A three-dimensional representation method for noisy point clouds based on growing self-organizing maps accelerated on GPUs

The research described in this thesis was motivated by the need of a robust model capable of representing 3D data obtained with 3D sensors, which are inherently noisy. In addition, time constraints have to be considered as these sensors are capable of providing a 3D data stream in real time. This thesis proposed the use of Self-Organizing Maps (SOMs) as a 3D representation model. In particular, we proposed the use of the Growing Neural Gas (GNG) network, which has been successfully used for clustering, pattern recognition and topology representation of multi-dimensional data. Until now, Self-Organizing Maps have been primarily computed offline and their application in 3D data has mainly focused on free noise models, without considering time constraints. It is proposed a hardware implementation leveraging the computing power of modern GPUs, which takes advantage of a new paradigm coined as General-Purpose Computing on Graphics Processing Units (GPGPU). The proposed methods were applied to different problem and applications in the area of computer vision such as the recognition and localization of objects, visual surveillance or 3D reconstruction.

Noninvasive imaging of three-dimensional micro and nanostructures by topological methods

We present topological derivative and energy based procedures for the imaging of micro and nano structures using one beam of visible light of a single wavelength. Objects with diameters as small as 10 nm can be located and their position tracked with nanometer precision. Multiple objects dis-tributed either on planes perpendicular to the incidence direction or along axial lines in the incidence direction are distinguishable. More precisely, the shape and size of plane sections perpendicular to the incidence direction can be clearly determined, even for asymmetric and nonconvex scatterers. Axial resolution improves as the size of the objects decreases. Initial reconstructions may proceed by gluing together two-dimensional horizontal slices between axial peaks or by locating objects at three-dimensional peaks of topological energies, depending on the effective wavenumber. Below a threshold size, topological derivative based iterative schemes improve initial predictions of the lo-cation, size, and shape of objects by postprocessing fixed measured data. For larger sizes, tracking the peaks of topological energy fields that average information from additional incident light beams seems to be more effective.

Three-dimensional kinetic adaptations of gait throughout pregnancy and postpartum

Biomechanical adaptations that occur during pregnancy can lead to changes on gait pattern. Nevertheless, these adaptations of gait are still not fully understood. The purpose was to determine the effect of pregnancy on the biomechanical pattern of walking, regarding the kinetic parameters. A three-dimensional analysis was performed in eleven participants. The kinetic parameters in the joints of the lower limb during gait were compared at the end of the first, second, and third trimesters of pregnancy and in the postpartum period, in healthy pregnant women. The main results showed a reduction in the normalized vertical reaction forces, throughout pregnancy, particularly the third peak. Pregnant women showed, during most of the stance phase, medial reaction forces as a motor response to promote the body stability. Bilateral changes were observed in hip joint, with a decrease in the participation of the hip extensors and in the eccentric contraction of hip flexors. In ankle joint a decrease in the participation of ankle plantar flexors was found. In conclusion, the overall results point to biomechanical adjustments that showed a decrease of the mechanical load of women throughout pregnancy, with exception for few unilateral changes of hip joint moments.

Critical behavior of the three-dimensional Ising spin glass

We have simulated, using parallel tempering, the three-dimensional Ising spin glass model with binary couplings in a helicoidal geometry. The largest lattice (L520) has been studied using a dedicated computer (the SUE machine). We have obtained, measuring the correlation length in the critical region, strong evidence for a second-order finite-temperature phase transition, ruling out other possible scenarios like a KosterlitzThouless phase transition. Precise values for the ν and ƞ critical exponents are also presented.

Critical behavior in the site-diluted three-dimensional three-state Potts model

We have studied numerically the effect of quenched site dilution on a weak first-order phase transition in three dimensions. We have simulated the site diluted three-states Potts model studying in detail the secondorder region of its phase diagram. We have found that the n exponent is compatible with the one of the three-dimensional diluted Ising model, whereas the h exponent is definitely different.

Three-dimensional kinetic adaptations of gait throughout pregnancy and postpartum

Biomechanical adaptations that occur during pregnancy can lead to changes on gait pattern. Nevertheless, these adaptations of gait are still not fully understood. The purpose was to determine the effect of pregnancy on the biomechanical pattern of walking, regarding the kinetic parameters. A three-dimensional analysis was performed in eleven participants. The kinetic parameters in the joints of the lower limb during gait were compared at the end of the first, second, and third trimesters of pregnancy and in the postpartum period, in healthy pregnant women. The main results showed a reduction in the normalized vertical reaction forces, throughout pregnancy, particularly the third peak. Pregnant women showed, during most of the stance phase, medial reaction forces as a motor response to promote the body stability. Bilateral changes were observed in hip joint, with a decrease in the participation of the hip extensors and in the eccentric contraction of hip flexors. In ankle joint a decrease in the participation of ankle plantar flexors was found. In conclusion, the overall results point to biomechanical adjustments that showed a decrease of the mechanical load of women throughout pregnancy, with exception for few unilateral changes of hip joint moments.

In vitro characterization of the three-dimensional strain pattern in human vertebrae affected by metastases

La colonna vertebrale è la principale sede di metastasi, le quali possono alterare la normale distribuzione dei tessuti ossei e ridurre la capacità della vertebra di sostenere carichi. L’instabilità spinale causata dalle metastasi, tuttavia, è di difficile determinazione. La caratterizzazione meccanica delle vertebre metastatiche permetterebbe di identificare e, di conseguenza trattare, quelle ad alto rischio di frattura. In questo studio, ho valutato il comportamento meccanico a rottura di vertebre umane affette da metastasi misurando in vitro il campo di deformazione. Undici provini, costituiti da due vertebre centrali, una metastatica e una sana, sono stati preparati e scansionati applicando carichi graduali di compressione in una micro-tomografia computerizzata (μCT). Le deformazioni principali sono state misurate attraverso un algoritmo globale di Digital Volume Correlation (DVC) e successivamente sono state analizzate. Lo studio ha rivelato che le vertebre con metastasi litiche raggiungono deformazioni maggiori delle vertebre sane. Invece, le metastasi miste non assicurano un comportamento univoco in quanto combinano gli effetti antagonisti delle lesioni litiche e blastiche. Dunque la valutazione è stata estesa a possibili correlazioni tra il campo di deformazione e la microstruttura della vertebra. L'analisi ha identificato le regioni in cui parte la frattura (a più alta deformazione), senza identificare, in termini microstrutturali, una zona preferenziale di rottura a priori. Infatti, alcune zone con un pattern trabecolare denso, presunte più rigide, hanno mostrato deformazioni maggiori di quelle dei tessuti sani, sottolineando l’importanza della valutazione della qualità del tessuto osseo. Questi risultati, generalizzati su un campione più ampio, potrebbero essere utilizzati per implementare nuovi criteri negli attuali sistemi di valutazione dell'instabilità spinale.

The three-dimensional single-bin-size bin packing problem: combining metaheuristic and machine learning approaches

The Three-Dimensional Single-Bin-Size Bin Packing Problem is one of the most studied problem in the Cutting & Packing category. From a strictly mathematical point of view, it consists of packing a finite set of strongly heterogeneous “small” boxes, called items, into a finite set of identical “large” rectangles, called bins, minimizing the unused volume and requiring that the items are packed without overlapping. The great interest is mainly due to the number of real-world applications in which it arises, such as pallet and container loading, cutting objects out of a piece of material and packaging design. Depending on these real-world applications, more objective functions and more practical constraints could be needed. After a brief discussion about the real-world applications of the problem and a exhaustive literature review, the design of a two-stage algorithm to solve the aforementioned problem is presented. The algorithm must be able to provide the spatial coordinates of the placed boxes vertices and also the optimal boxes input sequence, while guaranteeing geometric, stability, fragility constraints and a reduced computational time. Due to NP-hard complexity of this type of combinatorial problems, a fusion of metaheuristic and machine learning techniques is adopted. In particular, a hybrid genetic algorithm coupled with a feedforward neural network is used. In the first stage, a rich dataset is created starting from a set of real input instances provided by an industrial company and the feedforward neural network is trained on it. After its training, given a new input instance, the hybrid genetic algorithm is able to run using the neural network output as input parameter vector, providing as output the optimal solution. The effectiveness of the proposed works is confirmed via several experimental tests.

Metallic renal artery MR imaging stent: artifact-free lumen visualization with projection and standard renal MR angiography.

A cardiac-triggered free-breathing three-dimensional (3D) balanced fast field-echo projection renal magnetic resonance (MR) angiographic sequence was investigated for in-stent lumen visualization of a dedicated metallic renal artery stent. Fourteen prototype stents were deployed in the renal arteries of six pigs (in two pigs, three stents were deployed). Projection renal MR angiography was compared with standard contrast material-enhanced 3D breath-hold MR angiography. Artifact-free in-stent lumen visualization was achieved with both projection MR angiography and contrast-enhanced MR angiography. These promising results warrant further studies for visualization of in-stent restenosis.

Coronary MR angiography at 3T during diastole and systole

PURPOSE: To investigate the impact of end-systolic imaging on quality of right coronary magnetic resonance angiography (MRA) in comparison to diastolic and to study the effect of RR interval variability on image quality. MATERIALS AND METHODS: The right coronary artery (RCA) of 10 normal volunteers was imaged at 3T using parallel imaging (sensitivity encoding [SENSE]). Navigator-gated three-dimensional (3D) gradient echo was used three times: 1) end-systolic short acquisition (SS): 35-msec window; 2) diastolic short (DS): middiastolic acquisition using 35-msec window; and 3) diastolic long (DL): 75-msec diastolic acquisition window. Vectorcardiogram (VCG) data was used to analyze RR variability. Vessel sharpness, length, and diameter were compared to each other and correlated with RR variability. Blinded qualitative image scores of the images were compared. RESULTS: Quantitative and qualitative parameters were not significantly different and showed no significant correlation with RR variability. CONCLUSION: Imaging the RCA at 3T during the end-systolic rest period using SENSE is possible without significant detrimental effect on image quality. Breaking away from the standard of imaging only during diastole can potentially improve image quality in tachycardic patients or used for simultaneous imaging during both periods in a single scan.

Spin-labeling coronary MR angiography with steady-state free precession and radial k-space sampling: initial results in healthy volunteers.

The purpose of this study was to prospectively compare free-breathing navigator-gated cardiac-triggered three-dimensional steady-state free precession (SSFP) spin-labeling coronary magnetic resonance (MR) angiography performed by using Cartesian k-space sampling with that performed by using radial k-space sampling. A new dedicated placement of the two-dimensional selective labeling pulse and an individually adjusted labeling delay time approved by the institutional review board were used. In 14 volunteers (eight men, six women; mean age, 28.8 years) who gave informed consent, signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), vessel sharpness, vessel length, and subjective image quality were investigated. Differences between groups were analyzed with nonparametric tests (Wilcoxon, Pearson chi2). Radial imaging, as compared with Cartesian imaging, resulted in a significant reduction in the severity of motion artifacts, as well as an increase in SNR (26.9 vs 12.0, P < .05) in the coronary arteries and CNR (23.1 vs 8.8, P < .05) between the coronary arteries and the myocardium. A tendency toward improved vessel sharpness and vessel length was also found with radial imaging. Radial SSFP imaging is a promising technique for spin-labeling coronary MR angiography.

Optimization of spatial resolution for peripheral magnetic resonance angiography.

RATIONALE AND OBJECTIVES: To determine optimum spatial resolution when imaging peripheral arteries with magnetic resonance angiography (MRA). MATERIALS AND METHODS: Eight vessel diameters ranging from 1.0 to 8.0 mm were simulated in a vascular phantom. A total of 40 three-dimensional flash MRA sequences were acquired with incremental variations of fields of view, matrix size, and slice thickness. The accurately known eight diameters were combined pairwise to generate 22 "exact" degrees of stenosis ranging from 42% to 87%. Then, the diameters were measured in the MRA images by three independent observers and with quantitative angiography (QA) software and used to compute the degrees of stenosis corresponding to the 22 "exact" ones. The accuracy and reproducibility of vessel diameter measurements and stenosis calculations were assessed for vessel size ranging from 6 to 8 mm (iliac artery), 4 to 5 mm (femoro-popliteal arteries), and 1 to 3 mm (infrapopliteal arteries). Maximum pixel dimension and slice thickness to obtain a mean error in stenosis evaluation of less than 10% were determined by linear regression analysis. RESULTS: Mean errors on stenosis quantification were 8.8% +/- 6.3% for 6- to 8-mm vessels, 15.5% +/- 8.2% for 4- to 5-mm vessels, and 18.9% +/- 7.5% for 1- to 3-mm vessels. Mean errors on stenosis calculation were 12.3% +/- 8.2% for observers and 11.4% +/- 15.1% for QA software (P = .0342). To evaluate stenosis with a mean error of less than 10%, maximum pixel surface, the pixel size in the phase direction, and the slice thickness should be less than 1.56 mm2, 1.34 mm, 1.70 mm, respectively (voxel size 2.65 mm3) for 6- to 8-mm vessels; 1.31 mm2, 1.10 mm, 1.34 mm (voxel size 1.76 mm3), for 4- to 5-mm vessels; and 1.17 mm2, 0.90 mm, 0.9 mm (voxel size 1.05 mm3) for 1- to 3-mm vessels. CONCLUSION: Higher spatial resolution than currently used should be selected for imaging peripheral vessels.

Coronary MR angiography: comparison of quantitative and qualitative data from four techniques.

OBJECTIVE: The optimal coronary MR angiography sequence has yet to be determined. We sought to quantitatively and qualitatively compare four coronary MR angiography sequences. SUBJECTS AND METHODS. Free-breathing coronary MR angiography was performed in 12 patients using four imaging sequences (turbo field-echo, fast spin-echo, balanced fast field-echo, and spiral turbo field-echo). Quantitative comparisons, including signal-to-noise ratio, contrast-to-noise ratio, vessel diameter, and vessel sharpness, were performed using a semiautomated analysis tool. Accuracy for detection of hemodynamically significant disease (> 50%) was assessed in comparison with radiographic coronary angiography. RESULTS: Signal-to-noise and contrast-to-noise ratios were markedly increased using the spiral (25.7 +/- 5.7 and 15.2 +/- 3.9) and balanced fast field-echo (23.5 +/- 11.7 and 14.4 +/- 8.1) sequences compared with the turbo field-echo (12.5 +/- 2.7 and 8.3 +/- 2.6) sequence (p < 0.05). Vessel diameter was smaller with the spiral sequence (2.6 +/- 0.5 mm) than with the other techniques (turbo field-echo, 3.0 +/- 0.5 mm, p = 0.6; balanced fast field-echo, 3.1 +/- 0.5 mm, p < 0.01; fast spin-echo, 3.1 +/- 0.5 mm, p < 0.01). Vessel sharpness was highest with the balanced fast field-echo sequence (61.6% +/- 8.5% compared with turbo field-echo, 44.0% +/- 6.6%; spiral, 44.7% +/- 6.5%; fast spin-echo, 18.4% +/- 6.7%; p < 0.001). The overall accuracies of the sequences were similar (range, 74% for turbo field-echo, 79% for spiral). Scanning time for the fast spin-echo sequences was longest (10.5 +/- 0.6 min), and for the spiral acquisitions was shortest (5.2 +/- 0.3 min). CONCLUSION: Advantages in signal-to-noise and contrast-to-noise ratios, vessel sharpness, and the qualitative results appear to favor spiral and balanced fast field-echo coronary MR angiography sequences, although subjective accuracy for the detection of coronary artery disease was similar to that of other sequences.

The feasibility of 350 μm spatial resolution coronary magnetic resonance angiography at 3 T in humans.

PURPOSE: The purposes of this study were to (1) develop a high-resolution 3-T magnetic resonance angiography (MRA) technique with an in-plane resolution approximate to that of multidetector coronary computed tomography (MDCT) and a voxel size of 0.35 × 0.35 × 1.5 mm³ and to (2) investigate the image quality of this technique in healthy participants and preliminarily in patients with known coronary artery disease (CAD). MATERIALS AND METHODS: A 3-T coronary MRA technique optimized for an image acquisition voxel as small as 0.35 × 0.35 × 1.5 mm³ (high-resolution coronary MRA [HRC]) was implemented and the coronary arteries of 22 participants were imaged. These included 11 healthy participants (average age, 28.5 years; 5 men) and 11 participants with CAD (average age, 52.9 years; 5 women) as identified on MDCT. In addition, the 11 healthy participants were imaged using a method with a more common spatial resolution of 0.7 × 1 × 3 mm³ (regular-resolution coronary MRA [RRC]). Qualitative and quantitative comparisons were made between the 2 MRA techniques. RESULTS: Normal vessels and CAD lesions were successfully depicted at 350 × 350 μm² in-plane resolution with adequate signal-to-noise ratio (SNR) and contrast-to-noise ratio. The CAD findings were consistent among MDCT and HRC. The HRC showed a 47% improvement in sharpness despite a reduction in SNR (by 72%) and in contrast-to-noise ratio (by 86%) compared with the regular-resolution coronary MRA. CONCLUSION: This study, as a first step toward substantial improvement in the resolution of coronary MRA, demonstrates the feasibility of obtaining at 3 T a spatial resolution that approximates that of MDCT. The acquisition in-plane pixel dimensions are as small as 350 × 350 μm² with a 1.5-mm slice thickness. Although SNR is lower, the images have improved sharpness, resulting in image quality that allows qualitative identification of disease sites on MRA consistent with MDCT.