create panoramic images by stitching a series of overlapped image components. Image quality (IQ) models which is set up to quantify the overall image quality usually consist of a sub-set of quality attributes (QA) [31, 32, 33, 34, 35, 36]. Therefore, the number of selected QAs is a very important step. Therefore, an issue exists between the accuracy of selected quality attributes (QAs) and the quantity of available QAs. Additionally, when the model exhibits high dimensionality, it leads to a more comprehensive evaluation of image quality (IQ), encompassing numerous aspects but also increasing complexity [37, 38]. On the other side, having too few QAs might result in inaccurate estimation of quality. So, selecting the most accurate set of QA will be the crucial task in this scenario. Accordingly, Authors researched on a set of image attributes that would contribute a quality panoramic image output [2, 31, 35, 36, 37]. It was well studied the underline theory of creating panoramic images, called image stitching. During the literature review, attention was drawn to the challenge of fully automated panoramic image stitching, and it discussed two categories of techniques prevalent in the research: direct and feature-based approaches [39, 40]. These categories represent distinct methods employed to tackle the task of seamlessly stitching panoramic images. According to Szeliski, it has been explained how the image stitching techniques evolved from the past up to the modern level of techniques and what are the millstones in the techniques developments which were resulted to enhance the quality of the panorama creation process [10]. It is worth emphasizing that the primary challenges associated with panorama creation include the presence of seams, the blurring effect caused by parallax, lens distortion, scene motion, and exposure variations among the panoramas. This clarification underscores the key factors that contribute to the overall quality and potential issues encountered during the process of creating panoramas [10, 41]. Based on the investigation, it was observed that noise, distortion and color balance emerged as the three primary quality attributes (QAs) with high significance in the domain of panoramic images [42]. Additionally, noise and distortions were found to be closely intertwined, forming a combined factor during the evaluation of the visual quality of digital images on display. Consequently, for the purpose of evaluation, these two factors were treated as a single entity.

Figure 2.

Steps of research on quality attributes for panoramic images.

4.2 The process of capturing mural painting and developing panoramic images of mural paintings

In this process, it was identified the requirement of photo shooting a set of historically valued 2D artifacts. Considering the traditional value of the artifacts, three temples having large-scale murals were selected for the research as a real-world case study. Further, it was ensured to cover different nature of artifacts to avoid the homogeneity. Subsequently, it was required to acquire a series of overlapped image components of the same image for creation of panoramic images of selected 2D artifacts. In this task, there are three different image acquisition methods which are covered large-scale mural paintings in the context of panoramic image development. There are three distinct setups used for capturing images in panorama creation. In the first setup, the camera is mounted on a tripod, and images are acquired by rotating the camera. On the other hand, the second setup involves placing the camera on a sliding plate, and images are obtained by moving the camera along the sliding plate. The last setup differs from the previous two setups, as it involves holding the camera in a person’s hands. In this setup, images are captured by either rotating around a fixed spot or by walking in a direction perpendicular to the camera’s viewing direction (Figure 3).

Figure 3.

Developing a statistical model of predictor variables for the quality of panoramic images of mural paintings.

In all three set-ups, a still image digital camera or a smart phone embed with digital camera can be used to capture images. In this case study, majority of 2D artifacts which are existing in these traditional temples are in flat shape. Therefore, planner panorama images will have to be developed in this process. Further, authors wanted to use a simple approach which can be managed easily in the regular monitoring process of the conservation activities. So, third set-up is applied in this research which camera is held in a person’s hands and the images are captured by walking in a direction perpendicular to the camera’s view direction while ensuring the overlapping image components to avoid stitching issues.

4.3 Implications of the testing of panoramic image creations using existing methods

The purpose of this testing is to get the idea of developing panoramic images in different areas of digital images and the behavior of the final outputs of panoramic images with respect to color balance, noise and distortion quality attributes using different software tools. Accordingly, it was designed an experiment for this evaluation. Three types of digital images were selected and two types of available software which supports panoramic image creation were used for observing the quality and behavior of final outcomes. This testing was done for three types of image categories: existing 2D digital image set, 2D captured digital images set of an artifact and 2D captured digital image set of murals. Even though, several software tools were identified in the field, majority of them are expensive tools and are not available in the market for normal or academic purpose. Accordingly, two software tools: Photoshop (available in the market) and Hugin (an open software downloaded from internet) were used for testing the stitching technique under the above three testing cases.

By looking at the testing results, it was identified that there were some drawbacks and quality issues of the created panoramas in the areas of color balance, noise & distortion and overall quality for the selected three cases.

4.4 Proposing a new method for the development of panoramic images

Image stitching algorithm is used for the development of panoramic images. It was researched on a flexible and efficient mechanism to implement computer vision algorithms. Then, it was able to identify, OpenCV [43] that supports many algorithms related to computer vision and machine learning. According to the literature review, SIFT algorithm has been justified as a suitable algorithm for robust, reliable, efficient and quality output at the stitching operations for creating panoramas in area of 2D artifact even with noise and distortion. Based on the findings, it was identified that stitcher class in OpenCV software library is having stitching pipeline very similar to the algorithm proposed by Matthew and David [39]. Matthew and David has proposed their algorithm including the detection of SIFT features of images for panorama creation efficiently. Accordingly, stitcher class was selected for the implementation of the proposed algorithm. As authors have planned to use Python programming language, OpenCV-Python library was used in this implementation as Python bindings designed to solve computer vision problems.

4.5 Subjective evaluation for the quality of created panoramic images

To create panoramic images, the authors captured a series of digital image portions, meticulously covering selected large murals in the temples. Each captured portion was stored separately during the image acquisition process. The authors opted to create an odd number of panoramic image sets for each method, specifically generating five sets as part of this research.

Accordingly, 5 × 3 panoramic images were obtained in this process. In the case of panoramic images, no original digital images are available for the reference [44]. So, objective evaluation IQ matrix cannot be used. Furthermore, esthetic aspect is very important in the context of artifact quality evaluation. As it is known, objective evaluation IQ matrix does not incorporate this factor at the evaluation. Accordingly, subjective evaluation is selected for this research for the evaluation of panoramic images using the quality attributes: color balance, noise & distortion with the overall quality of the panorama.

In this experiment, participants selected for evaluation were specifically chosen from the field of visual arts to ensure a comprehensive understanding of individual perceptions regarding quality attributes. A total of 15 experts from the faculty of visual arts were selected to participate in the evaluation process. The panel of experts were individually presented with sets of panoramic images using three distinct software tools. They were then asked to assess the quality attributes of each image, including color balance, noise & distortion, as well as overall quality. For color balance and overall quality, the experts used the following rating scale: Excellent (E), Good (G), Average (A), and Poor (P). The rating scale for noise & distortion consisted of the following options: No noise (N), Average (A), High (H), and Too Much (T). After the evaluation was completed, a qualitative dataset was obtained based on the assessments made using the three different methods.

The authors conducted research to determine a suitable regression model for this specific type of data and found that the ordinal logistic regression method could be effectively applied to assess the significance of independent and dependent variables in the statistical model [27]. Subsequently, they performed regression analysis using ordinal logistic regression and introduced a set of predictor variables for a statistical model aimed at evaluating the quality of panoramic images of mural paintings through a novel, more accurate approach [28, 29, 45, 46, 47].

5. Results and discussion

5.1 Statistical data analysis: categorical data analysis for the data set obtained using new method

The primary objective of this research is to identify a comprehensive set of predictor variables to be incorporated into a statistical model for evaluating the quality of panoramic images depicting mural paintings. To accomplish this, an ordinal logistic regression model was utilized, taking into account the presence of four distinct ordered categories for the data, namely Excellent, Good, Average, and Poor. The evaluation process involved the utilization of the Minitab statistical package. Following statistical data analysis shows the testing of the level of significance of selected quality attributes to the overall quality for a statistical model for the quality of panoramic images of mural paintings through the results of the panoramic images created using the new method. The link function is Logit. The results of this categorical data analysis comprises several tables which are explained below.

Table 1 presents the statistics of frequencies of responses for the overall quality of the generated panoramic images using the proposed method. The data is categorized into four ordered categories: Excellent, good, average, and poor, along with their corresponding total frequencies (count).

Variable	Value	Count
Overall Quality	Excellent	16
	Good	46
	Average	12
	Poor	1
	Total	75

Table 1.

Response information.

Table 2 presents the key statistics derived from the regression analysis conducted in this study. This analysis offers valuable insights into the relevance of color balance and noise & distortion categories concerning the overall quality of panoramic images. Notably, the P-values for the “Average” and “Good” categories of the color balance predictor variable are both 0.000. These values being less than 0.05 indicate statistically significant associations between the “Good” and “Average” color balance categories and the overall quality. Conversely, the P-value for the “Poor” category of the color balance predictor variable is 0.994, indicating that there is no statistically significant association between the “Poor” category and the overall quality.

Predictor	Coef	SE Coef	Z	P	Odds Ratio	95% CI
						Lower	Upper
Const(1)	1.55373	0.705252	2.20	0.028
Const(2)	7.78226	1.46466	5.31	0.000
Const(3)	44.7692	6276.88	0.01	0.994
Color balance
Good	−2.9638	0.807985	−3.67	0.000	0.05	0.01	0.25
Average	−6.6842	1.41653	−4.72	0.000	0.00	0.00	0.02
Poor	−43.377	6276.88	−0.01	0.994	0.00	0.00
Noise and distortion
Average	−1.8036	0.722281	−2.50	0.013	0.16	0.04	0.68
High	−19.593	4454.98	−0.00	0.996	0.00	0.00

Table 2.

Logistic regression table.

Log-likelihood = −35.545.

Moving on to the noise & distortion predictor variable, the P-value for the “Average” category is 0.013. Given that this P-value is smaller than 0.05, it indicates a statistically significant association with the overall quality. Conversely, the P-value for the “High” category of the noise & distortion predictor variable is 0.996, surpassing the significance threshold of 0.05. Consequently, it can be concluded that there is no statistically significant association between the “High” category of noise & distortion and the overall quality.

Furthermore, the results highlight significant relationships between certain predictor variables and the overall quality of panoramic images. Notably, both the “Good” and “Average” categories of color balance show statistically significant associations with the overall quality. Additionally, the “Average” category of noise & distortion also demonstrates a statistically significant relationship with the overall quality. These findings shed light on the factors that impact the overall quality perception of panoramic images.

In addition to the previous findings, the results presented in Table 3 provide further support for the presence of a predictor variable (either color balance or noise & distortion) that significantly influences the overall quality of panoramic images. This is evidenced by the G value of 71.937, which is notably large, and the P-value being less than 0.05. These findings suggest compelling evidence to conclude that at least one of the estimated coefficients of the predictor variable is significantly different from zero. Consequently, it can be inferred that either the color balance or noise & distortion (or both) play a crucial role in impacting the overall quality of the panoramic images.

DF	G	P-Value
5	71.937	0.000

Table 3.

Test of all slopes equal to zero.

Table 4 displays the results of the Goodness-of-Fit Tests. The computed Chi-square statistics for both the Pearson and Deviance methods are 8.82540 and 9.99793, respectively. Furthermore, the associated P-values for these methods are 0.976 and 0.953, respectively. It is noteworthy that these P-values exceed the significance threshold of 0.05. Consequently, it can be inferred that there is insufficient evidence to suggest that the model inadequately fits the data.

Method	Chi-Square	DF	P
Pearson	8.82540	19	0.976
Deviance	9.99793	19	0.953

Table 4.

Goodness-of-fit tests.

In Table 5, the measure of association between the response variable and the predicted probabilities is presented. The results indicate that 84.7% of the pairs show concordance, 3.2% are discordant, and 12.1% are tied pairs. These figures provide valuable insights into the relationship between the response variable and the predicted probabilities.

Pairs	Number	Percent	Summery measures	Value
Concordant	1316	84.7	Somers’ D	0.81
Discordant	50	3.2	Goodman-Kruskal Gamma	0.93
Ties	188	12.1	Kendall’s Tau-a	0.46
Total	1554	100.0

Table 5.

Measure of association.

These findings indicate a high degree of agreement within the predicted probabilities, suggesting that the model possesses a strong predictive ability. Additionally, the statistics of Somers’ D, Goodman-Kruskal Gamma (close to 1.0), and Kendall’s Tau-a further support the superior predictive capacity of the model. This implies a robust association between the response variable and the predicted probabilities.

The combined findings from Tables 3–5 offer further compelling evidence in favor of the proposed predictor variables, namely color balance and noise & distortion, for the statistical model designed to evaluate the quality of panoramic images of mural paintings, as demonstrated in Table 2. These results reinforce the effectiveness of the selected variables in capturing and assessing the overall quality of such panoramic images.

These results demonstrate a higher level of accuracy and reaffirm the suitability of the chosen predictor variables for the model.

5.2 Ordinal logistic regression analysis for the data set obtained using an existing method, Photoshop

This Table 6 provides insights into the significance of the color balance and noise and distortion categories in relation to the overall quality of panoramic images. The statistical analysis yielded the following P-values for the respective categories of the color balance predictor variable: 0.254 for “Good,” 0.897 for “Average,” and 0.184 for “Poor.” Moreover, the P-values for the “High” and “Too Much” categories of the noise & distortion variable are 0.182 and 0.028, respectively. These results indicate that, apart from the “Too Much” category of noise & distortion, which shows a P-value lower than 0.05, there are no statistically significant associations between any of the color balance or noise & distortion categories and the overall quality.

Predictor	Coef	SE Coef	Z	P	Odds ratio	95% CI
						Lower	Upper
Const(1)	−2.10231	1.42105	−1.48	0.139
Const(2)	2.10230	1.42105	1.48	0.139
Color balance
Good	1.72536	1.51106	1.14	0.254	5.61	0.29	108.53
Average	−0.188025	1.45311	−0.13	0.897	0.83	0.05	14.30
Poor	−2.08513	1.56892	−1.33	0.184	0.12	0.01	2.69
Noise & distortion
High	−0.975611	0.731260	−1.33	0.182	0.38	0.09	1.58
Too Much	−1.44111	0.656656	−2.19	0.028	0.24	0.07	0.86

Table 6.

Photoshop: Logistic regression table.

Log-Likelihood = −52.615.

5.3 Ordinal logistic regression analysis for the data set obtained using an existing method, Hugin

Table 7 displays the P-values for the “Poor”, “Average,” and “Good,” categories of the color balance predictor variables. They are equal and the value is 0.999. Additionally, the P-values for the “Average,” “High,” and “Too Much” categories of the noise & distortion variable are 0.360, 0.980, and 0.404, respectively. Since all the P-values in this table exceed the significance threshold of 0.05, it can be concluded that there are no statistically significant associations between any of the color balance or noise & distortion categories and the overall quality.

Predictor	Coef	SE Coef	Z	P	Odds ratio	95% CI
						Lower	Upper
Const(1)	−25.5821	26863.0	−0.00	0.999
Const(2)	−21.3436	26863.0	−0.00	0.999
Color balance
Good	23.0328	26863.0	0.00	0.999	1.00696E+10	0.00	*
Average	20.7671	26863.0	0.00	0.999	1.04486E+09	0.00	*
Poor	18.9467	26863.0	0.00	0.999	1.69215E+08	0.00	*
Noise & distortion
Average	1.92115	2.09863	0.92	0.360	6.83	0.11	417.54
High	−0.0533333	2.10786	−0.03	0.980	0.95	0.02	59.03
Too much	−1.81660	2.17684	−0.83	0.404	0.16	0.00	11.59

Table 7.

Hugin: Logistic regression table.

Log-Likelihood = −33.404.

5.4 Comparison of the ordinal regression analysis of already existing two methods with the proposed new method

According to the research done for the identification of critical attributes for the visual quality of the panoramic images, it was proofed that color balance and noise & distortion are two significant attributes in this context. It implies that there should be a possibility to generate a statistical model which describes color balance and noise & distortion, are crucial attributes affecting the quality of panoramic images.

Comparing three logistic regression tables related to the new method and the other two methods, the logistic regression table derived from the novel method provides evidence supporting the enhanced accuracy of the proposed predictor variables, color balance, and noise & distortion, for the statistical model used to evaluate the quality of panoramic images of mural paintings, as presented in Table 2. This reaffirms the effectiveness and validity of the selected variables in accurately assessing the overall quality of such panoramic images.

Therefore, this result shows the superiority of the new method compared to other two existing methods.

6. Conclusion

The authors are able to provide a solid justification for accomplishing their primary objectives of this study: to identify the visual quality attributes of panoramic images and to propose predictor variables for a statistical model aimed at assessing the quality of panoramic images of mural paintings.

The research encompassed a diverse selection of mural paintings, varying in terms of painting types and content complexity. These murals were situated on both the ceilings and walls of temples, exhibiting different orientations, including both vertical and horizontal shapes. The murals depicted a range of subjects, with some showcasing multiple objects and others featuring individual objects. As a result, a significant implication of this research is that the conclusions drawn can be applied to mural paintings of any type.

Furthermore, the study highlights an important consideration regarding the image capturing process. It emphasizes the need for careful attention to the level of overlap between consecutive image components and the maintenance of parallelism between the camera and the object. This ensures minimal noise & distortion while maximizing color balance. In terms of future enhancements, the research could be extended to encompass 3D artifacts to investigate potential variations in quality attributes and predictor variables within a 3D context.

Examining the regression analysis table using the novel method reveals key statistical findings within the logistic regression analysis. Specifically, it highlights the significance levels of color balance and noise & distortion quality attributes in relation to the overall quality of panoramic images. Notably, the P-values within this table indicate that both the “Good” and “Average” categories of the color balance predictor variable are recorded as 0.000. Given that these P-values are below the threshold of 0.05, the analysis indicates that statistically significant associations exist between the “Good” and “Average” categories of color balance and the overall quality of the panoramas.

In summary, the research effectively accomplishes its two main objectives: identifying the visual quality attributes of panoramic images and proposing predictor variables for a statistical model to evaluate the quality of panoramic images of mural paintings.