FPGA implementations for parallel multidimensional filtering algorithms

PhD ThesisOne and multi dimensional raw data collections introduce noise and artifacts, which need to be recovered from degradations by an automated filtering system before, further machine analysis. The need for automating wide-ranged filtering applications necessitates the design of generic filtering architectures, together with the development of multidimensional and extensive convolution operators. Consequently, the aim of this thesis is to investigate the problem of automated construction of a generic parallel filtering system. Serving this goal, performance-efficient FPGA implementation architectures are developed to realize parallel one/multi-dimensional filtering algorithms. The proposed generic architectures provide a mechanism for fast FPGA prototyping of high performance computations to obtain efficiently implemented performance indices of area, speed, dynamic power, throughput and computation rates, as a complete package. These parallel filtering algorithms and their automated generic architectures tackle the major bottlenecks and limitations of existing multiprocessor systems in wordlength, input data segmentation, boundary conditions as well as inter-processor communications, in order to support high data throughput real-time applications of low-power architectures using a Xilinx Virtex-6 FPGA board. For one-dimensional raw signal filtering case, mathematical model and architectural development of the generalized parallel 1-D filtering algorithms are presented using the 1-D block filtering method. Five generic architectures are implemented on a Virtex-6 ML605 board, evaluated and compared. A complete set of results on area, speed, power, throughput and computation rates are obtained and discussed as performance indices for the 1-D convolution architectures. A successful application of parallel 1-D cross-correlation is demonstrated. For two dimensional greyscale/colour image processing cases, new parallel 2-D/3-D filtering algorithms are presented and mathematically modelled using input decimation and output image reconstruction by interpolation. Ten generic architectures are implemented on the Virtex-6 ML605 board, evaluated and compared. Key results on area, speed, power, throughput and computation rate are obtained and discussed as performance indices for the 2-D convolution architectures. 2-D image reconfigurable processors are developed and implemented using single, dual and quad MAC FIR units. 3-D Colour image processors are devised to act as 3-D colour filtering engines. A 2-D cross-correlator parallel engine is successfully developed as a parallel 2-D matched filtering algorithm for locating any MRI slice within a MRI data stack library. Twelve 3-D MRI filtering operators are plugged in and adapted to be suitable for biomedical imaging, including 3-D edge operators and 3-D noise smoothing operators. Since three dimensional greyscale/colour volumetric image applications are computationally intensive, a new parallel 3-D/4-D filtering algorithm is presented and mathematically modelled using volumetric data image segmentation by decimation and output reconstruction by interpolation, after simultaneously and independently performing 3-D filtering. Eight generic architectures are developed and implemented on the Virtex-6 board, including 3-D spatial and FFT convolution architectures. Fourteen 3-D MRI filtering operators are plugged and adapted for this particular biomedical imaging application, including 3-D edge operators and 3-D noise smoothing operators. Three successful applications are presented in 4-D colour MRI (fMRI) filtering processors, k-space MRI volume data filter and 3-D cross-correlator.IRAQI Government

Applying Artificial Intelligence Planning to Optimise Heterogeneous Signal Processing for Surface and Dimensional Measurement Systems

The need for in-process measurement has surpassed the processing capability of traditional computer hardware. As Industry 4.0 changes the way modern manufacturing occurs, researchers and industry are turning to hardware acceleration to increase the performance of their signal processing to allow real-time process and quality control. This thesis reviewed Industry 4.0 and the challenges that have arisen from transitioning towards a connected smart factory. It has investigated the different hardware acceleration techniques available and the bespoke nature of software that industry and researchers are being forced towards in the pursuit of greater performance. In addition, the application of hardware acceleration within surface and dimensional instrument signal processing was researched and to what extent it is benefitting researchers. The collection of algorithms that the field are using were examined finding significant commonality across multiple instrument types, with work being repeated many times over by different people. The first use of PDDL to optimise heterogenous signal processing within surface and dimensional measurements is proposed. Optical Signal Processing Workspace (OSPW) is presented as a self-optimising software package using GPGPU acceleration using Compute Unified Device Architecture (CUDA)for Nvidia GPUs. OSPW was designed from scratch to be easy to use with very little-to-no programming experience needed, unlike other popular systems such LabVIEW and MATLAB. It provides an intuitive and easy to navigate User Interface (UI) that allows a user to select the signal processing algorithms required, display system outputs, control actuation devices, and modify capture device properties. OSPW automatically profiles the execution time of the signal processing algorithms selected by the user and creates and executes a fully optimised version using an AI planning language, Planning Description Domain Language (PDDL), by selecting the optimum architecture for each signal processing function. OSPW was then evaluated against two case studies, Dispersed Reference Interferometry (DRI) and Line-Scanning Dispersed Interferometry (LSDI). These case studies demonstrated that OSPW can achieve at least21x greater performance than an identical MATLAB implementation with a further 13% improvement found using the PDDL’s heterogenous solution. This novel approach to providing a configurable signal processing library that is self-optimising using AI planning will provide considerable performance gains to researchers and industrial engineers. With some additional development work it will save both academia and industry time and money which can be reinvested to further advance surface and dimensional instrumentation research

Cross-Layer Rapid Prototyping and Synthesis of Application-Specific and Reconfigurable Many-accelerator Platforms

Technological advances of recent years laid the foundation consolidation of informatisationof society, impacting on economic, political, cultural and socialdimensions. At the peak of this realization, today, more and more everydaydevices are connected to the web, giving the term ”Internet of Things”. The futureholds the full connection and interaction of IT and communications systemsto the natural world, delimiting the transition to natural cyber systems and offeringmeta-services in the physical world, such as personalized medical care, autonomoustransportation, smart energy cities etc. . Outlining the necessities of this dynamicallyevolving market, computer engineers are required to implement computingplatforms that incorporate both increased systemic complexity and also cover awide range of meta-characteristics, such as the cost and design time, reliabilityand reuse, which are prescribed by a conflicting set of functional, technical andconstruction constraints. This thesis aims to address these design challenges bydeveloping methodologies and hardware/software co-design tools that enable therapid implementation and efficient synthesis of architectural solutions, which specifyoperating meta-features required by the modern market. Specifically, this thesispresents a) methodologies to accelerate the design flow for both reconfigurableand application-specific architectures, b) coarse-grain heterogeneous architecturaltemplates for processing and communication acceleration and c) efficient multiobjectivesynthesis techniques both at high abstraction level of programming andphysical silicon level.Regarding to the acceleration of the design flow, the proposed methodologyemploys virtual platforms in order to hide architectural details and drastically reducesimulation time. An extension of this framework introduces the systemicco-simulation using reconfigurable acceleration platforms as co-emulation intermediateplatforms. Thus, the development cycle of a hardware/software productis accelerated by moving from a vertical serial flow to a circular interactive loop.Moreover the simulation capabilities are enriched with efficient detection and correctiontechniques of design errors, as well as control methods of performancemetrics of the system according to the desired specifications, during all phasesof the system development. In orthogonal correlation with the aforementionedmethodological framework, a new architectural template is proposed, aiming atbridging the gap between design complexity and technological productivity usingspecialized hardware accelerators in heterogeneous systems-on-chip and networkon-chip platforms. It is presented a novel co-design methodology for the hardwareaccelerators and their respective programming software, including the tasks allocationto the available resources of the system/network. The introduced frameworkprovides implementation techniques for the accelerators, using either conventionalprogramming flows with hardware description language or abstract programmingmodel flows, using techniques from high-level synthesis. In any case, it is providedthe option of systemic measures optimization, such as the processing speed,the throughput, the reliability, the power consumption and the design silicon area.Finally, on addressing the increased complexity in design tools of reconfigurablesystems, there are proposed novel multi-objective optimization evolutionary algo-rithms which exploit the modern multicore processors and the coarse-grain natureof multithreaded programming environments (e.g. OpenMP) in order to reduce theplacement time, while by simultaneously grouping the applications based on theirintrinsic characteristics, the effectively explore the design space effectively.The efficiency of the proposed architectural templates, design tools and methodologyflows is evaluated in relation to the existing edge solutions with applicationsfrom typical computing domains, such as digital signal processing, multimedia andarithmetic complexity, as well as from systemic heterogeneous environments, suchas a computer vision system for autonomous robotic space navigation and manyacceleratorsystems for HPC and workstations/datacenters. The results strengthenthe belief of the author, that this thesis provides competitive expertise to addresscomplex modern - and projected future - design challenges.Οι τεχνολογικές εξελίξεις των τελευταίων ετών έθεσαν τα θεμέλια εδραίωσης της πληροφοριοποίησης της κοινωνίας, επιδρώντας σε οικονομικές,πολιτικές, πολιτιστικές και κοινωνικές διαστάσεις. Στο απόγειο αυτής τη ςπραγμάτωσης, σήμερα, ολοένα και περισσότερες καθημερινές συσκευές συνδέονται στο παγκόσμιο ιστό, αποδίδοντας τον όρο «Ίντερνετ των πραγμάτων».Το μέλλον επιφυλάσσει την πλήρη σύνδεση και αλληλεπίδραση των συστημάτων πληροφορικής και επικοινωνιών με τον φυσικό κόσμο, οριοθετώντας τη μετάβαση στα συστήματα φυσικού κυβερνοχώρου και προσφέροντας μεταυπηρεσίες στον φυσικό κόσμο όπως προσωποποιημένη ιατρική περίθαλψη, αυτόνομες μετακινήσεις, έξυπνες ενεργειακά πόλεις κ.α. . Σκιαγραφώντας τις ανάγκες αυτής της δυναμικά εξελισσόμενης αγοράς, οι μηχανικοί υπολογιστών καλούνται να υλοποιήσουν υπολογιστικές πλατφόρμες που αφενός ενσωματώνουν αυξημένη συστημική πολυπλοκότητα και αφετέρου καλύπτουν ένα ευρύ φάσμα μεταχαρακτηριστικών, όπως λ.χ. το κόστος σχεδιασμού, ο χρόνος σχεδιασμού, η αξιοπιστία και η επαναχρησιμοποίηση, τα οποία προδιαγράφονται από ένα αντικρουόμενο σύνολο λειτουργικών, τεχνολογικών και κατασκευαστικών περιορισμών. Η παρούσα διατριβή στοχεύει στην αντιμετώπιση των παραπάνω σχεδιαστικών προκλήσεων, μέσω της ανάπτυξης μεθοδολογιών και εργαλείων συνσχεδίασης υλικού/λογισμικού που επιτρέπουν την ταχεία υλοποίηση καθώς και την αποδοτική σύνθεση αρχιτεκτονικών λύσεων, οι οποίες προδιαγράφουν τα μετα-χαρακτηριστικά λειτουργίας που απαιτεί η σύγχρονη αγορά. Συγκεκριμένα, στα πλαίσια αυτής της διατριβής, παρουσιάζονται α) μεθοδολογίες επιτάχυνσης της ροής σχεδιασμού τόσο για επαναδιαμορφούμενες όσο και για εξειδικευμένες αρχιτεκτονικές, β) ετερογενή αδρομερή αρχιτεκτονικά πρότυπα επιτάχυνσης επεξεργασίας και επικοινωνίας και γ) αποδοτικές τεχνικές πολυκριτηριακής σύνθεσης τόσο σε υψηλό αφαιρετικό επίπεδο προγραμματισμού,όσο και σε φυσικό επίπεδο πυριτίου.Αναφορικά προς την επιτάχυνση της ροής σχεδιασμού, προτείνεται μια μεθοδολογία που χρησιμοποιεί εικονικές πλατφόρμες, οι οποίες αφαιρώντας τις αρχιτεκτονικές λεπτομέρειες καταφέρνουν να μειώσουν σημαντικά το χρόνο εξομοίωσης. Παράλληλα, εισηγείται η συστημική συν-εξομοίωση με τη χρήση επαναδιαμορφούμενων πλατφορμών, ως μέσων επιτάχυνσης. Με αυτόν τον τρόπο, ο κύκλος ανάπτυξης ενός προϊόντος υλικού, μετατεθειμένος από την κάθετη σειριακή ροή σε έναν κυκλικό αλληλεπιδραστικό βρόγχο, καθίσταται ταχύτερος, ενώ οι δυνατότητες προσομοίωσης εμπλουτίζονται με αποδοτικότερες μεθόδους εντοπισμού και διόρθωσης σχεδιαστικών σφαλμάτων, καθώς και μεθόδους ελέγχου των μετρικών απόδοσης του συστήματος σε σχέση με τις επιθυμητές προδιαγραφές, σε όλες τις φάσεις ανάπτυξης του συστήματος. Σε ορθογώνια συνάφεια με το προαναφερθέν μεθοδολογικό πλαίσιο, προτείνονται νέα αρχιτεκτονικά πρότυπα που στοχεύουν στη γεφύρωση του χάσματος μεταξύ της σχεδιαστικής πολυπλοκότητας και της τεχνολογικής παραγωγικότητας, με τη χρήση συστημάτων εξειδικευμένων επιταχυντών υλικού σε ετερογενή συστήματα-σε-ψηφίδα καθώς και δίκτυα-σε-ψηφίδα. Παρουσιάζεται κατάλληλη μεθοδολογία συν-σχεδίασης των επιταχυντών υλικού και του λογισμικού προκειμένου να αποφασισθεί η κατανομή των εργασιών στους διαθέσιμους πόρους του συστήματος/δικτύου. Το μεθοδολογικό πλαίσιο προβλέπει την υλοποίηση των επιταχυντών είτε με συμβατικές μεθόδους προγραμματισμού σε γλώσσα περιγραφής υλικού είτε με αφαιρετικό προγραμματιστικό μοντέλο με τη χρήση τεχνικών υψηλού επιπέδου σύνθεσης. Σε κάθε περίπτωση, δίδεται η δυνατότητα στο σχεδιαστή για βελτιστοποίηση συστημικών μετρικών, όπως η ταχύτητα επεξεργασίας, η ρυθμαπόδοση, η αξιοπιστία, η κατανάλωση ενέργειας και η επιφάνεια πυριτίου του σχεδιασμού. Τέλος, προκειμένου να αντιμετωπισθεί η αυξημένη πολυπλοκότητα στα σχεδιαστικά εργαλεία επαναδιαμορφούμενων συστημάτων, προτείνονται νέοι εξελικτικοί αλγόριθμοι πολυκριτηριακής βελτιστοποίησης, οι οποίοι εκμεταλλευόμενοι τους σύγχρονους πολυπύρηνους επεξεργαστές και την αδρομερή φύση των πολυνηματικών περιβαλλόντων προγραμματισμού (π.χ. OpenMP), μειώνουν το χρόνο επίλυσης του προβλήματος της τοποθέτησης των λογικών πόρων σε φυσικούς,ενώ ταυτόχρονα, ομαδοποιώντας τις εφαρμογές βάση των εγγενών χαρακτηριστικών τους, διερευνούν αποτελεσματικότερα το χώρο σχεδίασης.Η αποδοτικότητά των προτεινόμενων αρχιτεκτονικών προτύπων και μεθοδολογιών επαληθεύτηκε σε σχέση με τις υφιστάμενες λύσεις αιχμής τόσο σε αυτοτελής εφαρμογές, όπως η ψηφιακή επεξεργασία σήματος, τα πολυμέσα και τα προβλήματα αριθμητικής πολυπλοκότητας, καθώς και σε συστημικά ετερογενή περιβάλλοντα, όπως ένα σύστημα όρασης υπολογιστών για αυτόνομα διαστημικά ρομποτικά οχήματα και ένα σύστημα πολλαπλών επιταχυντών υλικού για σταθμούς εργασίας και κέντρα δεδομένων, στοχεύοντας εφαρμογές υψηλής υπολογιστικής απόδοσης (HPC). Τα αποτελέσματα ενισχύουν την πεποίθηση του γράφοντα, ότι η παρούσα διατριβή παρέχει ανταγωνιστική τεχνογνωσία για την αντιμετώπιση των πολύπλοκων σύγχρονων και προβλεπόμενα μελλοντικών σχεδιαστικών προκλήσεων

Humanoid Robots

For many years, the human being has been trying, in all ways, to recreate the complex mechanisms that form the human body. Such task is extremely complicated and the results are not totally satisfactory. However, with increasing technological advances based on theoretical and experimental researches, man gets, in a way, to copy or to imitate some systems of the human body. These researches not only intended to create humanoid robots, great part of them constituting autonomous systems, but also, in some way, to offer a higher knowledge of the systems that form the human body, objectifying possible applications in the technology of rehabilitation of human beings, gathering in a whole studies related not only to Robotics, but also to Biomechanics, Biomimmetics, Cybernetics, among other areas. This book presents a series of researches inspired by this ideal, carried through by various researchers worldwide, looking for to analyze and to discuss diverse subjects related to humanoid robots. The presented contributions explore aspects about robotic hands, learning, language, vision and locomotion

High-performance hardware accelerators for image processing in space applications

Mars is a hard place to reach. While there have been many notable success stories in getting probes to the Red Planet, the historical record is full of bad news. The success rate for actually landing on the Martian surface is even worse, roughly 30%. This low success rate must be mainly credited to the Mars environment characteristics. In the Mars atmosphere strong winds frequently breath. This phenomena usually modifies the lander descending trajectory diverging it from the target one. Moreover, the Mars surface is not the best place where performing a safe land. It is pitched by many and close craters and huge stones, and characterized by huge mountains and hills (e.g., Olympus Mons is 648 km in diameter and 27 km tall). For these reasons a mission failure due to a landing in huge craters, on big stones or on part of the surface characterized by a high slope is highly probable. In the last years, all space agencies have increased their research efforts in order to enhance the success rate of Mars missions. In particular, the two hottest research topics are: the active debris removal and the guided landing on Mars. The former aims at finding new methods to remove space debris exploiting unmanned spacecrafts. These must be able to autonomously: detect a debris, analyses it, in order to extract its characteristics in terms of weight, speed and dimension, and, eventually, rendezvous with it. In order to perform these tasks, the spacecraft must have high vision capabilities. In other words, it must be able to take pictures and process them with very complex image processing algorithms in order to detect, track and analyse the debris. The latter aims at increasing the landing point precision (i.e., landing ellipse) on Mars. Future space-missions will increasingly adopt Video Based Navigation systems to assist the entry, descent and landing (EDL) phase of space modules (e.g., spacecrafts), enhancing the precision of automatic EDL navigation systems. For instance, recent space exploration missions, e.g., Spirity, Oppurtunity, and Curiosity, made use of an EDL procedure aiming at following a fixed and precomputed descending trajectory to reach a precise landing point. This approach guarantees a maximum landing point precision of 20 km. By comparing this data with the Mars environment characteristics, it is possible to understand how the mission failure probability still remains really high. A very challenging problem is to design an autonomous-guided EDL system able to even more reduce the landing ellipse, guaranteeing to avoid the landing in dangerous area of Mars surface (e.g., huge craters or big stones) that could lead to the mission failure. The autonomous behaviour of the system is mandatory since a manual driven approach is not feasible due to the distance between Earth and Mars. Since this distance varies from 56 to 100 million of km approximately due to the orbit eccentricity, even if a signal transmission at the light speed could be possible, in the best case the transmission time would be around 31 minutes, exceeding so the overall duration of the EDL phase. In both applications, algorithms must guarantee self-adaptability to the environmental conditions. Since the Mars (and in general the space) harsh conditions are difficult to be predicted at design time, these algorithms must be able to automatically tune the internal parameters depending on the current conditions. Moreover, real-time performances are another key factor. Since a software implementation of these computational intensive tasks cannot reach the required performances, these algorithms must be accelerated via hardware. For this reasons, this thesis presents my research work done on advanced image processing algorithms for space applications and the associated hardware accelerators. My research activity has been focused on both the algorithm and their hardware implementations. Concerning the first aspect, I mainly focused my research effort to integrate self-adaptability features in the existing algorithms. While concerning the second, I studied and validated a methodology to efficiently develop, verify and validate hardware components aimed at accelerating video-based applications. This approach allowed me to develop and test high performance hardware accelerators that strongly overcome the performances of the actual state-of-the-art implementations. The thesis is organized in four main chapters. Chapter 2 starts with a brief introduction about the story of digital image processing. The main content of this chapter is the description of space missions in which digital image processing has a key role. A major effort has been spent on the missions in which my research activity has a substantial impact. In particular, for these missions, this chapter deeply analizes and evaluates the state-of-the-art approaches and algorithms. Chapter 3 analyzes and compares the two technologies used to implement high performances hardware accelerators, i.e., Application Specific Integrated Circuits (ASICs) and Field Programmable Gate Arrays (FPGAs). Thanks to this information the reader may understand the main reasons behind the decision of space agencies to exploit FPGAs instead of ASICs for high-performance hardware accelerators in space missions, even if FPGAs are more sensible to Single Event Upsets (i.e., transient error induced on hardware component by alpha particles and solar radiation in space). Moreover, this chapter deeply describes the three available space-grade FPGA technologies (i.e., One-time Programmable, Flash-based, and SRAM-based), and the main fault-mitigation techniques against SEUs that are mandatory for employing space-grade FPGAs in actual missions. Chapter 4 describes one of the main contribution of my research work: a library of high-performance hardware accelerators for image processing in space applications. The basic idea behind this library is to offer to designers a set of validated hardware components able to strongly speed up the basic image processing operations commonly used in an image processing chain. In other words, these components can be directly used as elementary building blocks to easily create a complex image processing system, without wasting time in the debug and validation phase. This library groups the proposed hardware accelerators in IP-core families. The components contained in a same family share the same provided functionality and input/output interface. This harmonization in the I/O interface enables to substitute, inside a complex image processing system, components of the same family without requiring modifications to the system communication infrastructure. In addition to the analysis of the internal architecture of the proposed components, another important aspect of this chapter is the methodology used to develop, verify and validate the proposed high performance image processing hardware accelerators. This methodology involves the usage of different programming and hardware description languages in order to support the designer from the algorithm modelling up to the hardware implementation and validation. Chapter 5 presents the proposed complex image processing systems. In particular, it exploits a set of actual case studies, associated with the most recent space agency needs, to show how the hardware accelerator components can be assembled to build a complex image processing system. In addition to the hardware accelerators contained in the library, the described complex system embeds innovative ad-hoc hardware components and software routines able to provide high performance and self-adaptable image processing functionalities. To prove the benefits of the proposed methodology, each case study is concluded with a comparison with the current state-of-the-art implementations, highlighting the benefits in terms of performances and self-adaptability to the environmental conditions

NASA Tech Briefs, April 1992

Topics covered include: New Product Ideas; Electronic Components and Circuits; Electronic Systems; Physical Sciences; Materials; Computer Programs; Mechanics; Machinery; Fabrication Technology; Mathematics and Information Sciences

Consideraciones acerca de la viabilidad de un sensor plenóptico en dispositivos de consumo

Doctorado en Ingeniería IndustrialPassive distance measurement of the objects in an image gives place to interesting applications that have the potential to revolutionize the field of photography. In this thesis a prototype of plenoptic camera for mobile devices was created and studied. This technique has two main disadvantages: the need for modifying the camera module and the loss of resolution. Because of this, the prototype was discarded in order to utilize another technique: depth from focus. In this technique the capture method consists in taking several images while varying the focus distance. The set of images is called focal-stack. Different focus operators are studied, which give a measure of defocus per pixel and plane of the focal-stack. The curvelet based focus operator is chosen as the most adequate. It is computationally more intensive than other operators but it is capable of decomposing natural images using few coefficients. In order to make viable its usage in mobile devices a new curvelet transform based on the discrete Radon transform is built. The discrete Radon transform has logarithmic complexity, does not use the Fourier transform and uses only integer sums. Lastly, different versions of the Radon transform are analyzed with the goal of achieving an even faster transform. These transforms are implemented to be executed on mobile devices. Additionally, an application of the Radon transform is presented. It consists in the detection of bar-codes that have any orientation in an image.La medida pasiva de distancia a los objetos en una imagen da lugar a interesantes aplicaciones con capacidad para revolucionar la fotografía. En esta tesis se creó y estudió un prototipo de cámara plenóptica para dispositivos móviles. Esta técnica presenta dos inconvenientes: la necesidad de modificar el módulo de cámara y la pérdida de resolución. Por ello, el prototipo fue descartado para utilizar otra técnica: la profundidad a partir del desenfoque. En esta técnica el método de captura consiste en tomar varias imagenes variando la distancia de enfoque. El conjunto de imágenes se denomina focal-stack. Se estudian distintos operadores de desenfoque, que dan una medida de desenfoque por pixel y por plano del focal-stack. Siendo elegido como óptimo el operador de desenfoque curvelet, que es computacionalmente más intensivo que otros operadores pero es capaz de descomponer imagenes naturales utilizando muy pocos coeficientes. Para hacer posible su uso en dispositivos móviles se construye una nueva transformada curvelet basada en la transformada discreta de Radon. La transformada discreta de Radon tiene complejidad linearítmica, no utiliza la transformada de Fourier y usa sólo sumas de enteros. Por último, se analizan distintas versiones de la transformada de Radon con el objetivo de conseguir una transformada aún más rápida y se implementan para ser ejecutadas en dispositivos móviles. Además se presenta una aplicación de la transformada de Radon consistente en la detección de códigos de barras con cualquier orientación en una imagen