Method and device for processing three-dimensional images that allows distortions to be minimised

Abstract

The present invention relates to a method and device for processing three-dimensional images that allows distortions to be minimised in a sensor measuring the direction of a signal from a source and that comprises the steps of: providing one or more measuring sensors for measuring a signal coming from a source, the sensors being associated with one or more spatial positions, wherein the measuring sensors are configured to obtain a direction of the measured signal with respect to said spatial positions; breaking down the sensor into one or more locations; generating one or more geodesic spheres in each location, wherein each geodesic sphere comprises a set of triangular elements with vertices that are almost evenly spaced apart; encoding a signal representative of the direction between the centre of the sphere and the position of the source in a set of vertices of the sphere; and generating a vector associated with each vertex, to store information about the signal intensity.

Description

[0001] METHOD AND DEVICE FOR PROCESSING THREE-DIMENSIONAL IMAGES THAT MINIMIZES DISTORTIONS

[0002] DESCRIPTION

[0003] OBJECT OF THE INVENTION

[0004] The present invention falls within the area of ​​signal measuring devices, methods and signal processing systems to minimize distortions in their representation.

[0005] The invention relates to a method and device for signal processing that allows generating three-dimensional reconstructions, reducing the distortions inherent in their processing and storage.

[0006] BACKGROUND OF THE INVENTION

[0007] There are multiple signal capture sensor devices that allow image generation and processing, based on a range of techniques that can be expressed through numerical matrices where each coordinate or index expresses a memory position, and which in turn is related to the primary origin of the signal to the sensor.

[0008] However, not all sensors are suited to planar geometries, where a constant resolution generally exists. When the sensor is capable of collecting the signal from any direction in space, this image representation must be converted or incorporate information about the sphere representing the signal's origin.

[0009] On the other hand, data interpretation is just as important as data acquisition. Interpretation must be able to be processed within a predefined time and in accordance with process expectations. A system that provides highly accurate information may be inefficient if the processing time exceeds the system's response time; therefore, for interactive applications, it is important to reduce this time, or computational cost. In general, the processing of a data set defines computational cost as the function that expresses the computational time based on the data to be processed. For example, if a sample of N data sets has a time cost of T, and twice as much data takes to process, proportional to this time, T, the cost is said to have an O(N) value for this sample of N data sets.If the computational cost does not depend on the amount of data, the computational cost is said to be of type 0(0), compared to this variation, and functions such as O(LOG(N)) can be defined, where what is indicated is that the time does not grow linearly, but logarithmically, O(N. A 2) where time grows quadratically etc.

[0010] Modern inertial navigation systems used in space, sensor systems that detect environmental information in this geometry, etc., require partitioning that makes processing difficult because there are always intermediate regions that the "maps" that convert the special 3D geometry to a plane do not allow continuity. This lack of continuity, known as the "poles" of the image, prevents the partition made by the sensor from being represented homogeneously. It is easy to verify on a map that when a sphere is partitioned by angles, if we keep the angular elements constant, near the north and south poles the surface they represent is smaller than in the equatorial zones.

[0011] Storing data in this special geometry poses a number of challenges, including how to partition it into elements that allow for consistent information per unit area and allow it to be accessed and processed with the specific computational requirements of each problem.

[0012] In general, when it comes to images and, in particular, when it comes to a representation of this in a system, it is desirable that the images do not present distortions inherent in the representation, this is because when processing using image processing techniques, it is important to maintain the aspect ratios of the entire image to make this processing correct throughout the image.

[0013] Furthermore, images can contain layers. A layer occurs when a scalar does not fully represent the signal. For example, in a color camera, RGB, each channel representing the red, green, or blue information can be represented in three color layers, combining the signal values ​​corresponding to different physical information into a single scalar. In a gamma camera, for example, it would be possible to store the spectroscopic information detected in a given direction. A layer can also contain the result of an operation performed between one or more layers, thus representing this information in the source direction.

[0014] For example, in a sensor that collects images from any direction, such as an antenna or a gamma radiation detector, the captured signal must be represented on the map, and the elements of this map—where a map is understood as a preferred direction in space and a value represented by the signal—must have similar intensities if the image is to be used for measurements. Distortions appear when the amount of signal is considerably different depending on the region of the map being represented. Signal distortions must be corrected to eliminate the effects introduced by the device itself so that, once corrected, the appropriate image processing can be applied.

[0015] A representation of the complete space can be made by a projected segmentation, however, there are cases where the image must cover a complete geometry (4TT) where it is not possible to 'partition the space' in the form of rectangles.

[0016] The problems of projecting spherical geometry are known in cartography where representations on a plane can be made using all types of projectors that have a global application:

[0017] • Spherical geometry

[0018] • Conic geometry

[0019] • Area-preserving geometries

[0020] • Angle-preserving geometries.

[0021] • Geometries that preserve distance.

[0022] All of these introduce aberrations (undesirable transformations), which affect the amount of information associated with the signal outside the application areas, so that these projections cannot be used as a data source that meets the requirements of the planar image.

[0023] As an example, a classic and rapid way of decomposing a sphere is through the use of the spherical coordinate system. In this system, coordinates are introduced that move in a direction along the surface of the sphere according to the following expressions: • X=cos(0)sin((p)

[0024] • Y=sin(0)sin((p)

[0025] • Z=cos((p)

[0026] This decomposition is a typical decomposition of ground planes, where latitude is represented by q> and longitude is represented by O. Furthermore, this decomposition follows regular angular spacing, so it is possible to quickly find coordinates. However, this spacing is regular in angles, but not in solid angles. Furthermore, this decomposition has two poles, where the square mesh is converted into triangles, and these triangles coincide at these points.

[0027] The advantage of rapid access to the coordinates 0 and tp is limited by the lack of homogeneity in the solid angle sustained by the angle (p) that generates two poles at 0 and 180 degrees.

[0028] These two singular points produce geometric distortions and metric differences between the equator and the poles, which make data processing difficult. One solution would be to exclude these poles from the main signal acquisition, but in sensors located in the real world, orientation can change when the object changes position or is rotated. This makes it difficult to use these systems to store consistent information when the sensor moves relative to space or when there is a set of sensors that we want to correlate.

[0029] It is common to represent two coordinate systems, one representing the world and the other representing the sensor. In both cases, by relativity criteria, if the sensor moves through the world, the signal will change accordingly. But it will also change if the system is static and there are variations in the signal externally (for example, if the source producing the signal moves). Therefore, for analytical purposes, the important reference system is that of the sensor, but for the purpose of representing reality, this reference system must be related to that of the world.

[0030] In general, sensors are subject to affine transformations that can change over time. An affine transformation is defined as a rotation and / or translation of the sensor relative to the world. When the representation system is centered on a sensor, the motion coordinates are translated into variations in the signal. Signal processing generally consists of applying a set of multiplication, addition, or comparison operations to a signal with adjacent signals, based on a set of pre-calculated formulas. This processing allows for improving signal contrast, identifying movement (displacement), or, if convolutional network techniques, typical of machine learning, classifying objects.

[0031] This type of process is computationally expensive and requires rapid access to the neighboring elements associated with the calculation. We distinguish two basic types of operations in this type of process:

[0032] 1. Characteristics within a still image composed of a group of scalars associated with a pixel.

[0033] 2. Similarly, motion detection and classification of these variations composed of two or more sequences of a group of scalars associated with a pixel.

[0034] Furthermore, for operations between sensor elements to be consistent, the amount of information per cell must be consistent, since it is not computationally easy to apply rotations in this case.

[0035] When the world system moves relative to the sensor (or the sensor moves around the world), it can be interesting to quickly maintain the world system's coordinates static (rotations). In this case:

[0036] • The world in general will be the source of signals (by generation as in a radiation detector or reflection as in the case of radars or sonars)

[0037] • The sensor will maintain a relative position of movement (translation) in the world.

[0038] • The sensor will maintain a relative rotation position in the world.

[0039] • The sensor will maintain a rotation and translation position in the world.

[0040] A temporal signal consists of the ability to store a limited number of cases like the ones above, in order to identify interesting signal differences through processing and quickly classify them. This information can be stored in layers as described above, or by maintaining copies of these representations that will be updated.

[0041] Furthermore, general techniques must allow for associating information, typically in the form of scalar numbers from the sensor, with other information that can be used in this representation. For example, if we are talking about a navigation system, maps of the areas where the sensor is moving can be incorporated, as well as any information currently available, such as positioning, optical signals, radiation sources detected by the sensor, etc.

[0042] On the other hand, there are techniques based on rectangular images that allow centering on a reference image, as used in spatial or medical imaging. These techniques range from feature identification to the identification of information patterns (entropy) in various areas. These techniques can be used on a fixed, infinite background, such as the sky observed by a sensor in space, or if a previous map of a scene is available and the same locations need to be traversed.

[0043] There are many ways to represent these transformations once the sensor moves relative to the world. In general, motion transformations can be perfectly represented by a vector. Rotation transformations, on the other hand, can be represented by a rotation matrix, which uses either quaternions, which avoid the gimbal locking effect (due to the poles of the polar coordinate system transformations), or rotation matrices (based on said polar geometry). This locking consists of the loss of a degree of freedom when we are dealing with transformations close to the rotation axes.

[0044] Furthermore, on certain occasions it is important to trace the movement of the sensor while maintaining the temporal sequences.

[0045] Just as important as the capture systems are the representation systems. Many of the representation-based problems relate to how the processed information can be stored and how to avoid signal distortions when the display of the representation moves into regions where spherical aberrations impose them.

[0046] However, no solution has been found in the state of the art that allows: storing and processing information with 4TT geometry of a sensor and representing different states in a multispectral way, where each pixel represents a state at different moments in time, maintaining the coherence of the coordinates between two points.

[0047] All of these issues related to sensor movement emphasize the need to maintain storage systems that maintain a proportional signal quantity regardless of the sensor's position and orientation.

[0048] DESCRIPTION OF THE INVENTION

[0049] The invention relates to a three-dimensional signal processing method that allows minimizing distortions in a sensor.

[0050] Thus, the information provided by the sensor can be stored and processed, representing a complete spatial view or 4TT geometry.

[0051] The method of the invention is of particular interest in applications that require storing sets of information without distortion, in order to be able to process said information jointly.

[0052] In particular, it is of interest in applications such as:

[0053] • 4TT geometry gamma cameras (Compton cameras)

[0054] • Device-centric radar systems

[0055] • Moving radar systems (time series)

[0056] • Real-time information presentation systems.

[0057] In these cases, consistency in signal processing is a critical part of the process, making it necessary to maintain information centered in this coordinate system and allow for the use of advanced signal processing without the aberrations typical of other Cartesian representations. Likewise, the method of the invention is useful in image support systems and immersive systems (where the user is within an environment and there are projectors in the central part). For example, in helmets and elements that can be attached to the user's head, where the method of the invention allows for the visualization of the information provided by the system, this information can be incorporated without distortion when head movements are applied.

[0058] The three-dimensional image processing method of the invention allows minimizing distortions in one or more sensors that measure the direction of a signal from a source or sources.

[0059] To this end, the method comprises a step of providing said one or more measuring sensors with a signal from a source, associated with one or more spatial positions. The measuring sensors are configured to obtain a direction of the measured signal with respect to said spatial positions. The sensor is divided into one or more locations.

[0060] Next, one or more geodesic spheres are generated at each location by successively partitioning Platonic geometries using consecutive triangulations. This partitioning results in a set of triangular elements with nearly equally spaced vertices. These steps allow for the processing of a Compton camera in a manner analogous to a set of pinhole cameras corresponding to each of the geodesic spheres.

[0061] A signal representative of the direction between the center of the sphere and the source position is then encoded at a set of vertices of the sphere and a vector associated with each vertex is generated to store information about the signal intensity.

[0062] The method may also comprise a step of modifying the vectors to replace the signal intensity information by applying noise reduction or signal-to-noise ratio improvement techniques using elements of said vector or adjacent vectors. For example, in the case of a Compton camera, the circles corresponding to back projections of a photon from the absorber may be eliminated, maintaining only the source position information derived from the processing of said circles. Likewise, the method may also comprise a step of modifying the vectors to replace the signal intensity information by applying mutual noise reduction techniques using elements of adjacent geodesic spheres. The noise reduction techniques in the different applications of the present invention may vary and are defined by mathematical models described in the prior art.

[0063] Additionally, the method of the invention could comprise a step of reconstructing the origin of the signal by means of combination operations performed with elements of said vector, adjacent vectors or vectors of other geodesic spheres.

[0064] The method may also comprise a step of generating one or more replicas of geodesic spheres, where each geodesic sphere replica has a smaller angular partitioning. In this case, the directional information of each measuring device, associated with a spatial position, is stored in each of the replicas to allow rapid access to information about the signal source and its intensity at each vertex of the sphere. In this way, the resolution of the stored information can be changed, increasing as a smaller angular partitioning is used.

[0065] The method may also comprise a step of reducing the number of geodesic spheres associated with each position, while maintaining directionality. In this case, the source direction information from a group of geodesic spheres is summarized into a single geodesic sphere representing the original group of spheres. In this case, the information summary may be performed vertex by vertex by weighting the values ​​of the original geodesic spheres.

[0066] This allows representations with different resolutions to be processed with reduced computational costs. In particular, when the error in obtaining the signal is high, the resolution can be reduced on geodesic spheres, obtaining the same result at a lower computational cost.

[0067] Preferably, the number of geodesic spheres and the resolution of each geodesic sphere can be determined based on the distance of the sensors from the source and a maximum permissible error. This maximum permissible error can be determined by the signal strength received at the sensor(s).

[0068] In embodiments where the vector comprises data representative of different temporal states, the method of the invention may further comprise an additional step of applying weighted subtraction, addition, multiplication between elements of said vector to obtain information about the temporal variation.

[0069] In the method of the invention, the vector elements can correspond to signals obtained at different energies and / or frequencies, called layers. Thus, the method can also allow obtaining a convolutional representation of one or more layers through an additional step of generating new layers in the vectors by weighting and using adjacency weights applied to the values ​​of a layer in a set of adjacent vertices and / or adjacent spheres.

[0070] Similarly, the method can allow obtaining a multi-layer convolutional representation, generating new information by weighting and using adjacency weights applied to values ​​from several layers associated with different sensor or source positions.

[0071] The method of the invention may also comprise an additional step of applying direct projection operations of each direction to a point in the space of the generated spheres by evaluating the signal at that point as the weighted sum of the values ​​ranging from the origin of the sphere and in the direction between the origin of the sphere and the point in space.

[0072] Preferably, the method of the invention may further comprise an additional step of applying direct projection operations to a set of spatial points representing a spatial volume, and iteratively correcting the inverse projection of the projected points to equalize the signal received at each of the sensors. In this case, the value of the points that are not in coincident directions is reduced in order to obtain an intensity value consistent with the actual signal intensity in the projection direction (direction between the origin of the sphere and the point in space). In this case, the method of the invention may also comprise an additional step of applying direct projection operations to sets of sensors such that the resolution is increased at each step by using higher-resolution representation groups.

[0073] In the case of Compton cameras, the information used to store each gamma ray detection is the projection of circles onto each geodesic sphere, representing a gamma ray from a Compton camera. In this case, each sphere represents a location in the scatterer's space, and each circle represents the backprojection of a photon from the absorber. Each element of the vector associated with the directions represents the sum of the photon's energy between the scatterer and the absorber.

[0074] Preferably, if the distance from the sensors to the source is greater than ten times the Compton camera's scatter width, the number of geodesic spheres required can be limited; in particular, a single geodesic sphere can be used to store information on the source's position. This would correspond to a far-field approximation.

[0075] Preferably, in the method of the invention the number of positions of the spheres, representing the Compton chamber, is increased by moving the Compton chamber or by increasing the number of Compton chambers.

[0076] The method of the invention also allows the background removal of the Compton camera signal to generate a new layer. To this end, the method further comprises a step of applying convolutional operations to generate a processed layer of the signal.

[0077] Furthermore, preferably, the method may comprise a step of applying to the signal layer or to the iteratively processed layer the step of correcting the inverse projection of the projected points to equalize the signal received at each of the sensors.

[0078] The invention also relates to a signal measurement device comprising one or more sensors configured to measure a signal and a processing module configured to carry out the method of the invention. The sensors can be radar, visible light camera, or ultrasound systems.

[0079] DESCRIPTION OF THE DRAWINGS

[0080] To complement the description being made and in order to help better understand the characteristics of the invention, in accordance with a preferred example of practical implementation thereof, a set of drawings is attached as an integral part of said description, in which the following has been represented for illustrative and non-limiting purposes:

[0081] Figure 1.- shows an example of a geodesic sphere according to a preferred embodiment of the method of the invention.

[0082] Figure 2.- shows an example of a projection on the plane of a rectangular partitioning used in the state of the art and the formed kernels.

[0083] Figure 3.- shows an example of a projection on the plane of the geodesic sphere according to a preferred embodiment of the method of the invention and the kernels formed.

[0084] Figure 3.- shows an example of a kernel development sequence from triangles.

[0085] Figure 5.- shows an example of back projection to a plane in a Compton camera application.

[0086] Figure 6.- shows an example of a geodesic sphere storing data of a volume inspected by a Compton camera according to a preferred embodiment of the method of the invention.

[0087] Figure 7.- shows an example of a volume to be inspected using a Compton camera and the reconstruction using 3 planes of 3 sources, generating 3 images where in each one 2 of the sources show pixelation effects and lack of contrast.

[0088] Figure 8 shows an example of a set of geodesic spheres storing data of a volume inspected by one or more Compton cameras according to a preferred embodiment of the method of the invention. Figure 9 shows an example of a plane in which a set of geodesic spheres are stored storing data of a volume inspected by one or more Compton cameras according to a preferred embodiment of the method of the invention.

[0089] PREFERRED EMBODIMENT OF THE INVENTION

[0090] The invention relates to a three-dimensional image processing method that allows minimizing distortions in a sensor.

[0091] The method is based on the fact that there are ways to decompose a sphere, based on Platonic polyhedra, which generate successive triangular partitions while maintaining certain properties across the entire scale. An example of this type of decomposition is shown in Figure 1.

[0092] In particular, the dodecahedron is the polygon with the most faces and the one that generates the least distortion. These decomposition forms are known as geodesic spheres or Goldberg polyhedra, which reduce the pole problem introduced by spherical geometries and decompose the sphere into an arbitrarily large number of hexagonal elements and 12 pentagonal elements, which can be represented as a set of triangular elements with nearly equally spaced vertices.

[0093] These successive partitions allow the generation of spheres with the following characteristics: a. Resolution can be increased. Each repartitioning exponentially multiplies the number of elements, improving resolution. b. They contain distinct structures such as vertices and triangles. c. It decomposes the sphere into elements of the same size. d. It does not contain strong poles, i.e., the number of adjacent neighbors of each partition element is constant, except in the regions of the 12 pentagons, i.e., it geometrically compensates the signal, and the variation in information per solid angle sector is reduced. e. Multiresolution techniques can be used (partitioning the sphere more or less). f. It is possible to index all points and vertices to apply image processing procedures. g. The sampling around any point is preferably 6 (or 5 only in 12 points) compared to the 4 proposed by rectangular geometries.

[0094] This provides the advantages of:

[0095] • When processing on a geodesic sphere, there is infinite continuity. That is, the afterimage effects that appear in a conventional image do not appear.

[0096] • Allows you to quickly run coordinate-based searches using a catalog.

[0097] • Rotations can be processed without rotating the sphere, simply by changing the search index generated by the catalog.

[0098] • It can be decomposed projectively into a plane.

[0099] In this case, adding a new event, that is, improving the statistical response, is not penalized because the event adds information to a matrix that contains both the direction of the collimation and the origin or approximate center of this origin.

[0100] Furthermore, if we project onto the plane, the elements that make up the projection have a hexagonal (and pentagonal) shape, as shown in Figure 2. In this projection, kernel centers or convolution functions can be selected. Using a geodesic sphere partitioning provides improved proximity between indices, which is more consistent than with square filters, shown in Figure 3, since in this case all nodes are at the same distance (or almost the same distance in the case of pentagonal elements).

[0101] Figure 2 shows the partitioning of a dodecahedron on the sphere, such that the points where the convolutions are performed are equidistant. However, as shown in Figure 3, in an orthogonal representation, the diagonal points are further from the centers than the lateral points or the upper and lower midpoints of each side, which are not equidistant.

[0102] Since the positions of the points of the Platonic solids are known, it is possible to perform partitions, for example, from an icosahedron, obtaining at least one duplication of points in each partition. This exponential growth allows high resolution to be obtained by applying decomposition into smaller angular partitions. Obtaining these partitions in a geodesic sphere gives two results: the points on the surface, which can be assigned an index, which is a cardinal number, and which we will call vertices; and the triangular surfaces bounded by three vertices, which we will call faces, which will be a triplet pointing to three of the aforementioned vertices. In the case of Compton cameras, with this partitioning, each time a photon is detected, it is represented in the mesh formed by the different spheres that represent positions.It is possible to represent using a circumference in that geodesic sphere using the kinematics of the cone (angle) formed by the signal collected at the position of the dispersion plane.

[0103] All points associated with these vertices can be classified with their adjacent faces, in general if the partitions are sufficient, this number will be 6 with the exceptions of the 12 points that contain pentagons.

[0104] From this classification we can add kernels of different sizes if we think of hexagonal geometry, the initial list corresponds to a central value and 6 points.

[0105] The extension condition for each point to the kernel (except for the first iteration, which is adjacent points) would be that the point is connected by two points from previous kernels. In each iteration, for larger kernel sizes, two additional points can be added for each circle, completing the geometry shown in Figure 2.

[0106] Since this extension can reach regions with pentagons, this quasi-circular extension will encounter certain discontinuities, which can be alleviated by performing bilinear interpolation or extrapolation with the points not collected in previous iterations.

[0107] Alternatively, kernels can be developed from triangles by adding triangles whose faces match the previous one and removing duplicates. Figure 4 shows an example of a kernel development sequence from triangles.

[0108] The method of the invention therefore allows for the processing of three-dimensional images obtained by a sensor capable of measuring the direction of a signal's origin, minimizing distortions. To achieve this, it is based, as mentioned, on the use of geodesic spheres.

[0109] The method of the invention comprises the steps of providing the sensor (or sensors) associated with one or several positions in space to measure a signal and obtaining a direction of the measured signal.

[0110] One or more geodesic spheres are then generated, which are partitioned by Platonic geometry points, resulting in a set of triangular elements with quasi-equally spaced vertices. Each vertex of each geodesic sphere is then associated with a direction, from the center of the geodesic sphere to the origin of the detected signal, and a vector (associated with each vertex) is generated to store the signal strength information.

[0111] The use of vectors associated with each of the vertices allows each of these vectors to be extended in order to store additional data, which may be a combination of operations performed with elements of said vector, adjacent vectors or vectors generated using another representation of the sensor.

[0112] As discussed, the use of geodesic spheres allows for the use of multiresolution techniques, for which the method may comprise additional steps of increasing or reducing the angular partitioning of the spheres.

[0113] In particular, the method of the invention may be applied in an embodiment where the sensor(s) is a Compton camera.

[0114] In this regard, it should be noted that near-field and far-field sensors exhibit different signal behavior when we are relatively close to the sensor element than when we are sufficiently far away. A clear example is the reconstruction systems typically used in Compton cameras.

[0115] Near field is understood as that where the signal sources produce a different and measurable angular signal depending on the incidence of this signal on the sensor, and far field is understood as when the signal sources are far enough away so that the sensor is not able to distinguish the original angular information; in the case of Compton cameras, it is a value close to ten times the scatter width.

[0116] A Compton chamber is a sensor composed of at least two detectors that act interchangeably as scatterer and absorber. These detectors are sensitive to energy and position.

[0117] When a gamma ray (an energetic photon) strikes one of the two detectors, two general phenomena can occur: either it is absorbed or it is scattered. When this photon is scattered and collected in another detector (a temporal coincidence), we can identify this photon as having produced a Compton effect in one of the detection planes, and therefore, due to its geometry, we can backproject its direction to a cone.

[0118] Each Compton collision is backprojected in circles from the detector acting as the scatterer in the direction of the axis running from the position of the scatterer to the detector acting as the absorber. The reconstruction consists of each of these photons being projected onto a plane as an ellipse with the semiaxes oriented in the corresponding directions, as shown in Figure 5.

[0119] This form of reconstruction causes the appearance of field aperture effects, so that a focal plane must be determined and elements that are outside this field are not recorded correctly (they are out of focus).

[0120] These algorithms are expensive to run because they require that each and every one of the specified photons be projected for each plane to be reconstructed.

[0121] Furthermore, a general problem is that the detection plane is not able to retain the information.

[0122] To address this issue, a method has been proposed in the state of the art that involves projecting all photons onto a single sphere, thus approximating a distant plane. To achieve this, the state of the art employs spherical coordinate geometry, so that all events are represented on a single sphere. The far-field approximation avoids field aperture effects, making the recording of elements independent of depth of field.

[0123] However, this form of reconstruction poses two problems:

[0124] 1. The difference in weights in spherical geometry of each circle must be calculated before projecting the spheres.

[0125] 2. This near-field geometry is not really useful because the projection of this field has the problem that the source angles are in the range of the detector size.

[0126] In the method of the invention, each location in the scatterer space is replaced by a geodesic sphere (which does not have strong poles as in the case of spherical geometry), as shown in Figure 6.

[0127] Compton cameras can receive photons coming from any location in the detector planes, which prevents matrix segmentation. As explained, the collimation of this camera is given by cones centered on the interaction point, and the interaction points are events that accumulate in the detector plane, which we call the scatterer. By its nature, this information must be compared and composed event by event; therefore, reconstruction involves processing the N events that provide the image and iterating these N events from the camera space to real space using a backprojection procedure. It is easy to see that, regardless of the complexity of the projections of these events, the improvement obtained for each event in terms of statistical reduction comes with a high computational cost associated with the interpretation of an iterative process of N events.Increasing the computational cost by a factor of at least O(N).

[0128] Therefore, this method is applicable only when the interactivity of the application is not a determining factor.

[0129] In order to implement the invention, the aim is to decompose the detection planes of the Compton cameras and provide a geodesic sphere at each location of this plane that represents all the interactions that have been carried out at said point of the sensor. In this way, the information associated with the event is only applied once. This is an advantage that allows the Compton camera to be used as a set of 4TT geometry cameras (pinhole) and to process iterative methods at a constant cost. Indeed, the reconstruction mechanisms of the Compton cameras are based on the iterative processing of all the reconstructed Compton events on the regions where the signal is intended to be reconstructed. The system allows each event to be encoded only once and allows this information to be directly used at a cost of 0(0) with respect to the number of events, as many times as necessary and in all the processes that are necessary.The use of homogeneous partitions (decomposition of hemispherical spheres) also introduces the advantage that the information used does not require form factors associated with the poles that this geometry introduces.

[0130] The use of the method of the invention provides computational advantages since the projection has constant cost and can be indexed.

[0131] In this way, a volume can be reconstructed, since the information from a specific area of ​​an image can be backprojected using the location where the information has maximum contrast. Thus, the search for maximum contrast can be performed in each area of ​​the image, locating the source positions in the locations with the greatest amplitude for each.

[0132] Furthermore, it is possible to evaluate response matrices for each pixel and store them in the pixel itself, incorporating the information into a corresponding vector of the geodesic sphere.

[0133] Figure 7 shows the combined information with the projection itself. In this case, when projecting onto planes, a pixelation effect and lack of contrast are observed due to the presence of three sources, only one of which is projected onto the corresponding plane in each case.

[0134] The method of the invention allows a volume to be analyzed by directly projecting the signal from each pixel in the camera space into real space. This allows the location of the different sources to be reconstructed without image artifacts and to be reconstructed immediately to any plane, since the scenes do not have to be back-projected to a specific plane each time, as in state-of-the-art solutions. Instead, the different scenes can be stored in a set of geodesic spheres, each of which can store a different location of the scatterer or absorber. An alternative application of the method of the invention relates to a receiver-transmitter system, i.e., a radar or sonar-type system, where an active source emits a known signal (in frequency and intensity) and, subsequently, reflections are captured by a receiver.

[0135] In this case, the important part is the signal reception, while the source is the environment itself.

[0136] In order to represent this information, state-of-the-art solutions use information matrices based on simple axes where the search for an element can be located with:

[0137] 1. X axis: Represents the direction of the detected object in the horizontal plane (azimuth).

[0138] 2. Y axis: Represents the direction of the detected object in the vertical plane (elevation).

[0139] 3. Z axis: Represents the distance from the radar to the detected object (range),

[0140] The Z axis is, in general, a hyper-cube of information and can represent or store any other scalar, such as frequency changes, signal intensity return time, processing of some of the layers and more.

[0141] This way of representing (angular) allows access to information quickly, but it poses a series of drawbacks:

[0142] • This representation has at least two poles, that is, points where the information cannot be represented in order to apply mathematical algorithms.

[0143] • These poles can be treated in static installations, but it is not possible to treat them in moving systems such as aircraft.

[0144] • In addition, they produce a series of information inhomogeneities that add artifacts.

[0145] • The treatment of distant or close objects may have different convolutions despite being in the same position (azimuth-elevation) due to the distance of the object.

[0146] • In moving systems (such as airplanes, ships, or vehicles), this pole shifts according to its position on the plane of the Earth's sphere. In particular, on an aircraft radar, the poles would appear in the vertical region of the aircraft, where the upper region may not be relevant, but the lower region marks the area of ​​ground closest to the aircraft. Selecting the front-to-back of the aircraft is also not recommended. In any case, combining these regions with the aircraft's motion introduces distortions when treated as time series.

[0147] On the contrary, storing the information in an indexed mesh, as in the method of the invention, where each mesh point represents a location and the adjacent regions, provides the following advantages:

[0148] • Information can continue to be processed by applying signal filtering techniques, which does not reduce the capabilities of operating systems.

[0149] • Processing becomes motion immune.

[0150] • Coordinate orientation is not included in the design parameters of the processing system.

[0151] Another advantage of this type of representation is that when the sensor carried by the aircraft moves relative to the aircraft, the new projections must be distorted to correlate the new positions with the positions of the previous orientation, making processing in real-time systems difficult and introducing costs. In contrast, using orientations stored in a geodesic sphere, as in the present invention, this entire effect disappears, and all transformations are limited to rotations about the axes of the previous positions. In order to store information when dealing with temporal signals, it is necessary to convert the scalar representing each vertex of the geodesic into a vector, where each time-space is associated with a vector index.In order to perform this type of storage, a method that is conveniently used is 'circular' vectors where this index allows to traverse 'time' in an interval defined by its length in a cyclical manner.

[0152] A third application of the method of the invention relates to a Magnetic Resonance Imaging (MRI) machine. A Magnetic Resonance Imaging (MRI) machine uses a series of radiofrequency coils, which act as antennas, to transmit and receive radio signals. These coils are key to creating images in an MRI.

[0153] In general, the operating scheme of an MRI machine is as follows: 1. Radiofrequency emission: A main coil emits a radiofrequency signal that excites hydrogen nuclei in the patient's body. This signal is highly specific and tuned to interact with the hydrogen nuclei.

[0154] 2. Relaxation and signal emission: Once the radiofrequency signal is turned off, the hydrogen nuclei "relax" and return to their original state, in turn emitting a radio signal. This signal is what MRI detects and uses to create images.

[0155] 3. Signal Detection: The receiving coils detect the radio signal emitted by the hydrogen nuclei. Each coil receives a signal that is a combination of the signals from all the hydrogen nuclei within its range.

[0156] 4. Signal digitization: The analog radio frequency signal collected by the coils is digitized. This is a conversion process that transforms the analog signal into a form that can be processed by a computer.

[0157] 5. Signal processing: Digital signals are processed using techniques such as the Fourier Transform or conventional convolutions to convert time signals (radio frequency signals over time) into space signals (the spatial distribution of hydrogen nuclei).

[0158] 6. Image Creation: The processed data is used to create a three-dimensional image of the body's tissues. Each dot in the image corresponds to a small volume of tissue, and its brightness depends on the amount of radiofrequency signal received from that volume of tissue.

[0159] In this case, although there are similarities in the way MR systems process and store data compared to the aforementioned application of transmitter-receiver devices (e.g., in airplanes), there are also many differences in the details of how they operate and are used.

[0160] For example, MRI systems typically require a high level of control over the environment (such as temperature and magnetic field), while radar or sonar systems often operate in uncontrolled, even hostile, environments. On the other hand, in MRI devices, the operating precision of information gathering is perfectly controlled, while the projections on the capture antennas in transmitter-receiver devices come from geometries with a strong spherical component.

[0161] Despite these differences, in the application of MRI, the ability to obtain distortion-free calculation matrices and process them using the method of the invention is essential. In this case, it is very important to know that the antennas have near-field behavior, since the distance to the patient is limited. When antennas have near-field information, the complexity is that the radiation or capture methods have a strong local dependence determined by the distance to the point. Modeling this data (emitted signal / received signal in a direction) allows for reducing the near-field reconstruction time and limiting the number of operations to correct aberrations inherent in spherical or flat projection, where other geometric effects appear. In this sense, a matrix of elements of an MRI signal can be viewed and processed in the same way that the various sensor elements of Compton gamma cameras are processed.Furthermore, triangulations would not be affected by the differences in spherical projections imposed by other state-of-the-art representations.

Claims

CLAIMS 1. A three-dimensional signal processing method that enables a continuous and homogeneous representation while minimizing distortions, and which comprises the steps of: providing one or more measurement sensors with a signal from a source, associated with one or more positions in space, where the measurement sensors are configured to obtain a direction of the measured signal with respect to said positions in space; breaking down the sensor into one or more locations; generating one or more geodesic spheres at each location, where each geodesic sphere comprises a set of triangular elements with almost equally spaced vertices; encoding a signal representative of the direction between the center of the sphere and the position of the source at a set of vertices of the sphere;and generating a vector associated with each vertex, to store signal strength information where the method further comprises the step of: modifying the vectors to replace the signal strength information by applying mutual noise reduction techniques using elements of adjacent geodesic spheres; and / or reconstructing a signal source by combining operations performed with elements of said vector, adjacent vectors or vectors of other geodesic spheres.

2. A method according to claim 1, further comprising a step of modifying the vectors to replace the signal intensity information by applying noise reduction or signal-to-noise ratio improvement techniques using elements of said vector or adjacent vectors.

3. Method according to any of the preceding claims, further comprising a step of generating one or more replicas for each geodesic sphere with a smaller angular partitioning, where the directional information of each measuring device, associated with a position in space, is stored in each of the replicas, to allow rapid access to the information of the origin of the signal and its intensity at each vertex of the sphere.

4. A method according to any preceding claim, further comprising a step of reducing the number of geodesic spheres associated with each position while maintaining directionality and summarizing source direction information from a group of geodesic spheres into a single geodesic sphere representing the original group of spheres.

5. Method according to any of the preceding claims, wherein the number of geodesic spheres and the resolution of each geodesic sphere are determined based on the distance of the sensors to the source and a maximum permissible error.

6. Method according to any of the preceding claims, wherein the vector comprises data representative of different temporal states, and further comprising an additional step of applying a weighted subtraction, addition, multiplication between elements of said vector to obtain information about the temporal variation.

7. Method according to any of the preceding claims, wherein the elements of the vector correspond to signals obtained at different energies and / or frequencies, called layers, which also comprises an additional step of generating new layers in the vectors by weighting and using adjacency weights applied to the values ​​of a layer in a set of adjacent vertices and / or adjacent spheres to obtain a convolutional representation of one or several layers.

8. Method according to claim 7, further comprising an additional step of generating new information by weighting and using adjacency weights applied to values ​​of various layers associated with different positions of the sensors or the source.

9. Method according to any of the preceding claims, further comprising an additional step of applying direct projection operations of each direction to a point in the space of the generated spheres by evaluating the signal at that point as the weighted sum of the values ​​ranging from the origin of the sphere and in the direction between the origin of the sphere and the point in space.

10. The method of claim 9, further comprising an additional step of applying direct projection operations to a set of points in space representing a spatial volume, and iteratively correcting the inverse projection of the projected points to equalize the signal received at each of the sensors.

11. Method according to any of the preceding claims, wherein the information to be stored is the projection of circles on each geodesic sphere, representing a gamma ray from a Compton camera where each sphere represents a location in the space of the scatterer, and each circle represents the back projection of a photon from the absorber, and where each element of the vector associated with the directions represents a sum energy of the photon between the scatterer and the absorber.

12. Method according to claim 11, wherein if the distance of the sensors to the source is greater than ten times a scatter width of the Compton camera, a single geodesic sphere is used.

13. Method according to claims 11 to 12, wherein the number of positions of the spheres representing the Compton chamber is increased by moving the Compton chamber or by increasing the number of Compton chambers.

14. Device for measuring a signal comprising a sensor, configured to measure a signal, and a processing module configured to carry out the method described in any of claims 1 to 13.

15. Device according to claim 14, wherein the device is a radar, a visible light camera or an ultrasound system.

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