Video Stabilization Using Modified Blurriness Index Employing De-Blurring with Temporal Derivatives Using Motion Smoothing

Numerous strategies have been put forth by researchers to effectively stabilize video sequences. To produce stabilized videos, VS approaches are needed and are broadly classified in Figure 1 as global motion estimation, motion smoothing, and motion compensation algorithms. Either directly pixel-based methods or feature-based methods can be used to estimate global motion.

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Figure 1. Broad classification diagram of the VS methods

2.1 Review of feature based VS methods

There are many feature based VS methods available in the literature. Wang et al. [1] proposed to solve problems like camera jitter and visual distortion; video stabilization (VS) systems have undergone substantial evolution of motion decomposition method. Many researchers [2, 3] have employed SIFT features to eliminate the p additionally, an adjusted Chauvenet parameter is used in the method to identify and suppress outlier features, purposeful inter-frame motions by lining up the feature points. Luchetti et al. [4] devised a way for making 360 videos viewing more fluid and enjoyable for watching. To begin, the motions are produced employing an innovative approach that employs a Particle Swarm Optimization approach while accounting for the estimation of uncertainty among features. A modified Chauvenet parameter is also utilized to locate and suppress outlier features in the algorithm. The method appears to be a little hazy for different types of motion.

Lee et al. [5] stabilization process of the video signal plays a significant part in improving the clarity of the image. Early methods for recovering 2D or 3D frame motion in movies faced challenges owing to their reliance on feature tracking, which struggled with local feature mining and tracking in noisy environments. To address this stability issue, recent learning-based approaches have employed deep neural networks to identify frame transformations by using high-level information. In their work, Xu et al. [6] employed Features from Accelerated Segment Test (FAST) method to detect features in individual frames. Subsequently, a rapid binary descriptor based on Binary Robust Independent Elementary Features (BRIEF) was used to match the corresponding features between consecutive frames. The combination of aligned FAST and rotated BRIEF, known as ORB, is particularly effective for feature detection and matching and accelerating motion prediction without the need for hardware enhancement. Furthermore, an improved motion smoothing technique that utilizes linear models to smooth motion variables without requiring continuous global motion estimation is proposed. The speed of the feature-based approaches depends greatly on how well the feature point selection is done. There may be few good features in scenes that have inadequate texture, repetitive patterns, or severe blur, which might result in erratic tracking and subpar stabilization. Additionally, feature based methods may not be able to reliably capture complicated camera actions like zooming and rolling shutter distortion, which could result in errors affecting the stabilized footage. For predicting slow inter-frame motion, such as in handheld videos, direct pixel-based approaches are used.

2.2 Review of global direct video stabilization methods

Many VS methods use direct pixel based approaches. Rawat and Singhai [7] presented a comparative analysis of VS with different temporal derivatives. These derivatives include two- and four-point central differences and simple pixel difference approaches. It was observed that different derivatives responded differently to different occasions. Farid and Woodward [8] applied a direct pixel-based technique, which minimizes the quadratic error function for estimating motions via Taylor series expansion. Matsushita et al. [9] proposed a direct full-frame VS approach based on multilayer differential motion estimation. This technique employs motion-in-painting to provide a complete video frame. Choi et al. [10] proposed a novel method for real-time video stabilization that transforms shaky video into a video that is maintained as if it were stabilized in real time using gimbals. Our design can be trained without the use of particular equipment (such as two stereo cameras or additional motion sensors), as it can be trained without supervision. Our system comprises a transformation estimator between specified frames for modifications to the overall stability, then a scene motion control module using temporally normalized optical flow for greater stability.

Shi and He [11] evaluated various ME techniques used in VS, including mechanical and optical approaches. Their study focused on challenges in stabilizing video from handheld cameras, which are particularly susceptible to inadvertent movements. Barron et al. [12] have proposed a good 4-point central difference method for ME. The method is adopted in current research for VS applications. Pang et al. [13] have used a dual tree-based wavelet transform application for VS. An extended video feature extraction method is presented in the book by Bovik [14]. But these methods are simple and are suitable for slow object motion. Yu and Ramamoorthi [15] have suggested a unique neural network (NN) approach to derive optical flow fields of the input video from the per-pixel shift fields needed for video stabilization. In contrast to other video stabilization methods that use machine learning to indirectly infer frame movements from color videos, our approach employs an optical flow to directly analyze motion and learn stabilization. They also suggested an optical flow-based pipeline. Yu et al. [16] system relies on gated transformations trained using millions of images. The proposed closed multiplication addresses the limitations of vanilla convolution, which treats all input images as valid, by implementing a learnable dynamic feature-selection process for each channel at every spatial location across all layers. This approach applies partial compression and resolves the issues associated with standard convolution techniques. Additionally, global and local GANs created for a single rectangle mask are not suitable because free-form masks can exist everywhere in images of any shape. e Souza et al. [17] stated that the growth of multimedia data has helped many applications, like telemedicine, business video conferencing, monitoring and protection, entertainment, remote learning, and robotics. The VS is a technique for detecting and identifying removing motion or instabilities from a video channel that is put on by handling the camera during the recording phase. Souza presents and examines a unique approach that uses local features to identify errors in the camera's global motion prediction

2.3 Review of motion smoothing

Over 2 decades ago, several methods have been suggested to smooth undesirable camera motions. The VS algorithm utilizing feature point filtering and differential optical flow, was proposed by Cai and Walker [18] in 2009. Unwanted motions were eliminated using a first-order IIR filter. Rawat and Singhai [19] presented a good use of the IIR filter for motion smoothing of a video sequence for VS. They also considered the Taylor series expansion method for the ME and global motion-smoothing approaches. Muthu et al. [20] researched stationary, small, or slow-moving objects that, when covered, can improve the results of motion classification but are frequently missed by standard methods. Our method integrates motion inputs with logical object-based segmentation to identify the total moving objects and their motion characteristics and to execute segmentation. To calculate the object-specific motion parameters, connection matching and selected object-based samples were used. Wang et al. [21] leading to substantial improvements in video stabilization. On the other hand, previous surveys have primarily focused on traditional methodologies and lack comparative performance. Wang et al. [21] have provided an outstanding assessment of VS techniques for various types of motions and applications. Kumar et al. [22] proposed quadratic smoothing for VS problem resolution. Wang and Huang [23] recently developed a global pixel-based VS technique using motion smoothing.

Liu et al. [24] present an article that offers a frame generation technique for stabilizing full-frame video. They first calculated the strong warping fields from nearby frames and then merged the warped elements to create a stable image. Our main technical innovation is the learning-based hybrid space combination, which reduces errors produced by incorrect optical flow and fast-moving objects. Rawat and Sawale [25] have published the application of Gaussian kernel filtering (GKF) for VS tasks. The GKF method is widely used for motion compensation (MC) in full-frame VS applications. However, excessive kernels may lead to over-blurriness in a video sequence. Thus, this study focuses on designing a smoothing approach that eliminates the requirement of the GKF. This method is specific to trajectory-based approaches. Zhao and Ling [26] presented a pixel-based warping approach for video stabilization. However, it is necessary to design simple algorithms and reduce the computational cost of this stage for the MC. Mosleh et al. [27] used good use of a simple edge completion method for efficient VS and MC. They also used an IIR filter with a GKF for smoothing motions. Shankarpure and Abin [28] considered the frame–to–frame approach for VS by removing the Jitter method to be slow. To discover the temporal derivatives, a method using 1D separable kernel filters was applied.  

A fast VS technique based on block matching and edge completion was proposed by Tang et al. [29] in 2011. Souza and Pedrini [30] have designed a camera trajectory filtering method for the VS task. Yang et al. [31] have demonstrated a good use of the particle filter but for the specific case of the profile motion of the camera path. Method was not suitable for slow motions.

2.4 De-blurring and blurriness index measures

Matsushita et al. [9] that boost sharpness by transferring clearer pixels to corresponding fuzzy pixels using weighted interpolation. However, the approach was only applied to a small number of nearby frames with significant modifications. In the past year, several blind and non-blind image de-blurring techniques have been proposed. Since the blur kernel is unknown, blind deconvolution becomes more challenging [32, 33]. A useful comparison of numerous blind and non-blind de-blurring techniques has been provided by Simmons et al. [32]. They have proposed a technique for de-blurring that does not require PSF data and employs the EDGETAPR function to lessen ringing effects.

The first dataset addressing real-world challenges in rolling-shutter correction for dynamic scenes (RSCD) was introduced by Zhong et al. [33]. This dataset, named BS-RSCD, incorporates both object and ego motions in dynamic instances. The researchers employed a beam-splitter-based collection method to automatically capture authentic damaged and blurry videos along with their corresponding ground truth. Existing approaches for rolling shutter correction (RSC) and global shutter de-blurring (GSD) are applied directly. However, owing to fundamental issues in the network architecture, GSD methods often yield poor results when applied to RSCD. In response, we introduced the first learning-based model, called JCD, specifically designed for RSCD tasks.

Kulkarni et al. [34] have provided a detailed description of video stabilization. Using feature point matching, certain unexpected effects can result from poor video recording, such as picture skewing and blurring. Multiple studies have investigated these limitations to improve video quality. An algorithm for stabilizing unstable videos was presented in this paper. Without the effect of jitter, which is caused by handheld camera shaking while recording video, a stable output video can be produced. Rota et al. [35] have close attention to the primary architectural elements, motion management techniques, and loss functions. They examined common benchmark datasets and utilized deep learning (DL)-based methods to provide an overview of the effectiveness of video restoration techniques. Ciaparrone et al. [36] have presented the good use of the DL for tracking the multiple objects motioning the video sequences to address the concept of blurriness. However, the DL-based method requires large amounts of data available for a specific class of motion.

A multi-image de-blurring method is proposed by for de-blurring, Bojarczak and Lukasik [37] compared the wiener filter and TSVD technique. In 2010, Shen and Ma [38] used the Inverted Sum of Square Gradients (ISSG) metric to identify the blurry frames and assess the relative blurriness. Utilizing derivative filters in the x and y directions, respectively, the gradients are found. This measurement is only applied to a few nearby frames where major changes are not seen. To enhance the performance of VS, Okade and Biswa [39] suggested employing SIFT features for feature matching and pre-processing blurry shots. The Blurriness Index has been determined through Image Gradients (BIG) in the x and y directions. When the background objects are influenced by blur, employing the image gradients might not be able to accurately estimate blur in both the foreground and background at the same time.

Methods using DL are also being considered. DL has come to be a powerful method to acquire depictions of features directly from data. According to Pae et al. [40], constraint optimization has been proposed for smoothing and VS of video sequences. Liu et al. [41] have presented the good use of the video costing methods to improve the quality of recovered videos. Reichert et al. [42] recorded every moment independently using a fixed camera, but the duration of the video and potential standardization problems make analyses difficult. By automatically removing man oeuvres from these full sessions using an image visualization framework to quickly find relevant moments, we hope to make easy our understanding of such videos in this work. Guilluya et al. [43] have presented detailed and extended reports of the various VS challenges and is good for any researcher working in this field to explore. Zhao et al. [44] have used an iterative approach for stabilizing video with full frames. Souza et al. [45] have addressed various VS challenges. Finally, in early work, Tang et al. [46] proposed using a temporal mean filter for image stabilization. Since the elements in the scene are moving at different rates while the scene is being captured, this causes unwanted camera motion, which blurs the objects in the scene. Thus, VS approaches are needed to eliminate the unwanted camera motions that are frequently visible in video shots with handheld cameras. Existing VS algorithms are either complicated or perform poorly for handheld slow-motion footage. Since de-blurring is typically utilized as a post-processing step in these systems, motion vector estimation is imprecise. As a result, before video stabilization, it is necessary to comprehend how object motion affects blur performance.

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(a) Experimental setup

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(b) Detail VS procedure

Figure 3. Process of proposed VS methodology

4.1 Identification of blurry frames using the proposed blurriness index and de-blurring

The amount of blur present in the video sequences depends upon the various environmental conditions (scene or background) and different kinds of object motions. Thus, blurring does not uniformly present in all the frames of the video sequences. Usually, a sharper frame does not suffer from the large blur [8], but large objects with sharp edges are more affected by the motion blur. Thus, it is required to identify the blurry frames before de-blurring the video sequence.

4.1.1 Modified blurriness index

The VS technologies are employed for enhancing the quality of source videos by reducing blur and jitter thus producing videos that are pleasing to the human viewing system. Sophisticated digital cameras feature high-powered zoom lenses, which amplify undesirable camera movement. Unwanted motions are caused by slow and smooth hand motions. Jitters are quick and random handshakes that cause the entire scene to alter. In recent years, video stabilization has become an essential component of hand-held digital camera systems to improve their visual performance. This research aims to identify blurred frames within video sequences that are essential for video stabilization. The suggested method computes a new blurriness index by converting brightness for every pixel with the sum of squares of orthogonal temporal derivatives. The blurriness index calculated represents the enhanced foreground and background object motions. The proposed blurriness index is calculated for each i^th frame using the derivative f_x, and f_y as:

$b_i=\sum_{x=1}^{{row }} \sum_{y=1}^{{col }} f(x, y, t) *\left(f_x(x, y, t)^2+f_y(x, y, t)^2\right)$     (15)

where, f(x, y, t) represents the brightness of p(x, y) pixel of the i^th video frame.

The modified blurriness index can effectively identify the fine edge variations present because of camera motion within the foreground as well as the objects. Consequently, it can also represent the effect of object motion on the blurriness index. The employing of modified 4-point central difference derivatives for BI can represent a more precise and enhanced motion. The performance of the suggested blurriness index is compared to the performance of two generally used blurriness indexes based on the Inverse of the Sum of Square Gradients (ISSG) [7, 39], and the Blurriness index utilizing Image Gradients (BIG) [40].

The proposed method calculates the modified blurriness index using Eq. (15), for each frame. The blurriness index of each frame is compared with the threshold (Th) is defined as Th=mean(b_i). If blurriness index b_i<Th then the corresponding i^th frame is identified as the blurry frame. Only the identified frames with significant blur will be De-blurred. The threshold Th is taken as the mean value since it is independent of the speed and direction of motions, and perform equally well in all type of motions.

De-blurring the blurry frames: The blind de-convolution is the most commonly used de-blurring method but it is computationally complex. Therefore, this paper proposes to implement the Wiener filter with reduced computational complexity and better acceptable restoration results. Wiener filter is a minimum mean square error (MSE) filter that employs a linear De-convolution method [10]. Thus it is computationally less intensive. But it gives poorer results in the presence of noise. The filter is designed by minimizing the estimated MSE between the original frame f(x,y,t) and its estimate $f^{\wedge}(x, y, t)$ by using the Wiener filter defined by Bojarczak and Lukasik [37]. However, sometime de-blurring would cause some ringing effects in the de-blurred frame caused by the high-frequency drop-off. Thus, in addition, the function that is used to solve this problem is edge-taper. Edge-tapering blur the edges of the input frame slightly, before applying the de-convolution thus reducing the ringing effects.

4.2 Global ME via hierarchical differential motion

The study introduced a layered approach to motion estimation for analyzing changes between successive video frames. This hierarchical method's core concept involves evaluating motion at a reduced resolution, which helps mitigate aliasing effects. The technique employs a Gaussian pyramid with L=3 levels [6] and is built over a pair of frames, f(x,y,t) and f(x,y,t-1). The movement of two consecutive frames f(x,y,t) and f(x,y,t-1) is represented using a six-parameter affine transformation [6, 18, 33], which is expressed as:

$\begin{gathered}f(x, y, t)=f\left(\mathrm{~m}_1 \mathrm{x}+\mathrm{m}_2 \mathrm{y}+\mathrm{m}_5, \mathrm{~m}_3 \mathrm{x}+\mathrm{m}_4 \mathrm{y}+\mathrm{m}_6, t\right. \\ -1)\end{gathered}$     (16)

where, m₁, m₂, and m₃, m₄ form 2×2 affine matrix A, and m₅, m₆ are translation vector $\bar{T}$ as:

$\mathrm{A}=\left(\begin{array}{ll}m_1 & m_2 \\ m_3 & m_4\end{array}\right)$, and $\bar{T}=\binom{m_5}{m_6}$     (17)

The following quadratic error function has to minimize to estimate the affine parameters.

$\begin{gathered}\mathrm{E}(\mathrm{m})=\sum_{\mathrm{x}, \mathrm{y} \in \Omega}\left[\mathrm{f}(\mathrm{x}, \mathrm{y}, \mathrm{t})-\mathrm{f}\left(\mathrm{m}_1 \mathrm{x}+\mathrm{m}_2 \mathrm{y}+m_5, \mathrm{~m}_3 \mathrm{x}\right.\right. \left.\left.+\mathrm{m}_4 \mathrm{y}+\mathrm{m}_6, \mathrm{t}-1\right)\right]^2\end{gathered}$     (18)

Using the Taylor series expansion technique outlined by Hany Farid in studies [6, 18], the motion vectors are determined through differential global motion estimation. The only modification is that the temporal derivatives are calculated using the Barron method [13]. The derivatives in the x and y direction are given in Eqs. (12)-(13), and the time derivative is given by:

$\begin{aligned} f_t(x, y, t)= & \operatorname{conv}((f(x, y, t-1) *[0.25\ 0 .25])+ (f(x, y, t) *-[0.25\ 0 .25]))\end{aligned}$     (19)

The estimated global motion vectors calculated for each pair of frames are represented as:

$\operatorname{GMV}(\mathrm{t})=\left\{\mathrm{GMV}^{\mathrm{x}}(\mathrm{t}), \mathrm{GMV}^{\mathrm{y}}(\mathrm{t})\right\}=\overline{\mathrm{T}}=\left\{\mathrm{m}_5, \mathrm{~m}_6\right\}$

where, GMV^x(t)=m₅ is a translation in the x direction and GMV^y(t)=m6, is the translation in the y direction. The rotation and scaling parameters matrix are set as $A=\left[\begin{array}{ll}m_1 & m_2 \\ m_3 & m_4\end{array}\right]$. These parameters represent undesired motions in video sequences. If the length of a video sequence is large then the error due to accumulation of global motion vectors also increases. This causes missing frame areas and thus loss of information. Hence, the motion-smoothing method is required to remove the undesired motions, which minimizes the missing frame areas.

4.3 Motion smoothing

Researchers have developed numerous techniques to reduce unwanted camera movements. However, most of these approaches were either computationally intensive or only effective for basic and slow camera motions. Their performance diminishes when dealing with substantial objects and camera movements, particularly in handheld mobile video recordings. Consequently, there is a need to efficiently minimize jitters and the calculated accumulated global motion vectors $A G M V(t)$. The proposed approach employs a first-order adaptive IIR filter [9] to smooth out accumulation errors. This IIR filter was chosen for motion smoothing primarily due to its straightforward implementation and effectiveness.in systems that operate in real time and consume less memory. The combined vectors of global motion $A G M V(t)$ are calculated from estimated motion vectors, as:

$A G M V(t)=\sum_{i=2}^t G M V(t-1)+G M V(t)$     (20)

where, AGMV(t) is represented as:

$A G M V(t)=\left\{A G M V^x(t), A G M V^y(t)\right\}$     (21a)

To obtain the smoothed accumulated motion vectors, implement a first-order IIR filter on Eq. (21). This can be expressed as:

$\begin{gathered}\operatorname{ASM}(\mathrm{t})=\tau * \operatorname{ASMV}(\mathrm{t}-1)+(1-\tau) \\ * \operatorname{AGMV}(\mathrm{t}-1)\end{gathered}$     (21b)

In this context, $A G M V(t)$ which represents the cumulative smoothed motion vectors, is defined as follows:

$\operatorname{ASMV}(\mathrm{t})=\left\{\operatorname{ASMV}^{\mathrm{x}}(\mathrm{t}), \operatorname{ASMV}^{\mathrm{y}}(\mathrm{t})\right\}$     (22)

where, $\tau$ is defined as a smoothing parameter that generally ranges between 0≤τ≤1. for the Paresh et al. [19] $\tau$ is set to 0.96 since it is the uppermost limit.

4.3.1 Proposed FIR filter design

The comparative smoothened motions produced by the FIR filter are satisfactory and pleasant to the human visual system. FIR filters might hold several advantages against IIR filters while it comes to motion smoothing as:

Guaranteed Stability: Because FIR filters are inherently stable, their output won't increase uncontrollably. This is important because unstable filters might result in undesired distortions as well as artifacts while processing videos.

Phase Response: A linear phase response is a possible design for FIR filters. This implies that the delay experienced by each frequency component is the same, which is crucial for maintaining the temporal links between various video signal components. This corresponds to smoother transitions as well as prevents the introduction of jerky movements as a result of phase shifts in motion smoothing.

Filter depends on the current and past four frames motion vectors. Frames are filtered with filter coefficients b₀=2^-1, b₁=2^-2, b₂=2^-3, b₃=2^-4, and b₄==2^-4. The quantity of previous frames can be adjusted as necessary, with corresponding modifications to the coefficients. The filtering process is executed as:

$B M V_{\text {filter }}(n, b l k)=\sum_{\mathrm{K}=0}^{\mathrm{d}} \mathrm{b}_{\mathrm{k}} * B M V_{\text {old }}(n-k, b l k)$     (23)

This paper has proposed using the lower order fast FIR filter design with the filtered numerator coefficient vector $b$=0.2 with denominator coefficient vector normalized to a=1. The proposed method of FIR filter smoothens and stabilizes the motion better. Uses of FIR filter almost eliminates the requirement of compensation stage. However, FIR filter needs more computation and memory as limitations. Thus, it is concluded that FIR filters are a suitable alternative for motion smoothing where stability, linear phase response, with economy of design are priorities.

4.4 Warping and motion compensation

In the stabilization algorithm, the warping technique aligns a newly received frame with the positions of the preceding frame. Substantial movements are detected at the coarse level through warping, utilizing Bi-cubic interpolation. This process is then refined iteratively across each level of the pyramid. When the calculated motion vectors at a specific pyramid level L are m₁, m₂, m₃, m₄, and m₅, m₆, the estimated affine matrix A should be used to warp the original frame, along with the smoothened global translation vector $\bar{T}$ given as:

$A=\left[\begin{array}{ll}m_1 & m_2 \\ m_3 & m_4\end{array}\right]$. and $\bar{T}=\binom{2^{L-1} m_5}{2^{L-1} m_6}$     (24)

Upon completing each level of the pyramid, it will be necessary to repeatedly transform the initial frame using the motion calculated at every pyramid stage. Two affine matrices A₁ and A₂ with their corresponding translation vectors T₁ and T₂ are combined as:

$A=A_1 A_2$ and $\bar{T}=A_2 T_1+T_2$     (25)

The use of a hierarchical pyramid approach with Bi-cubic interpolation for warping improves the stabilization performance under large objects and camera motion. The paper proposed to use the GKF [9, 31] for motion compensation because they are simple to implement. The standard deviation is set to $\sigma=\sqrt{k}$ [9] where k is the kernel parameter or the size of the neighborhood. The value of the kernel parameter k must not exceed 6. Employing GKF helps reduce areas with missing frames. The compensated motion transformation between frames i and j in a video sequence is determined using the following calculation:

$C_t=\sum_{i \in N_t} T_j^i * G(k)$     (26)

where, G(k) the GKF, is referred to by Matsushita et al. [9], and N_t, is a set of neighboring frames given as N_t=m: k-n≤m≤k+n. The compensated motion frames $f_t^{\prime}$ can be warped from the original frame f_t by:

$f_t^{\prime}(x, y, t)=C_t * f_t(x, y, t)$     (27)

4.5 Edge completion

Despite motion smoothing, some areas of missing frames persist due to cumulative errors and rotational effects. The proposed approach achieves seamless stitching of these missing frame regions by employing a simplified edge completion technique [12]. This method bears a slight resemblance to the edge completion approach described by Matsushita et al. [9]. It utilizes the surrounding present frames to fill in the areas where frames are missing:

$f_k(i, j)={median}\left[f_N(i, j)\right]$     （28a)

$N \in[(k-n, . ., k+n]$     (28b)

where, k is the number of currents is frames, and n is the integer. The application of Gaussian motion compensation effectively reduces the areas that are missing, making it possible to use small values like 3 or 5 for n in Eq. (28) to successfully fill in these gaps.

Guilluy et al. [43] have presented a comprehensive survey of video stabilization technologies. The primary goal of this contribution is to provide answers to such issues as well as a sufficiently integrative paradigm to offer a greater awareness of the advancement of this research field, which has significant academic and industrial significance. The main problems, practical issues, and mathematical core principles of VS algorithms are discussed in this work. VS is being revolutionized by AI and deep learning techniques can be investigated by researchers as a means of improving the analysis and compensation of intricate camera motions, particularly in difficult situations including rapid movements or obstacles.

Recently, Zhao et al. [44] have presented the use of the iterative optimization algorithm to improve the efficiency of the VS systems for hand held devices for full frame video generation. The study of the roll and panning is also the open field of research. It is also point of interest in future to consider the depth of field for analysis. VS has been introduced by Souza et al. [45] with a succinct physical interpretation.