2.1.

Background in Mosaicking

Given a sequence of $K$ images $\mathcal{I}={\{{\mathbf{I}}_k\}}_{k=1}^K$, the goal of mosaicking is to find a two-dimensional representation of the scene or mosaic $\mathbf{M}:{\mathrm{\Omega }}_M\to {\mathbb{R}}^3$ (RGB) where ${\mathrm{\Omega }}_M\subset {\mathbb{R}}^2$ is denoted the mosaic space. Provided that the camera observes a planar scene, a homography $\mathbf{H}$ exists between corresponding points in two views $\mathbf{p}={[\begin{array}{cc}{p}_x& p_y\end{array}]}^T$, ${\mathbf{p}}^{\prime }={[\begin{array}{cc}{p}_x^{\prime }& p_y^{\prime }\end{array}]}^T$, which lie in their respective image spaces ${\mathrm{\Omega }}_p$, ${\mathrm{\Omega }}_{p^{\prime }}\subset {\mathbb{R}}^2$. This homography can be parametrized as a $3\times 3$ matrix such that

Then, Eq. (1) can be written as ${\tilde{\mathbf{p}}}^{\prime }\propto \mathbf{H}\tilde{\mathbf{p}}$ where $\mathbf{H}$ is defined up to scale and the tilde indicates that the points are expressed in homogeneous coordinates.¹⁶

If the same planar scene is observed from both views, a homography $\mathbf{H}$ can be directly inferred from image matching information.¹⁷ In this work, we use a landmark-based registration approach^18–20 since these approaches usually allow for sparse feature detection which can be faster than using the information in the whole image.

Pairwise mosaicking (PM) relies on estimations of pairwise homographies ${\mathbf{H}}_{k+1,k}$ which project any point from the space ${\mathrm{\Omega }}_k$ of image ${\mathbf{I}}_k$ onto the space ${\mathrm{\Omega }}_{k+1}$ of image ${\mathbf{I}}_{k+1}$. Pairwise homographies are then used to compose homographies from a fixed reference, which without loss of generality, can be placed on the first frame as

Globally consistent approaches such as bundle adjustment¹⁰ take into account the relationship between all pairs of images in the sequence to create globally consistent mosaics.²¹ However, they are generally not fast enough for online operation; the main reasons are the acquisition of the correspondences between all images and the run-time of the nonlinear optimization procedure.

Let us define $\mathcal{L}$ as the set of all pairs of image indices in which correspondences have been successfully acquired. We aim to obtain a set of estimated homographies ${\widehat{\mathbf{H}}}_1,\dots ,{\widehat{\mathbf{H}}}_{K-1}$, where the hat denotes that they are an estimate, that minimizes the reprojection errors of the matching points in all images in the sequence, namely:

$N_{l,m}$ is the number of matches found in the pair $\{l,m\}$, $f(·)$ is the conversion from homogeneous to Cartesian coordinates so that $\mathbf{p}=f(\tilde{\mathbf{p}})$, and ${\sigma }_v^2$ is the variance associated with the location of a feature once propagated to the space of its matched pair. This variance is associated with the fact that we model the error between a fixed point in an image, and its corresponding pair propagated from the other image as a Gaussian random variable. Note that, since one frame is defined as the reference (here chosen as the first frame, without loss of generality), we only require to estimate $K-1$ homographies, the remaining one being set to identity.

Let $\mathcal{X}={\{{\mathbf{x}}_k\}}_{k=1}^K$ be the set of corresponding true camera poses. In addition, let $\mathcal{Z}={\{{\mathbf{z}}_k\}}_{k=1}^K$ be the respective EMT measurements of these poses, where we assume ${\mathbf{z}}_k$ to be a noisy instance of the true camera ${\mathbf{x}}_k$. We parametrize each camera pose ${\mathbf{x}}_k={[{\mathbf{r}}_k,{\mathbf{t}}_k]}^T$ as a rotation ${\mathbf{r}}_k$ and translation ${\mathbf{t}}_k$. The vector ${\mathbf{z}}_k$ is parametrized in the same way. The three-parameter rotation vector ${\mathbf{r}}_k$ is extracted from the skew symmetric matrices $[{\mathbf{r}}_k{]}_x\in \mathfrak{s}\mathfrak{o}(3)$, which can be converted into the rotation matrix ${\mathbf{R}}_k=\exp ([{\mathbf{r}}_k{]}_x)\in SO(3)$.²² $SO(3)$ refers to the special orthogonal group of matrices of dimension $3\times 3$ with determinant 1, and $\mathfrak{s}\mathfrak{o}(3)$ is its corresponding lie algebra. With a rotation matrix ${\mathbf{R}}_k$ and a translation ${\mathbf{t}}_k$, we can compose the rigid transformation ${\mathbf{T}}_k\in SE(3)$, where $SE(3)$ is the special Euclidean group corresponding to rigid transformations in three-dimensional space

A set of camera poses (provided by the EMT system) on their own do not give us enough information to create a mosaic. To that end, a set of homographies is necessary, requiring also the planar structure modeling the scene. We now detail how to obtain a set of homographies from both poses and the surface plane. Provided that only camera poses are measured, we need to establish a link between these and imagery.

Let us consider a virtual camera with its virtual image plane located in the origin of coordinates, which we use as a reference, whose image plane space is ${\mathrm{\Omega }}_M$. We can then link the spaces of the images obtained by the cameras, and their respective motions provided that the imaged plane is known. Since it is so, there is a homography $\mathbf{H}$ defined that propagates any point in the virtual image to any other image through the following equation, that for convenience we define as $g(·)$

We use this relation in order to relate the visual content in the images with EMT readings of the camera poses. The complete derivation of Eq. (5) can be found in Ref. 16.

In the following work, Ref. 6 introduced a probabilistic graphical model that infers the set of poses $\mathcal{X}$ and planar structure $\mathbf{v}$ by solving the minimization problem

This prevents the poses to be estimated from drifting provided that the EMT measurements have a common reference, which do not allow drift to separate the cameras from the measured position. In other words, the solution obtained as a result of Eq. (7) reflects a guided estimation of the parameters using the EMT system.

2.2.

Pruning Strategies for Sequential Bundle Adjustment

In this section, we present our two pruning strategies: (i) the use of the EMT system to identify and discard nonoverlapping frames for which no matching should be attempted, and (ii) the introduction of the concept of superframe; an extension of a typical frame that allows for more efficient mosaicking schemes. We present two pipelines that increasingly incorporate the contributions mentioned above.

2.2.2.

Pairwise compression

A practical problem in mosaicking¹² algorithms is that hundreds of correspondences are typically stored and used in the optimization procedure per image as can be seen in Eq. (9). Instead, we parametrize the pairwise relation as five equivalent correspondences in the following way: (i) after the pairwise homography estimation using RANSAC simultaneously with the correspondences acquisition,¹⁷ we take the bounding box that includes all the interest points in the image. In particular we take the top-centered, bottom-centered, left, and right point locations as well as the center of the bounding box to account for the spread of these points in the original image space. (ii) We propagate them using the estimated homography that relates both images to obtain the second set of points, which completes the collection of correspondences. These correspondences will then be kept for the optimization, reducing the run-time of the cost function greatly.

The more correspondences we acquire, the more correspondences must be taken into account in the cost function. This might not be a problem at the beginning of the sequence, but as the number of correspondences increases, the computational cost increases as well, hindering online operation. We now introduce an additional strategy that generalizes a regular frame in a more efficient representation for mosaicking.

Figure 2(a) shows the proposed pipeline proposed in this section while Fig. 2(b) shows the diagram of the pipeline proposed in Sec. 2.2.3. In both pipelines, the pairwise compression mentioned in Sec. 2.2.2 is applied. Contributions to the mosaicking pipeline are outlined with a blue border.

Fig. 2

(a) Pipeline proposed in Sec. 2.2.1 using the EMT system to filter out incoherent matching attempts. (b) Pipeline proposed in Sec. 2.2.3 using the superframe. In both pipelines, the pairwise compression mentioned in Sec. 2.2.2 is applied. Contributions to the mosaicking pipeline are outlined with a blue border.

2.2.3.

Superframe representation

The superframe representation is a generalization of a frame that incorporates one or more frames. The main idea is to partition the image set $\mathcal{I}={\{{\mathbf{I}}_k\}}_{k=1}^K$ into subsets of $W$ images grouped into $N$ superframes with $K=NW$. Since it is a generalization of an image, the superframe can be incorporated into the standard bundle adjustment pipeline reducing its computational burden drastically. Let us formally define the concept of superframe.

We define a superframe as a representation of a subset of $W$ frames ${\mathcal{I}}_i={\{{\mathbf{I}}_k\}}_{k\in {\mathcal{K}}_i}$ that encodes the most salient information of the region observed by all images in the superframe which are indexed by ${\mathcal{K}}_i=\{k\in \mathbb{Z}|L{F}_i-u\le k\le L{F}_i+u\}$. A lead image ${\mathbf{I}}_{L{F}_i}$ with index $L{F}_i=(i-1)W+u+1$ is defined as the central image in the superframe of window of size $W=2u+1$, $u$ being an integer. If the lead image was taken in isolation, then this would be equivalent to the concept of keyframes.¹² In contrast, the superframe uses information of all the images in the window.

Analogously to the standard pipeline, interest point locations ${\mathbf{P}}_k$ and descriptors ${\mathbf{D}}_k$ are extracted for all frames within each superframe. We propose to use the lead image space as a common space where all interest points in the superframe lay, defining the superframe as ${\mathcal{S}}_i=\{{\mathcal{P}}_{S_i},{\mathcal{D}}_{S_i}\}$. To propagate the locations of interest points into this common space, we define ${\tilde{\mathbf{P}}}_k\in {\mathbb{R}}^{3\times N_k}$ as a matrix containing all point locations in homogeneous coordinates, where $N_k$ is the number of interest points found in image $k$. If expressed this way, the points can be propagated onto the lead image space as

Eq. (12)

$${\mathcal{P}}_{S_i}={\{f({\mathbf{H}}_{L{F}_i,k}{\tilde{\mathbf{P}}}_k)\}}_{k\in {\mathcal{K}}_i},$$

while the descriptors are grouped as

Eq. (13)

$${\mathcal{D}}_{S_i}={\{{\mathbf{D}}_k\}}_{k\in {\mathcal{K}}_i},$$

where the homography ${\mathbf{H}}_{L{F}_i,k}$ is the homography that relates the frame $k$ within the superframe with the lead frame $L{F}_i$. This homography is obtained by first running a local, small-scale visual bundle adjustment with all $W$ images following the methodology described in Sec. 2.1. Within the superframe, the aligned homographies are then considered fixed in the rest of the pipeline. Figure 3(a) depicts the process of the creation of a superframe, and Fig. 3(b) shows the differences in matching between two images (top) and two superframes (bottom).

Fig. 3

(a) Creation of a superframe. From top to bottom: $W$ images are registered using bundle adjustment¹⁰ and their interest points are propagated to the space of the lead frame $i$, forming a superframe. (b) Matching of two frames (85 inliers) and two superframes (165 inliers).

2.2.4.

Superframe in the mosaicking pipeline

To integrate the superframe into the mosaicking pipeline, we extend the probabilistic framework⁶ summarized in Sec. 2.1. However, now superframes replace single frames. To highlight why this is possible, let us describe the simple scenario where two superframes are created. In that case, their descriptors can be matched directly since the input to the matching algorithm is two sets of descriptors. From there, the matching process is analogous to the one described in the PM in Sec. 2.1. Figure 2(c) shows the diagram of the pipeline using the superframe, marking in blue the contributions in the pipeline. In applying directly,⁶ only one EMT measurement is assumed to be associated with each frame. Therefore, there would be $W-1$ EMT measurements unused per superframe. Instead, we propose to modify the pipeline to include all EMT measurements in the window $W$ for better placement of the superframe in the mosaic.

These measurements can be used to obtain homographies ${\mathbf{H}}_k^{\mathrm{EMT}}$ using Eq. (5) and the previously estimated ${\mathbf{v}}_{i-1}$ resulting from Eq. (7). Figure 4 shows the nomenclature and indexing, displaying each homography composed using the EMT system. Using the EMT measurements and the fixed homographies ${\mathbf{H}}_{L{F}_i,k}$ found in the initial bundle adjustment to build the superframe,, we can obtain measurements of the lead homography ${\mathbf{H}}_{L{F}_i}^{\mathrm{EMT},k}$ coming from each of the EMT measurements in a given superframe as

Eq. (14)

$${\mathbf{H}}_{L{F}_i}^{\mathrm{EMT},k}={\mathbf{H}}_{L{F}_i,k}{\mathbf{H}}_k^{\mathrm{EMT}}k\in {\mathcal{K}}_i.$$

Fig. 4

A superframe indexed by $i$ is composed of a set of single frames indexed by $k$. Each homography ${\mathbf{H}}_{L{F}_i}^{\mathrm{EMT},k}$ is created from the EMT measurement ${\mathbf{z}}_k$ and the previous plane estimation ${\mathbf{v}}_{i-1}$.

We consider these homographies as measurements of the true homography that places the lead image into the mosaic space, and formulate the problem as

Eq. (15)

$$(\widehat{\mathcal{X}},\widehat{\mathbf{v}})=\underset{(\mathcal{X},\mathbf{v})}{\arg \min }(C_{\mathrm{EMT}}+\lambda C_v+{\lambda }^{\prime }{C}_H),$$

where $\lambda$ and ${\lambda }^{\prime }$ are weights. The two first costs are precisely the costs defined before in Eqs. (9) and (8), and the proposed additional term for the global alignment cost function $C_H$ is defined as

Eq. (16)

$${ϵ}_k(c,i)=f({\mathbf{H}}_{LFi}^{\mathrm{EMT},k-1}{\tilde{\mathbf{p}}}_c)-f[g{({\mathbf{x}}_k,{\mathbf{v}}_{i-1})}^{-1}{\tilde{\mathbf{p}}}_c],$$

Eq. (17)

$$C_H=\frac{1}{NWQ}\sum _{i=1}^N\sum _{k\in {\mathcal{K}}_i}\sum _{c=1}^Q{ϵ}_k^T(c,i){\sum }_{hVis}^{-1}{ϵ}_k(c,i),$$

where ${\mathbf{p}}_c$ represents $Q$ control points. Specifically, we used the four corners and the center point of an image as control points. Setting ${\sum }_{hVis}$ is not trivial since it depends on the accuracy of the EMT system and previous estimation of the normal vector. Therefore, we use it conservatively setting a standard deviation of 10 pixels.

Once all homographies from the mosaic space to the lead frames of each superframe are obtained, one must place the superframes into the mosaic space. To do that, each one of the images within the superframe has to be placed in the mosaic space. Therefore, we must obtain individual homographies ${\mathbf{H}}_k$ for each frame in the sequence that relates it with the mosaic space. One must note, however, that when running bundle adjustment on the superframes, the reference is in the space of the first lead frame, which corresponds to index $L{F}_1$. For simplicity, we denote the estimated homographies as ${\mathbf{H}}_{L{F}_i}$, skipping the second subindex, which would be $L{F}_1$. However, one must keep in mind that they are actually from the first lead frame $L{F}_1$ to $L{F}_i$ as ${\mathbf{H}}_{L{F}_i,L{F}_1}$. Therefore, to compose a mosaic in the space of the first image, not the first superframe, one must use

Eq. (18)

$${\mathbf{H}}_k={\mathbf{H}}_{k,L{F}_i}{\mathbf{H}}_{L{F}_i,L{F}_1}{\mathbf{H}}_{L{F}_1,1}.$$

Once the absolute set of homographies is obtained, one can project the images onto the mosaic space to be blended.

3.1.

Datasets

We generated two datasets formed by a set of images and EMT data; synthetic (SYN, 273 frames, $373\times 378\mathrm{px}$) and a phantom based (PHB, 701 frames, $780\times 781\mathrm{px}$) datasets. SYN is a translation-based raster scan generated by simulating ground truth camera motions, from which EMT measurements are generated by applying Gaussian noise,⁶ and for which the images were extracted as projections of the scene observed by the cameras. In that case, the scene consisted of a planar, high-resolution digital image. PHB was recorded by imaging a printed image of a placenta. The setup consisted of a camera head IMAGE1 H3-Z SPIES mounted on a 3-mm straight scope 26007 AA 0° (Karl Storz Endoskope, Tuttlingen, Germany), an EMT system NDI Aurora with a planar field generator, and a Mini 6 DoF sensor. A collection of homographies by semiautomated registration of each fetoscopic image to the original image of the placenta, where a landmark-based approach was used to align the images after the initial manual alignment.

3.2.

Algorithms

As a baseline, we compare our algorithms to both the established FBA as well as the standard PM approach, which is very fast but accumulates drift. We apply the matching compression strategy presented in Sec. 2.2.2 as well as the use of the EMT system to discard inconsistent matching attempts (SAT). Our second contribution is the introduction of the superframe (SF) and its incorporation to the mosaicking pipeline. By default, we have chosen $W=5$. We explicitly name $\mathrm{SF}(W)$ to a run where $W$ corresponds to the size of the window used in the superframe.

3.3.

Metrics and Implementation Details

We compare the homography $\mathbf{H}$ and the ground truth homography $\mathbf{G}$ by computing the mean residual error ${ϵ}_k$ of a projected grid of $N_g$ points ${\rho }_i$ from the image space to the mosaic space. Then, the error $ϵ$ between two mosaics is computed as the mean of individual errors ${ϵ}_k$. This error is defined in the mosaic space, which is the space in which the final composition is performed. Note that we use ${ϵ}^k$ with superindex $k$ to refer to the residual error between two sequential mosaics at each time instant whereas ${ϵ}_k$ with subindex $k$ refers to the error of the alignment of a single image $k$. To make this metric independent to the choice of reference space, we compute the average of the errors using all images as a reference, as in

In terms of feature-based method, we used SURF.²⁰ The matching was performed using fast approximate nearest neighbors.²³ The fetoscope was precalibrated using the Matlab Camera Calibration Toolbox. We also precomputed and applied the Hand-eye Calibration²⁴ matrix from a sequence of images of a checkerboard as well as synchronized sensor poses. The window size of the superframe was determined from the trade-off analysis as $W=5$, which is presented later in Sec. 3.3. In addition, given that superframes contain many more correspondences than actual frames, a kd-tree²³ can be trained and stored per superframe. Then, fast approximate nearest neighbor can be used to accelerate the matching between superframes. The experiments have been performed in an Ubuntu 16.04 with Intel Core I7 at 2.5 GHz and 6 GB of memory.

Next, we evaluate sequential bundle adjustment and evidence the decrease in computational time that the proposed strategies provide.

3.4.

Speedup: Correspondence Acquisition

In this section, we analyze the computational cost of a sequential bundle adjustment in an online setting. More precisely, we focus on correspondence acquisition.

In Fig. 5, we display the run-time of correspondences acquisition in the three algorithms for both datasets. As expected, SAT is faster than FBA in both cases, and SF shows the best in terms of computational cost. In the case of the phantom-based dataset, we can observe that SAT is not necessarily faster all the time. This is due to the trajectory that the camera has followed in this particular dataset. If the overlap between images is too large, then the algorithm suggests all images as possible candidates.

Fig. 5

Runtime of the correspondences acquisition with respect to the number of iterations for both SYN and PHB datasets.

To further evidence where the computational savings have happened spatially, we analyze the percentage of potential image candidates that have been selected using an occupation matrix. This matrix shows whether there has been a match from image $i$ (corresponding to row $i$) to image $j$ (corresponding to column $j$). For a more informative representation, we have color-coded the matrices. Out of all image matches that would have been obtained using an FBA (white), only a portion of them would be selected by SAT (green). Due to the use of symmetrical matching, we only display the upper right triangle in the occupancy matrix. Figure 6 shows that, in the case of SYN (a), 100% of the proposed candidates are correct, and no matches have been missed, saving a total of 54.2% matching attempts. As mentioned before, the path followed by the camera in the PHB [Fig. 6(b)] makes saving matching attempts more complicated. 100% of the proposed candidates are correct; however, there is only a total saving of 5.2% attempts, which happened to be toward the end of the sequence.

Fig. 6

Occupancy matrix. The pixel $(i,j)$ shows a color-coded outcome of the matching process. Potential matching candidates are in white. Proposed candidates that have been matched are in green. Black pixels reflect that no candidate was selected but there was no real match. Occupation matrices in (a) the synthetic dataset (SYN) and (b) the phantom-based dataset (PHB).

We now study the run-time of the nonlinear optimization as the second bottleneck for bundle adjustment to reach sequential operation.

3.5.

Speedup: Nonlinear Optimization

The computational cost of the nonlinear optimization is due to the run-time of the cost functions in Eqs. (9) and (8) and the number of iterations to convergence. In contrast to standard bundle adjustment where we do not have any initial estimate a priori, subsequent estimations can be used as an initial estimate in a sequential version of bundle adjustment, providing a speedup at each iteration due to the proximity to the minimum. Although this is a desirable property, the question that might prevent desirable update rates is whether the number of iterations to convergence grows with time.

In Fig. 7, we show the number of iterations to convergence in both SYN and PHB datasets.

Fig. 7

Number of iterations of the nonlinear optimization procedure for FBA, SAT, and SF.

The fact that the approaches show a constant tendency over time is crucial since it indicates that the number of iterations in the nonlinear optimization does not seem to be a bottleneck for offline operation. Given the textureless nature of fetoscopic images, using only a subset of all frames is not a very robust option. Instead, we would like to use the redundancy in the complete video sequence. Figure 8 shows the optimization times for FBA, SAT, and SF. It can be seen how if compression is used (SAT), the slope decreases with the number of iterations. Now that we have demonstrated the decrease in computational burden in the proposed algorithms, we need to evaluate their accuracy and show that despite the improvement in speed, there is no significant loss in accuracy.

Fig. 8

Runtime of the nonlinear optimization for FBA, SAT, and SF.

3.6.

Efficiency

In this section, we analyze the performance of the proposed algorithms for classical pipelines. In particular, we computed the error in each sequential mosaic for NV and FBA as a baseline, comparing it to SAT, and SF with different window sizes $W=\mathrm{1,3},\mathrm{5,7},9$ in SYN and PHB datasets, respectively. Figure 9 shows the errors for each of the methods. The error in NV spikes from the beginning. This is well known due that there is no global correction and therefore, drift is accumulated. While SF results in the best performance regarding computational advantage, the decrease in accuracy for all the window sizes except $W=1$ for which the behavior should be very similar to SAT. When the window increases, the accuracy of the SF remains stable.

Fig. 9

Error in NV, FBA, SAT, and SF with a window size of 1, 3, 5, 7, and 9 for SYN and PHB.

Since the data reflects this trade-off between computational power and accuracy, we propose to analyze this trade-off with the graph in Fig. 10. This graph shows the error in the $y$ axis and the time per iteration in the $x$ axis. We have plotted each algorithm in a different color. In here, temporal evolution is not shown; however, one can observe the temporal trail by looking at the lines connecting the dots, taking into account that first iterations are the fastest. For an efficient algorithm, we would like the error and computational time to be low. Therefore, we identify the most efficient algorithm as the one whose results lie in the bottom left corner. The same tendency can be seen for both datasets; despite being efficient, the NV drifts in large measure, making the algorithm not worth pursuing. The FBA is not a good option concerning the trade-off since the computational time is too large, yet it does keep the accuracy very low. SAT performs similarly, albeit much more efficiently than FBA. On top of that, all versions of SF perform more efficiently than SAT. In particular, we see that as we increase the window size, the efficiency starts to be better until $W=5$. The selection of the best algorithm is not trivial since $W=3$ shows a faster start yet slower end than $W=5$ in both datasets due to the need for matching more superframes. After this, efficiency starts to fall systematically. We believe that the increase of computational time that takes to perform the first bundle adjustment causes this effect, growing with $W$. Since many of the operations in the creation of the superframe could be performed in parallel, we expect slightly better results for a parallelized version of the approach.

Fig. 10

The trade-off between the error ${ϵ}^k$ in the $y$-axis and computational time in the $x$-axis. To the left, a zoomed version of the graph in the right for both (a) SYN and (b) PHB. Each color represents a different algorithm and despite the graph does not aim to show the temporal evolution, the connection between points provide an indication.

In Figs. 11 and 12, we show mosaics for SYN and PHB datasets, respectively, for the NV, FBA, and SFW5. While the figure shows some steps of the sequential estimation of the mosaic, we encourage the reader to visualize the videos included in the supplementary material for a more thorough visualization of the results.

Fig. 11

Sequential screenshots of the mosaic using (a) NV, (b) FBA, and (c) SFW5 in the SYN dataset (Video 1, MP4, 1426 KB [URL: https://doi.org/10.1117/1.JMI.6.3.035001.1; Video 2, MP4, 8195 KB [URL: https://doi.org/10.1117/1.JMI.6.3.035001.2; Video 3, MP4, 2447 KB [URL: https://doi.org/10.1117/1.JMI.6.3.035001.3).

Fig. 12

Sequential screenshots of the mosaic using (a) NV, (b) FBA, and (c) SFW5 in the PHB dataset (Video 4, MP4, 2844 KB [URL: https://doi.org/10.1117/1.JMI.6.3.035001.4; Video 5, MP4, 3443 KB [URL: https://doi.org/10.1117/1.JMI.6.3.035001.5; Video 6, MP4, 811 KB [URL: https://doi.org/10.1117/1.JMI.6.3.035001.6).