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If you're looking for the best cheap MacBook sale prices, you've come to the right place, as we've just updated our guide with the latest 2018 models. The decision of whether or not you should pick up a new MacBook is an easy one: does it play to your strengths? Maybe you need the lightest and most portable machine out there today, one with good battery life. Or, maybe you just don’t like Windows? Whatever your reason, there are plenty of deals out there to help you save on a MacBook deal. Our exclusive price comparison tool will check the price of every readily available model of MacBook on all major retail websites, so you can be sure you’re always getting the best MacBook deal.

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We've stopped comparing MacBook prices on some older models if they're not widely available or if they generally cost more than newer versions despite the dated tech inside. All you need to do now is work out whether it’s a, a or a that you want. We'll help though. If you're not quite set on a MacBook (they are rather pricey), then we have some alternative options for you, along with the best prices.

Take a look at our selection of for other top performing machines or our for solid buys that won't break the bank as we search for great prices all year round. And given Christmas is coming soon, you may well find this is the best time of year to get a cheaper MacBook price. The 2018 version of the 13-inch Apple MacBook Pro is the best yet, comes with the Touch Bar as standard and features a range of improvements over the older models. The screen resolution may be the same with the excellent Retina display, but now there's True Tone technology inside that senses ambient lighting in the room or outdoors to adjust the brightness of the screen for the best possible picture.

The keyboard is quieter and less 'clicky' too. You're getting the brand new 8th-gen Coffee Lake core processor and the quad-core CPUs have doubled the performance of the 2017 models. With more options for larger RAM too, options really open up for creatives and professionals with the MacBook Pro 2018.

The larger 15-inch version of the 2018 MacBook Pro with the Touch Bar is generally going to cost a fair bit more than the 13-inch model, but that's not just because of the larger screen. This model packs a lot more under the hood too, with Apple providing multiple options with increased RAM, extra processing power with a six core Coffee Lake processor and larger SSD storage options. Naturally, you're getting the same improvements over the 2017 version too like the True Tone screen technology and quieter keyboard. This really is a powerhouse laptop for designers and industry creatives. If you don't need all the power though, we'd consider the cheaper 13-inch model, or maybe even one of the older versions found below if the prices are right for you. We check over 130 million products every day for the best prices The cheapest MacBook Air (2017) sale prices The MacBook Air series is making a comeback We have to admit, we thought Apple was done with the MacBook Air line after the new Pro lineup was just as compact and almost as light.

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Apple has given the 13-inch MacBook Air its first update since 2015 though. This means you can now get a much healthier 8GB of RAM instead of 4GB along with a processor upgrade to 1.8GHz (over 1.6GHz) making it much better at multi-tasking. Older MacBook Air stock is gradually disappearing from retailers now although prices have been stubbornly high even on refurbs. In all honesty, you're getting much better value by opting for this modern version instead. We check over 130 million products every day for the best prices The cheapest Macbook (2017) prices The Kaby Lake upgrade you've been waiting for? The screen and compact dimensions on the 2017 MacBook are the same as the 2016 edition.

But if you're weighing up the actual differences between the new 2017 and 2016 MacBooks, here are some key points to consider. You're now getting the 7th-gen Kaby Lake processors with i5 and i7 options now available. 2015 MacBook owners are more likely to appreciate the improvements really. The prices we're seeing lately though aren't that much more expensive than the 2016 models. We check over 130 million products every day for the best prices MacBook Pro (2017) 13 and 15-inch deals (with Touch Bar) A touch above the rest? The 2017 updates to the MacBook Pro lineup didn't change an awful lot in all honesty. The main improvement was the upgrade to Kaby Lake processors.

The 7th-gen chips offer increased performance for 4K streaming and media editing. Eventually the 2016 versions will disappear at most retailers, but it's worth keeping an eye on the comparison chart below to see if there any are discounted models lingering around. Load more deals MacBook Pro (2016) 13 and 15-inch deals (with Touch Bar) 2016 was crying out for a refresh of the MacBook Pro and Apple once again came up with something rather special.

In addition to the internal spec getting a long awaited upgrade and that gorgeous Retina display (available in 13-inch and 15-inch flavours), Apple introduced its long-rumoured Touch Bar technology. This mini-LED display replaces the Function keys and comes up with different touch display controls for loads of different programs. Uses so far include safari bookmarks, predictive text, search field, emojis, photo galleries or even more intensive actions like photo editing or mixing records. Simple, yet innovative. Load more deals 2017/2016 MacBook Pro 13-inch deals (no Touch Bar) The 2016 and 2017 models are MacBook Air rivals with Pro spec The older 13-inch MacBook Pros are amongst the cheaper options if you want to go Pro.

These versions don't come with a Touch Bar which is something to factor in when comparing how much you'll save versus the added functionality the new tech could add to your work and computing life in general. These are incredibly light for MacBook Pros, but they still pack an incredible punch with 2.3GHz (2.0GHz on the 2016 model) and dual core processors ranging from i5 to i7. The trackpads are larger than older MacBook Pros too and you're getting fantastic Retina displays which still look stunning today. We check over 130 million products every day for the best prices MacBook Pro 13-inch with Retina display (2015) deals The older and smaller MacBook Pro is still a force of nature The 2015 MacBook Pro didn't undergo a dramatic reimagining, but then there wasn't anything particularly wrong with it in the first place. Improvements to its performance meant it was better value than before, and the noticeably improved battery life makes it even more of a mobile workhorse.

MacBook Pro 15-inch with Retina display (2015) deals Looking for something a bit bigger? If you're looking for the larger-sized laptop experience in the MacBook range, the 2015 model 15-inch MacBook Pro with Retina display is still an impressive piece of kit and arguably worth a shout even today if you can get a good price. The Intel Core i7 2.5 GHz processor combined with 16GB of RAM will make light work of anything you can throw at it. 512GB of super fast flash storage, a new Force Touch trackpad and that incredible four million pixel-packing display make this a fantastic laptop.

25 Design and Implementation of a Navigation System for Laparoscopic Tumor. Paolucci et al. Ultrasound system (LUS).

A clamp with an integrated sensor is attached to the LUS to measure its 6D pose. The LUS is calibrated 5 and therefore the system knows the geometric transformation between the 2D US image and the coordinate system of the EM tracking. 2.1 Target Selection & Navigation Workflow The surgeon first scans the liver using the 2D LUS as in conventional treatments. When the tumor has been identified on the US image the surgeon marks the approximate center by pressing on it in the US image viewer on the touchscreen interface. This causes the image to freeze, and provides commands to move the target horizontally, vertically and orthogonal to the image plane. Additionally, the size of the tumor can be adjusted to simplify the selection of the center.

While the surgeon adjusts the target a second live US image is provided with an overlay of the currently defined target, which allows the surgeon to verify the selection (Figure 1 left). Once the target has been defined appropriately, the navigation state begins. During navigation, the surgeon is provided with a cross hair viewer which allows the alignment of the needle guidance device to the tumor. Additionally the predicted lateral error and the depth to the target are visualized. The predicted needle trajectory is also projected onto the ultrasound image, allowing the surgeon to verify that the trajectory will not interfere with important anatomical structures. This second part of the software is shown on the right screenshot in Figure 1.

The overlay of the defined target on the US image allows the surgeon to detect displacement of the tumor and reacquire the target if necessary. 1: The selection of the tumor center on the left and the navigation using the cross hair viewer on the right.

The red line overlay shows the predicted needle trajectory and the yellow circle the defined target. 2.2 Tracked needle and needle guides During navigation, the ablation needle has to be accurately placed into the target.

After the entry point is chosen and the needle is touching the skin the surgeon has three degrees of freedom to control: two rotational axes and the depth to the tumor. This control is supported by information from the tracked instruments, which can be used interchangeably.

In Figure 2 these instruments are shown and explained in the subsequent paragraphs. 2: The three tracked instruments from left to right: trocar, seestar and tracked ablation needle. 32 Soft Tissue Surgery CURAC 2016 (a) (b) Figure 2: (a) Separate parts of the 3D printed prostate model from the printer, and (b) assembled model as it may be used in doctor-patient interview. The application employs computer vision algorithms on printed images, so called image targets.

Once those targets have been recognized, digital content can be aligned and fitted into the scene. Two different targets are used, each with their own purpose: one target is used to simulate buttons, the other one augments the 3D prostate model. The application was written in C#, using Unity3D, a game development software, in combination with the Vuforia Augmented Reality Plugin. User Interaction We offer two different interaction paradigms, one based on standard touch input on the ipad, the other based on a technique called virtual buttons (VB). VB are image targets that may be occluded by the user, i.e.

Hovering the hand over it whilst in the field of view (FoV) of the tablets camera. This fires a subsequent action, similar to a button press. Printed on a piece of paper, see Fig. 4, the virtual buttons offer the same functionality as the user interface (UI) of the application. Evaluation A user study (n = 11, 11 male, age: 31.2 ± 5.6 years) was conducted to check our usability hypothesis. The evaluation was done twofold: first, the results of the questionnaires were simply compared to each other, and secondly the summed scores of each participant per questionnaire were statistically evaluated.

Both paradigms in the systems were tested for usability with two different questionnaires, ISONORM based on ISO 9 and QUESI 10. It was hypothesized, that the display based paradigm would score considerably better in both questionnaires, based on the following assumptions: touch displays are already a ubiquitous way of interaction with mobile devices, thus users are already accustomed to using them and, furthermore, the video see-through paradigm is altered in the VB based paradigm is altered by the distortion between the fields of view in both the devices camera and the user. Depending on a randomly assigned number (1 or 2), participants were asked to work through a block of four tasks, once with the display based paradigm and once with the virtual buttons. The tasks included typical use cases of the application, such as displaying and hiding of specific structures and changing their opacity. The assigned number determined, which paradigm should be used first.

The order of tasks was shuffled, so to minimize simple repetition. A pilot test confirmed feasibility and functionality of the study.

3 Results From the ISONORM questionnaire, some questions have been excluded from evaluation due to inapplicability to our project. Those questions dealt with menus and masks, error tolerance and individualization. Results are shown in Fig. These results show that participants evaluated the usability of the display based paradigm better than that of the VB paradigm. The one tailed, paired t-test we employed for significance testing confirms 13. 67 Quantitative measurements of surface reconstructions obtained with images a. Milosavljevic et al.

For comparison, it was important to obtain a ground truth surface reconstruction of the same object. XtremeCT, by Scanco Medical AG 17, was used for X-ray CT-imaging and reconstructing of the thresholded images with the Marching Cubes algorithm. After mirroring, this gave a dense 3D reconstruction of the object as ground truth. 2 Materials and methods In this qualitative measurement, procedures are explained stepwise through our materials and methods, as shown in Figure 1.

The navigated Leica stereo microscope was used, which is capable of bidirectional communication Figure 1: Schematic representation of our program. And equipped with two Baumer 9 ethernet color cameras TXG06c, with pixel size 8.3 x 8.3 μm 2. From the bidirectional microscope communication zoom level and focus information were obtained. Stereo calibration was performed separately for each of the zoom steps. This was done to avoid distortions and changes in the baseline between two cameras.

To perform the stereo calibration (based on Zhang paper 21) itself, the aluminium chessboard (9 x 6 squares) was used, where each square was 3 x 3 mm 2, in order to fit to the microscope field of view degrees of freedom were available for chessboard orientation, due to fact that in some corners focus would be lost. As known for microscopes, the bigger the zoom, the less space in focus is available. Images of the chessboard from left and right view were taken simultaneously from both cameras, totalling 14 pairs. This was done with minimal zoom and maximal focus. From this, intrinsic parameters (focal length, image sensor format, principal and root mean squared error RMS point) were obtained. This error represented a geometric quantity, where image points were compared with reprojected points with use of camera parameters 5.

In OpenCV, pixel unit is advantage since it does not depend on the geometry 15. A non-symmetrical wooden object was used, (size was 10 x 10 x 10 cm 3 ). This object was marked with Swarovski retro-reflective balls 20 for point registration. Pairs of images for wooden object were taken at the minimal zoom level and maximum focus and then rectified with stereo calibration parameters, as shown in Figure 2; (a) is the left image before rectification, (b) and (c) are rectified images reprojected to the common image plane, which makes both cameras parallel and, this is proven by the red line. These rectified images were processed separately with BM 19 or SGBM 5 methods to obtain disparity maps.

Filtered BM and SGBM were used with weighted least square filter as is implemented into disparity map post filtering 5 in OpenCV This helped to avoid problems with half-occlusions and depth discontinuities. Point cloud points were mapped with color points in PCL 7. Scaling was solved with Q matrix 5 obtained from stereo rectification in OpenCV. The.ply data was then displayed in VTK 8 custom-written application and exported for use in Meshlab 6. 68 Endoscopy & Microscopy CURAC 2016 Figure 2: The difference between non-rectified and rectified images: (a) Normal left image, (b) and (c) are left and right rectified images with the calibration parameters. For SURF 2, SIFT 1, KAZE 3 and AKAZE 4, rectified images with same calibration parameters were used for feature detection and matching.

To eliminate outliers, several test had to be passed: Ratio test: Checking the distance between points, as described in Lowe s paper 1. Symmetry test: Matching from left to the right image, and vice versa. By doing so, the picked points, were the matches that survived both methods. Fundamental matrix calculation: By using this calculation, keypoints were checked with RANSAC 16 8-point method, keypoints were updated only with inliers from this method. Points which survived those tests were undistorted with OpenCV 5 by the introducing intrinsic calibration parameters from both cameras and triangulated with simple triangulation 10. PCL 7 was used to convert from xyz format to polygon data, which later was used for comparison with Scanco data.

A Scanco microct 17 was used to get the 3D reconstruction of the object, as displayed in Figure 3. The surface was decimated from to triangles, to allow registration between this and the point cloud obtained from the microscope reconstructions. Meshlab 6 was introduced to grab both polygon files and to perform surface registration between them. Figure 3: Scanco: Reconstructed non-symmetrical object with Swarowski points (marked in blue circles) 49. 69 Quantitative measurements of surface reconstructions obtained with images a.

Milosavljevic et al. 3 Results and discussion The calibration procedure was done with RMS error 0.18 and focal length of 25 cm. Surface reconstructions with different parameters for ordinary BM 19 or SGBM 5 were not obtained due to problems with depth perception as shown in Figure 4.

Any block size or number of disparities would produce noise, since the object was too close to the optical lenses of the microscope. Even a small noise resulted in wrong point cloud coordinates. Sample (a), represents depth perception for normal BM 16 without filter, where black parts are missing information, while (b) represents filtered disparity map. Same results were obtained for SGBM 5, (c) and (d). Time consumption and metrics from reconstructed objects is represented in Table 1. Both point clouds were aligned by using 4 points, in this case Swarowski balls. Figure 4: Disparity representation: (a) Normal BM (b) filtered BM (c) normal SGBM and (d) filtered SGBM disparity.

Figure 5: Reconstructed: (a) BM filtered and (b) SGBM filtered Figure 6: Aligned objects: Scanco (gray) and microscope (color) reconstruction For SURF, SIFT, KAZE and AKAZE, the results of matching are displayed in Figure 7, which shows that there was no enough points for triangulation. For each method we obtained more than 148 keypoints, but only around 35 matches were valid for some of them, after they went through analyses, as shown in Table 2. 70 Endoscopy & Microscopy CURAC 2016 Method Filtered BM Filtered SGBM Scanco Time (ms) 7 3 Top size (mm) Top to bottom (mm) Registration error Table 1: Results for filtered BM and filtered SGBM Figure 7: Valid keypoints: (a) SURF (b) SIFT (c) KAZE (d) AKAZE Results were slightly different for filtered BM and filtered SGBM when lighting conditions or object distances were changed, causing the outliers in the Z coordinate.

For SURF, SIFT, KAZE and AKAZE, results were poor, but maybe the BRIEF 13 descriptor could solve those problems. This will be the subject of further investigations. After quantitative measurements, these algorithms will be tested on objects with richer textures, such as real surgical scenes. In future, these methods could be used even for eye or neurosurgery, since in those cases the surgical place is not homogeneous, which would provide much more salient features, but has low textured features (neuro) and specific illumination conditions govern ophthalmic surgery. Real-time stereo reconstruction 11 will be performed, since it was already used in endoscopy for dense 3D reconstruction and enhanced by gyroscope regularization to detect a poor quality features 12.

This pilot served to determine the best algorithms for the Quantitative Surgery project, where surface reconstruction of surgical spot will be combined with preoperative imagery (MR or CT), while using surgical navigation to provide certainty of resection borders. In this case, it is planned to use NDI Certus Optotrack optical navigation to determine camera pose related to the scanned object. 4 Summary Surface reconstructions with use of surgical stereo microscopes are possible and they depend strongly on calibration parameters, scene conditions and rig characteristics. Stereo calibration was performed for different setups of surgical microscope and images were rectified for further processing. Ordinary BM 19 or SGBM 5 were unable to create disparity maps of our wooden model, without big gaps 51 71 Quantitative measurements of surface reconstructions obtained with images a.

Milosavljevic et al. Method SURF SIFT KAZE AKAZE Time (ms) Keypoints Valid Keypoints Table 2: Processing times and valid features. For filtered BM or SGBM, viable disparity maps were created that allowed the surface reconstruction. Point clouds from filtered BM 19 and filtered SGBM 5 were compared with reconstructed surface from microct, by surface registration and showed similar dimensions. For SURF 2, SIFT 1, KAZE 3 and AKAZE 4 small number of valid points was obtained after performing symmetry and ratio tests, due to low texture differences. Valid points are shown and method how to get the stereo microscope surface reconstruction. 5 Acknowledgment Supported by funds of the Oesterreichische Nationalbank (Oesterreichische Nationalbank, Anniversary Fund, project number: 16154).

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6 References 1 Lowe D, Distinctive Image Features from Scale-Invariant Keypoints, IJCV,60, (2004). 2 Bay H, Tuytelaars T, Van Gool L, SURF: Speeded Up Robust Features, Computer Vision and Image Understanding, 110, (2008). 3 Alcantarilla P, Bartoli A, Davison A, KAZE Features, ECCV, Fiorenze, October (2012).

4 Alcantarilla P, Bartoli A, Davison A, Fast Explicit Diffusion for Accelerated Features in Nonlinear Scale Spaces, BMVC, Bristol, September (2013). 5 OpenCV documentation, (docs.opencv.org) 6 Meshlab, ( 7 PCL - Point Cloud Library, ( 8 VTK - The Visualization Toolkit, ( 9 Baumer - GAPI SDK v1.7 Programmers Guide, ( 10 Hartley R, Zisserman A, Multiple View Geometry in Computer Vision, ISBN, Cambridge University Press, Cambridge, (2004). 11 Visentini-Scarzanella M, Stoyanov D, Stereo Real-time stereo reconstruction in robotically assisted minimally invasive surgery, Medical Image Computing and Computer-Assisted Intervention 13, (2016). 12 Poling B, Lerman G, Enhancing feature tracking with gyro regularization, Image and Vision Computing, 50, 42-58, (2016). 13 Tafti A, Baghaie A, Kirkpatrick A, Holz J, Owen H, D Souza R, Yu Z, A comparative study on the application of SIFT, SURF, BRIEF and ORB for 3D surface reconstruction of electron microscopy images, CMBBE, 4, 1-14, (2016). 14 Schoob A, Kundrat D, Kahrs L, Ortmaier T, Comparative study on surface reconstruction accuracy of stereo imaging devices for microsurgery, International Journal of Computer Assisted Radiology and Surgery, 11, (2016). 15 Mertens B, Delchambre A, 3D-reconstruction: Why should the accuracy always be presented in the pixel unit?, Image and Vision Computing, 48-49, 57-60, (2016).

16 Fischler M, Bolles R, Random Sample Consensus: A Paradigm for Model Fitting with Applications to Image Analysis and Automated Cartography, Communications of the ACM, 24, (1981). 17 Scanco Medical, Bruttisellen, Switzerland ( 18 Forsyth D, Ponce J Computer Vision: A Modern Approach, X, Pearson, New York, (2011). 19 Je C, Park H, Optimized hierarchical block matching for fast and accurate image registration, Signal Processing: Image Communication, 28, (2013). 20 Swarovski, Wattens, Austria ( 21 Zhang Z, A Flexible New Technique for Camera Calibration, IEEE Transactions on Pattern Analysis and Machine Intelligence, 22, (2000). 52 72 Endoscopy & Microscopy CURAC D-Reconstruction by Polarization Imaging in Endoscopy J.

Sandvoss 1, T. Wittenberg 1,A.Nowak 1,J.Ernst 1 1 Fraunhofer Institute for Integrated Circuits IIS, Erlangen, Germany Abstract: Kontakt: Polarization cameras are a relatively new technology to capture, assess and analyze the properties of shiny surfaces and tissues in real-time. By making use of the acquired polarization parameters it is possible to recover 3D-surfaces from glossy tissues and organs via the so-called Shape-from-Polarization technique. Thus potential applications of these possibilities are scenarios like endoscopic MIS, SILS and NOTES interventions, in which monocular endoscopes provide limited depth perception.

This paper illustrates the principle of the Shape-from- Polarization approach for surface reconstruction by using the Shape-from-Shapelets method. The presented techniques have been validated by polarization images from test phantoms as well as for approximating a 3D height map of a pig liver phantom. Keywords: Endoscopy, Laparoscopy, Shape-from-Polarization, Shape-from-Shapelets 1 Problem Recovering depth information is one main challenge in interventional endoscopy, such as MIS (Minimal Invasive Surgery), SILS (Single-Incision Laparoscopic Surgery) or NOTES (Natural Orifice Transluminal Endoscopic Surgery Interventions).

Providing depth maps of the operating areas to surgeons may lead to safer and faster interventions. Besides the well-known and widely discussed 3D-reconstruction techniques such as Shape-from- Shading, Shape-from-Stereo, Shape-from-Color 9, laser scanners or Time-of-Flight cameras 8, shape and depth analysis using polarization imaging has recently attracted some attention 4.

Polarization cameras are a relatively new and fast approach to acquire, process and visualize polarization effects of glossy surfaces or tissues in real-time, without mounting and moving a polarization filter and capturing a series of images with varying polarization angles. The captured polarization data is then used by the Shape-from-Polarization technique for reconstruction purposes. This paper studies the Shape-from-Polarization approach for a qualitative 3D surface reconstruction of shiny tissues surfaces, as they occur in laparoscopic interventions.

2 Material and Methods The Shape-from-Polarization method relies on the observation, that unpolarized light becomes partially linearly polarized when it is reflected, depending on the surface normal and the refractive index of the medium it incides on 10. With nowadays polarization cameras offering one-shot image acquisition, measuring the polarization state of those reflected light rays, has become feasible.

If the refractive index is known, a relation between the polarization parameters and the surface normals of the lit-up scene can be derived. 1 reveals, the Shape-from- Polarization model assumes telecentric lenses to be used, so only reflected light rays parallel to the optical axis are captured by the camera. Similar to Shapefrom-Shading, 3D height maps are generated out of gradient fields derived from normal maps. 2.1 Determination of Surface Normals If one assumes a continuous surface f(x, y) =z, the corresponding surface normals n are given by ) n = = ( f(x,y) x f(x,y) y 1 Z z camera Y y x X Surface f(x, y) Plane of Incidence Light Rays Normal Vector Angle of Reflection Angle of Incidence Azimuth Angle Zenith Angle Figure 1: Shape-from-Polarization principle ( tanθcosφ ) tanθsinφ 1, (1) 53 73 3D-Reconstruction by Polarization Imaging in Endoscopy J. Sandvoss et al. Degree of polarization, n t =1.5 1 degree of polarization θ li θ br θ re incident angle θ i (a) Ambiguity of the azimuth angle φ (b) Ambiguity in calculation of the zenith angle θ Figure 2: Ambiguity of in derivation of azimuth and zenith angle whereas the gradient fields are denoted by f(x,y) x, f(x,y) y and the zenith and azimuth angle are written as θ, φ.

The plane of incident is spanned by the surface normal and the incident ray. If we only consider specular reflection, in which light gets partially linearly polarized perpendicular to the plane of incidence, the polarization angle ϕ and azimuth angle φ differ by 90, which means that φ = ϕ ± 90 (see Figure 2a). Such ambiguity can not only be observed in the azimuth angle φ, but also in the zenith angle θ, which is calculated out of the specular degree of polarization ρ, described as ρ = 2sin2 θ n 2 t sin 2 θ n 2 t sin 2 θ + sin 4 θ n 2 t sin 2 θ n 2 t sin 2 θ + 2sin 4 θ. (2) The curve in Figure 2b illustrates the behavior of ρ for a refractive index of n t =1.5.

In addition it can be seen, that a single constant value of ρ has two intersections indicating two possible zenith or incident angles θ li, θ re, except for ρ = 1, which indicates completely polarized light observed at the Brewster angle θ br. 2.2 Shape-from-Shapelets Frankot and Chellappa s reconstruction algorithm 3 applied to Shape-from-Shading projects the surface gradients onto the integrable, non-redundant Fourier basis functions. An alternative way to get the integration done, is to take a set of redundant, non-orthogonal and finite basis functions, the so-called Shapelets (in most cases: 2D Gaussians) 5. Instead of processing the gradients directly, the implicit integration is done by summation of the correlation between azimuth and zenith angles of the scaled Shapelets and the captured object. Due to linearity of the first derivative, correlation between gradients derived out of azimuth and zenith angles is equivalent to direct correlation between the two signals. The correlation of zenith angles is calculated by C,i = m s,i, whereas s,i and m are gradient magnitudes of the object and the i-th scaled basis function, which are given by = tan(θ). The similarity of azimuth angles is measured over C φ,i = cos(φ m φ s,i ) and adds to the total summation of correlation C i = C,i C φ,i over different scales i, which leads to a full reconstruction f (x, y) = i C i = i m s,i cos(φ m φ s,i ).

(3) 2.3 Acquisition Setup The polarization images were captured by a polarization camera (POLKA, Fraunhofer IIS 2), which has the possibility to obtain polarization information of a scene in one shot. Although the Shape-from-Polarization model assumes telecentric lenses, a projective lens was used, because of further practical applications.

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Due to the spectral sensitivity of the camera a ring of independently controlled infrared-leds (ca. 850 nm) is mounted on a lighting dome. Thus a diffuse, homogeneous illumination of objects is guaranteed, which is schematically shown in Figure 3. 74 Endoscopy & Microscopy CURAC 2016 r a r i z h x y (a) Case of the dome (b) Illumination principle (c) LED ring used for diffuse lighting Figure 3: Acquisition setup 3 Results First the presented technique for generating 3D height maps out of polarization data was validated with three glossy lacquered test objects out of metal. Simple test phantom geometries, namely a calotte, an edge and a cone were evaluated. The cone test geometry and its corresponding surface approximation are depicted in Fig. Obviously the cone shape can be recovered correctly, but the object s original ratio of diameter to height is changed because the scaling property of Shapelets shows up.

To test the practical application, shape parts from a animal liver phantom were extracted, as it is visualized in Figure 5. The resulting depth map of the selected region of interest (ROI) (Fig. 5a), which is calculated by applying the Shape-from-Shapelets algorithm, is plotted in two different perspectives in Figure 5b and 5c.

It is important to mention, that in this case the Shapelets are working with ambiguous azimuth and disambiguous zenith angles θ li. 92 Computer Aided Orthopedic Surgery CURAC 2016 number manufacturer market name base material additive grayscale value 1 Turner MedTech GMASS tungsten ABS wolfram Turner MedTech GMASS bismuth ABS bismuth ColorFabb bronzefill PLA bronze ColorFabb copperfill PLA copper ColorFabb brassfill PLA brass ProtoPlant stainless steel PLA steel ProtoPlant magnetic iron PLA iron TreeD filaments CAEMENTUM PLA concrete ColorFabb glowfill PLA aluminate ColorFabb Standart White ABS none Table 1: Filaments used for the reference geometry. Average grayscale values are taken from the X-ray image taken with an Exposcop 8000, Ziehm Imaging GmbH.

A value of 0 represents black, a value of 255 represents white. Each pad has a thickness of 3 mm. Figure 1: From left to right: PSI for application in the acetabulum (the cylinder on the backside represents the desired implant axis and can be used to align a bone fixated linear guide), embedded reference wire inside the PSI, simulated application, photo (top) and X-ray (bottom) of pads made from different filaments.

Each pad has a thickness of 3 mm. Figure 2: Different design concepts of references geometries.

(I) Needle, 30 mm length (II) pattern, 1 mm edge length (III) notch and bead sighter 1, 13.2 mm hypotenuse (IV) notch and bead sighter 2, 12 mm outer diameter. For a first evaluation of the designs different methods have been used based on the test setup seen in Fig. In this setup a X-ray apparatus (Exposcop 8000, Ziehm Imaging GmbH) is used to create 2D projection images of a PSI dummy with reference structure. The PSI is mounted on a three degree of freedom (DOF) positioning table, which can be adjusted using micrometer screws. After a brief introduction three orthopedic surgeons, three engineers and three uninvolved test persons where asked to evaluate the different systems for the task of correctly orienting a PSI only with a single X-Ray image of the malpositioned PSI as reference. The difference between the planned and the actual orientation of the PSI adjusted by the participants was used as quality 73. 97 Exact Determination of the Scaling Factor in X-ray Images for pre-operative.

Gieseler et al. 1: Structure and geometry of an X-ray apparatus Fig. 2: Test setup for hip joint center determination during motion 3 Results To evaluate the method we created a test arrangement composed of an artificial femur bone pivot-mounted in a table holder, representing the pelvis (Fig.

X-ray images were generated with a Ziehm Vario 3D C-arm (23cm image intensifier, 97cm source detector distance). The application of the procedure will be carried out in the X-ray room before image acquisition, while the patient is lying in supine position, and shall not take more time than accurate placement of a calibration body. In a first trial setup a calibration body positioned exactly in the joint plane has been used to calculate a reference scaling factor.

Scaling factors determined by our approach differ by less than 2% from this reference factor. 4 Discussion and Conclusion In summary, the first tests justify the assumption that our approach offers a more accurate and reproducible way to determine the scaling factor of X-ray images. In contrast to conventional methods it neither depends on statistical factors nor on a more or less accurate positioning of calibration bodies. Potential inaccuracies may arise from limited camera 3D accuracy and unintentional relative movement of the DRB to the thigh bone and finally the hip joint center, due to soft tissue elasticity.

Influence of the last one has not yet been considered. In forthcoming steps the practical applicability, possible error sources and achievable accuracy will be further investigated. 5 Acknowledgements Part of this work is carried within the framework of the ZIM project KF KJ4 funded by the German Federal Ministry BMWi. 6 References 1 Clarke IC, Gruen T, Matos M, Amstutz HC Improved methods for quantitative radiographic evaluation with particular reference to total hip arthroplasty. Clin Orthop Relat Res. 121: 2 King R J, Makrides P, Gill J A, Karthikeyan S, Krikler S J, Griffin D R A novel method of accurately calculating the radiological magnification of the hip. J Bone Joint Surg Br 2009;91-B: 3 Riddick A, Smith A, Thomas D P.

Accuracy of preoperative templating in total hip arthroplasty Journal of Orthopedic Surgery 2014;22(2):173-6 4 Wimsey S, Pickard R, Shaw G. Accurate scaling of digital radiographs of the pelvis J Bone Joint Surg Br 2006;88-B: 5 Blake CA, van der Merwe J, Raubenheimer JE.

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A practical way to calibrate digital radiographs in hip arthroplasty SA Orthopedic Journal Vol 12, No 4 6 Heinert G, Hendricks J, Loeffler M D. Digital templating in hip replacement with and without radiological markers J Bone Joint Surg Br 2009;91-B: 98 Continuum Robots and Flexible Manipulators 79 99 80. 101 Initial Feasibility Study for Transurethral Kidney Surgery using a Tubular. Bormann et al. Figure 2: Tubular continuum manipulator composed of three tubes with tube length l 1,l 2,l 3, translational parameters β 1,β 2,β 3 and rotational parameters α 1,α 2,α 3. Exists no robotic system until now which considers transurethral access to the kidney.

However, continuum robots have been proposed for transurethral prostate surgery (e.g. To design a tubular continuum manipulator for a specific surgical task, the design and configuration parameters have to be optimized according to specific design and anatomical constraints. As the design parameter space is diverse, researchers proposed the use of optimization algorithms, such as 5, 6, 7, 8.

However, most of these algorithms only consider non-linear optimization algorithms with one scalar error metric to be maximized or minimized. None of the existing algorithms considers multiple objectives, or consider a pareto-optimal set of solutions. However, in many surgical applications exist competing objectives such that a single error metric cannot sufficiently reflect the complexity. Thus, we propose a new optimization approach using a multiobjective particle swarm algorithm to optimize tube parameters (length and curvatures) of the tubular continuum manipulator for transurethral kidney surgery. The contributions of this paper are: 1) design constraints for the tubular manipulator, 2) workspace characterization of three patient kidneys, 3) a new optimization algorithm which utilizes particle swarm optimization and considers multiple objectives for tube parameter optimization and 4) evaluation of the proposed algorithm considering three patient kidneys.

2 Material and Methods 2.1 Tubular Continuum Manipulator Tubular continuum manipulators are composed out of n (n 2) concentric, precurved, superelastic tubes. In this paper, we consider tubes made from the shape memory alloy Nitinol (NiTi), which remains strains up to 8% without damage. The tubes are inserted into one other and mechanical translation and rotation of each tube generates a tentacle-like motion in 3D space. In this paper, n = 3 concentric tubes are considered. Each tube i is defined by an inner and outer diameter ID i and OD i, a straight length L si and a curved length L ci with constant curvature κ i. The overall length of a tube is defined as: l i = L si + L ci,wherel 1 l 2 l 3 with l 1 being the innermost tube and l 3 the outermost tube Configuration Space The configuration space of a tubular continuum manipulator is of dimension 2n, with the rotational parameters α i π, π) and translational parameters β i l i, 0 for each tube i which are subject to β 1.

Β n 0, (1) l n + β n. (2) The manipulator s shape is characterized by its space curve g(s) SE(3), which is parameterized in terms of arc length s, wheres = 0 is defined at the constrained outlet of the manipulator, as illustrated in Figure 2. The manipulator s space curve g(s) and can be determined by e.g. Using the forward kinematics model in 9 Design Constraints Design constraints are formulated according to the specific anatomical constraints and the diameter of the working channel of the endoscope. Prior defined tube parameters are: ID 1 = 1 mm, OD 1 =1.2 mm, ID 2 = 82. 104 Continuum Robots and Flexible Manipulators CURAC 2016 with w being the inertia weight, c 1 and c 2 are constants controlling the influence of personal versus global best and r 1 and r 2 are randomly chosen in the range of 0, 1. If vm t+1 exceeds a prior defined maximum velocity v max,thenvm t+1 = v max.

The maximum velocity v max is defined as 10% of the range of values of each particle s dimension. Enforce Constraints: To enforce constraints on the parameter space, particles exceeding the boundary are truncated at the boundary and their value is reflected by their boundary exceeding value, defined as upper u bp or lower boundary l bp: x t ubp (x t m m p = p u bp ),if x t m p u bp l bp +(l bp x t m p ),if x t (8) m p.

107 First Study on a Monolithically Manufactured Variable-Length Continuum Robot. Kundrat et al. Scribes fabrication of miniaturized silicone-based manipulators with similar concepts to 7 but without moderating sleeve to increase dexterity. Finally, an extensible manipulator solely based on tendon-driven actuation in combination with a telescopic push-pull mechanism was presented 12. Magnetic repulsive forces enable an equal distribution of spacer disks within each segment.

The deformable and telescopic backbone furthermore facilitates follow-the-leader movements. Beyond, further groups addressed additive fabrication of snake-like structures 13, 14. For the sake of completeness, stiffness control in continuum robots can also be established model-based if previously mentioned mechanism designs do not enable intrinsic stiffness adjustment 16. Regarding aforementioned references, this work targets miniaturization of soft robotics for medical applications and exploration of frontiers in state-of-the-art manufacturing technology. We propose a novel monolithically fabricated soft manipulator for MIS considering a tendon- and hydraulic-driven actuation scheme. In this context, following hypothesis are raised: (1) manufacturing of soft continuum robots is feasible without well-established but time consuming and costly casting procedures and (2) a combination of tendon and hydraulic actuation can be successfully applied to variable-length manipulators in MIS. The remainder of the paper describes the conceptual design and manufacturing of our prototypes.

Finally, an early evaluation is provided to underline applicability of our approach. 2 Materials and Methods Requirements Our concept targets application in MIS. In this regard, a design constraints and requirements are defined based on potential medical scenarios focusing mechatronic assistance in manipulation.

We consider scenarios requiring improved dexterity in anatomical cavities such as arise physiologically (e.g. Laryngeal compartment) or artificially (e.g. Abdominal CO 2 insufflation prior to single-/multi-port laparoscopy).

Targeting these objectives, the outer diameter of the manipulator should not exceed a maximum of 8 mm in order to enable feeding through standard trocars or the oral cavity. Moreover, increased dexterity is expected from two actuated continuum segments (two degrees of freedom (DoF) each) and variable-length sections resulting for adjustable bending radii. This work targets an elongation of at least 50% and a segmental bending angle of at least 90, respectively.

Additionally, the concept should prospectively enable an adaptive stiffening mechanism for stabilizing the manipulator while executing tasks under occurring external loads. A hybrid actuation concept should combine intrinsic (hydraulic) and extrinsic (tendon-driven) actuation for specific DoF. Finally, proposed continuum segments are manufactured additively in a single process for demonstration of cost effective specific robotic designs and for exploration of limits in state-of-the-art manufacturing. Concept and Design Our design is inspired by aforementioned references and combines advantages of tendon actuation and superior force transmission as well as length extension controlled by hydraulics. Up to the authors knowledge, this design has not been presented before for continuum manipulators and in particular not in the context of additive manufacturing of miniaturized instrumentation. Figure 1: CAD model of proposed manipulator.

A) Overall set-up with antagonistic tendon routing. Tendons (yellow/red) are attached to end disks of each segment.

B) Cut-out to expose design of hydraulic chamber. Components (light blue/green/red) are fabricated in ABS material whereas bellow elements (black) are fabricated with flexible materials. Our concept basically aims at a fluid-filled spine composed of elastic elements to implement extension and contraction while adjusting hydraulic pressure. Additionally, we provide a stiffening mechanism by increasing internal pressure while maintaining a constant tendon length as proposed in 4. The manipulator concept presented in Figure 1 is composed of two actuated continuum segments sharing a single hydraulic chamber. The chamber is implemented as flexible spine composed of stacked bellow segments. Two consecutive bellow elements share one common spacer disk which guarantees tendon routing.

Our proof-of-concept prototype 88. 108 Continuum Robots and Flexible Manipulators CURAC 2016 employs antagonistic coupled actuation as described in 4. Further design modifications also address a triangular layout of independent tendons 12.

Holes for tendon guidance are equally distributed depending on their location within the first (eight/six holes) or the second (four/three holes) segment. Bending of each segment is achieved in two degrees of freedom with an antagonistic pair of tendons fixed to the end effector disks of each segment. In this regard, each spacer disk ( 7.5 mm) is connected to two elastic bellows. Hence, this arrangement forms a chain of springs with intermediate non-elastic elements enabling equal distribution of spacers due to elastic forces.

Thus, constant curvature modeling can be applied 15. All bellow-spacer units share a common fluidic reservoir to enable equally distributed expansion. Within the range of applicable materials, we expect both segments to expand dominantly in axial direction. In contrast to 4 and 7, this design is not dependent on additional sleeves to constrain radial expansion of inflatable continuum bodies or bladders because routed tendons impose a radial constraint.

Manufacturing & Assembly The described manipulator is manufactured additively in a single print using state-of-the-art Polyjet technology (Objet 350 Connex3, Stratasys Ltd., MN, USA). The desired material properties are achieved by applying a multi material configuration including ABS and rubber-like materials (TangoBlackPlus). The average printing time for a single manipulator is approx. Subsequent to the printing procedure, support material is removed and tendons (NiTi wire, 0.2 mm) are routed and glued to the end effector disks of each segment. Optional parts (e. Plugs and connectors) are fabricated simultaneously. The final end effector disk is sealed with a plug to establish an enclosed hydraulic chamber.

The base element is connected to the hydraulic reservoir by introducing a customized connector. Afterwards, the hydraulic chamber is filled with distilled water (less deposition) representing the employed hydraulic fluid. Experimental bench The experimental set-up for evaluation is shown in Figure 2. The base of the continuum robot is attached to a mounting block and fixated to an optical table. As mentioned above, distilled water is used as hydraulic fluid which is pressurized by using a syringe connected to the hydraulic chamber of the continuum robot. Tendons are guided centrally though the mounting block and employed for manual actuation of both segments. At the current state, the presented prototype is manually actuated and bending behavior is preliminary estimated from top view images.

Figure 2: Experimental set-up to characterize the mechanical and kinematic behavior of developed continuum robot. 109 First Study on a Monolithically Manufactured Variable-Length Continuum Robot. Kundrat et al. 3 Results Preliminary experiments have been conducted in order to characterize the mechanical and kinematic behavior of our proposed manipulator with image-based analysis. First, a planar movement was performed exemplarily in relaxed configuration (no hydraulic compression or extension) involving partial bending of both segments.

As depicted in Figure 3, the end effector was moved manually from right to left site of the base traversing a straight configuration. In Figure 3a, circular segments are overlaid to the initial configuration to verify the effect of equidistantly distributed spacer disks due to elastic material forces exerted from bellow components. Hence, both segments show constant bending radii R 1 and R 2.

Figure 3: Image sequence of planar bending motion employing embedded tendons incorporating bending of both continuum segments. A) Inital configuration including overlay of circle segments to validate constant curvature assumptions to c) straight and d) final configuration. The second experimental set targets to reach a variety of three-dimensional configurations in order to characterize the behavior within workspace boundaries. Figures 4a to 4c show an excerpt of motion sequences while manipulating both segments independently. Motion sequences with lateral movement and quasi-constant orientation are achievable. As presented in Figure 4c, maximum bending angles of 90 of individual segments with respect to the base line can be estimated. Furthermore, compliance of the continuum structure is depicted in Figure 4d, simulating tissue contact.

The structure diverts under applied lateral load and returns to its prior configuration after removal of external loading. Increasing the hydraulic pressure while maintaining a constant tendon length results in increased stiffness being in accordance with the findings regarding pneumatic manipulators 4. Figure 4: Out-of-plane bending motions and manipulator compliance. A) - c) Arbitrary robot configurations to exploit the reachable workspace. D) Structural compliance is demonstrated by applying an external force.

The final experiment described in Figure 5 considered the evaluation of proposed variable-length design. The hydraulic pressure was decreased until ultimate compression of all integrated bellows is recognized. This configuration defines the minimal length min = 37 mm and does not allow bending due to geometric and m.