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This paper presents a novel lattice based biomimetic neural network trained by means of a similarity measure derived from a lattice positive valuation. For a wide class of pattern recognition problems, the proposed artificial neural network, implemented as a dendritic hetero-associative memory delivers high percentages of successful classification. The memory is a feedforward dendritic network whose arithmetical operations are based on lattice algebra and can be applied to real multivalued inputs. In this approach, the realization of recognition tasks, shows the inherent capability of prototype-class pattern associations in a fast and straightforward manner without need of any iterative scheme subject to issues about convergence. Using an artificially designed data set we show how the proposed trained neural net classifies a test input pattern. Application to a few typical real-world data sets illustrate the overall network classification performance using different training and testing sample subsets generated randomly.
Gerhard X. Ritter; Gonzalo Urcid; Luis-David Lara-Rodríguez. Similarity Measures for Learning in Lattice Based Biomimetic Neural Networks. Mathematics 2020, 8, 1439 .
AMA StyleGerhard X. Ritter, Gonzalo Urcid, Luis-David Lara-Rodríguez. Similarity Measures for Learning in Lattice Based Biomimetic Neural Networks. Mathematics. 2020; 8 (9):1439.
Chicago/Turabian StyleGerhard X. Ritter; Gonzalo Urcid; Luis-David Lara-Rodríguez. 2020. "Similarity Measures for Learning in Lattice Based Biomimetic Neural Networks." Mathematics 8, no. 9: 1439.
Lattice associative memories were proposed as an alternative approach to work with a set of associated vector pairs for which the storage and retrieval stages are based in the theory of algebraic lattices. Several techniques have been established to deal with the problem of binary or real valued vector recall from corrupted inputs. This paper presents a thresholding technique coupled with statistical correlation pattern index search to enhance the recall performance of lattice auto-associative memories for multivariate data inputs degraded by random noise. By thresholding a given noisy input, a lower bound is generated to produce an eroded noisy version used to boost the min-lattice auto-associative memory inherent retrieval capability. Similarly, an upper bound is generated to obtain a dilated noisy version used to enhance the max-lattice auto-associave memory response. A self contained theoretical foundation is provided including a visual example of a multivariate data set composed of grayscale images that show the increased retrieval capability of this type of associative memories.
Gonzalo Urcid; Rocío Morales-Salgado; Nieves- Vázquezsjosé- Angel. Multivariate Data Retrieval Modified by Random Noise using Lattice Autoassociative Memories with Eroded or Dilated Input Residuals. MATEC Web of Conferences 2019, 292, 04007 .
AMA StyleGonzalo Urcid, Rocío Morales-Salgado, Nieves- Vázquezsjosé- Angel. Multivariate Data Retrieval Modified by Random Noise using Lattice Autoassociative Memories with Eroded or Dilated Input Residuals. MATEC Web of Conferences. 2019; 292 ():04007.
Chicago/Turabian StyleGonzalo Urcid; Rocío Morales-Salgado; Nieves- Vázquezsjosé- Angel. 2019. "Multivariate Data Retrieval Modified by Random Noise using Lattice Autoassociative Memories with Eroded or Dilated Input Residuals." MATEC Web of Conferences 292, no. : 04007.
Gonzalo Urcid; Rocio Morales-Salgado. A Mapping and Sorting Hybrid Technique for Color Image Palette Extraction. Seventh International Conference on Advances in Computing, Communication and Information Technology - CCIT 2018 2018, 50 -54.
AMA StyleGonzalo Urcid, Rocio Morales-Salgado. A Mapping and Sorting Hybrid Technique for Color Image Palette Extraction. Seventh International Conference on Advances in Computing, Communication and Information Technology - CCIT 2018. 2018; ():50-54.
Chicago/Turabian StyleGonzalo Urcid; Rocio Morales-Salgado. 2018. "A Mapping and Sorting Hybrid Technique for Color Image Palette Extraction." Seventh International Conference on Advances in Computing, Communication and Information Technology - CCIT 2018 , no. : 50-54.
This paper presents a new algorithm to find several types of extreme points of higher dimensional lattice polytopes enclosing a given finite set as derived from the canonical min/max lattice autoassociative memories. The algorithm first computes the basic extreme points that include the corners of the hyperbox containing the data together with the translated min/max points. Then, the algorithm computes additional extreme points such as entry or exit line points from the basic ones. Using convex geometry and lattice algebra, we discuss the rationale of the proposed technique with simple illustrative examples.
Gerhard X. Ritter; Gonzalo Urcid. Extreme Points of Convex Polytopes Derived from Lattice Autoassociative Memories. Privacy Enhancing Technologies 2018, 116 -125.
AMA StyleGerhard X. Ritter, Gonzalo Urcid. Extreme Points of Convex Polytopes Derived from Lattice Autoassociative Memories. Privacy Enhancing Technologies. 2018; ():116-125.
Chicago/Turabian StyleGerhard X. Ritter; Gonzalo Urcid. 2018. "Extreme Points of Convex Polytopes Derived from Lattice Autoassociative Memories." Privacy Enhancing Technologies , no. : 116-125.
We describe a dendritic lattice hetero-associative memory (DLHAM) that performs multivariate numerical data mapping with respect to a set of prototype data vectors selected by diverse objective or subjective criteria. The memory is a feedforward four-layer dendritic neural network based on lattice algebra operations that computes the nearest match between input and prototype data vectors. Our approach shows the inherent capability of n-dimensional vector association to realize coarse or fine data mapping that is computationally simple. Specifically, we apply the DLHAM in a two stage algorithm to the quantization and transfer of Red-Green-Blue (RGB) color coded images. Input color pixels are first quantized and then the resulting representative colors are mapped to another set of palette colors by hetero-association. Examples and quantization error are included to show the DLHAM performance.
Gonzalo Urcid; Rocio Morales-Salgado; Gerhard X Ritter. Multivariate data mapping based on dendritic lattice associative memories. 2017 IEEE Latin American Conference on Computational Intelligence (LA-CCI) 2017, 1 -6.
AMA StyleGonzalo Urcid, Rocio Morales-Salgado, Gerhard X Ritter. Multivariate data mapping based on dendritic lattice associative memories. 2017 IEEE Latin American Conference on Computational Intelligence (LA-CCI). 2017; ():1-6.
Chicago/Turabian StyleGonzalo Urcid; Rocio Morales-Salgado; Gerhard X Ritter. 2017. "Multivariate data mapping based on dendritic lattice associative memories." 2017 IEEE Latin American Conference on Computational Intelligence (LA-CCI) , no. : 1-6.
This chapter presents a novel method based on discrete frequency transforms to segment various pathologies in eye fundus color images such as exudates, blood vessels, and aneurysms. Non-uniform illuminated eye fundus images are corrected by applying a homomorphic high-pass frequency filter. Then, a super-Gaussian band-pass filter defined in the frequency transform domain is used to distinguish between background and foreground objects. The filtering step works with the green channel that usually contains the most relevant information to segment different pathologies. Specifically, exudates detection after transform inversion of the filtered image requires a gamma correction to enhance foreground objects. Otsu’s thresholding method is applied to the enhanced image and masked over the effective area to get the segmented exudates. For blood vessels and aneurysms, back in the spatial domain, the negative of the filtered image is required. Then a median filter is applied to reduce noise or artifacts followed by gamma contrast enhancement. Again, Otsu’s thresholding method is used for image binarization. Next a morphological closing operation is applied and masking the effective image area gives the segmented blood vessels or aneurysms. Illustrative examples using retinographies from a free public domain clinical database are included to demonstrate the capability of the frequency filter approach.
Gonzalo Urcid; Luis David Lara-R; Elizabeth López-M. Pathologies Segmentation in Eye Fundus Images Based on Frequency Domain Filters. Transactions on Engineering Technologies 2017, 137 -151.
AMA StyleGonzalo Urcid, Luis David Lara-R, Elizabeth López-M. Pathologies Segmentation in Eye Fundus Images Based on Frequency Domain Filters. Transactions on Engineering Technologies. 2017; ():137-151.
Chicago/Turabian StyleGonzalo Urcid; Luis David Lara-R; Elizabeth López-M. 2017. "Pathologies Segmentation in Eye Fundus Images Based on Frequency Domain Filters." Transactions on Engineering Technologies , no. : 137-151.
This paper introduces an autonomous hybrid technique designed for the digital restoration of the missing parts and occluding artifacts in damaged historical or artistic color documents. For this purpose, a hyperspectral imaging device is used to acquire sets of images in the visible and near infrared ranges. Assuming the presence of linearly mixed pixels registered from the spectral images, our technique uses two lattice auto-associative memories to extract the set of pure pigments spectra. Fractional abundance maps indicating the distributions of each pigment along the image are obtained by spectral linear unmixing. These maps are then used to locate holes and cracks in the document under study. The restoration process is performed by the application of a modified morphological region filling algorithm, followed by a vectorial linear interpolation scheme to restore the original color appearance of the filled areas. For illustration purposes, our procedure has been applied successfully to the restoration of superimposed scripts and an art painting.
Juan C. Valdiviezo-N; Gonzalo Urcid; Edwin Lechuga. Digital restoration of damaged color documents based on hyperspectral imaging and lattice associative memories. Signal, Image and Video Processing 2016, 11, 937 -944.
AMA StyleJuan C. Valdiviezo-N, Gonzalo Urcid, Edwin Lechuga. Digital restoration of damaged color documents based on hyperspectral imaging and lattice associative memories. Signal, Image and Video Processing. 2016; 11 (5):937-944.
Chicago/Turabian StyleJuan C. Valdiviezo-N; Gonzalo Urcid; Edwin Lechuga. 2016. "Digital restoration of damaged color documents based on hyperspectral imaging and lattice associative memories." Signal, Image and Video Processing 11, no. 5: 937-944.
Gonzalo Urcid; Luis David Lara Rodríguez; Elizabeth López-Meléndez. A dendritic lattice neural network for color image segmentation. Applications of Digital Image Processing XXXVIII 2015, 95992O -95992O-10.
AMA StyleGonzalo Urcid, Luis David Lara Rodríguez, Elizabeth López-Meléndez. A dendritic lattice neural network for color image segmentation. Applications of Digital Image Processing XXXVIII. 2015; ():95992O-95992O-10.
Chicago/Turabian StyleGonzalo Urcid; Luis David Lara Rodríguez; Elizabeth López-Meléndez. 2015. "A dendritic lattice neural network for color image segmentation." Applications of Digital Image Processing XXXVIII , no. : 95992O-95992O-10.
This paper presents a Fourier transform approach to detect microcalcifications in digital mammograms. The basic idea consists in the design of parametric Butterworth bandpass filters in the Fourier domain used to extract sharpened border like structures that correspond to detected mammography microcalcifications. Image thresholding of the filtered image is accomplished, first by homogenizing the background (fibroglandular tissue) with a median filter, after which a gamma correction is applied to change the global contrast. Second, by postprocessing the resulting image using histogram based local and global statistics we obtain a properly binarized image that emphasizes the desired objects (microcalcifications) and segmentation is completed using a sequence of morphological binary operations. Several illustrative examples taken from a clinical database are included to demonstrate the capability of the proposed approach in comparison with other edge detection techniques such as the difference of Gaussians (DoG) and the Laplacian of a Gaussian (LoG).
Elizabeth López-Meléndez; Luis David Lara Rodríguez; Gonzalo Urcid. Fourier-based segmentation of microcalcifications in mammograms. Applications of Digital Image Processing XXXVIII 2015, 9599, 1 .
AMA StyleElizabeth López-Meléndez, Luis David Lara Rodríguez, Gonzalo Urcid. Fourier-based segmentation of microcalcifications in mammograms. Applications of Digital Image Processing XXXVIII. 2015; 9599 ():1.
Chicago/Turabian StyleElizabeth López-Meléndez; Luis David Lara Rodríguez; Gonzalo Urcid. 2015. "Fourier-based segmentation of microcalcifications in mammograms." Applications of Digital Image Processing XXXVIII 9599, no. : 1.
Gerhard X. Ritter; José-A. Nieves-Vázquez; Gonzalo Urcid. A simple statistics-based nearest neighbor cluster detection algorithm. Pattern Recognition 2015, 48, 918 -932.
AMA StyleGerhard X. Ritter, José-A. Nieves-Vázquez, Gonzalo Urcid. A simple statistics-based nearest neighbor cluster detection algorithm. Pattern Recognition. 2015; 48 (3):918-932.
Chicago/Turabian StyleGerhard X. Ritter; José-A. Nieves-Vázquez; Gonzalo Urcid. 2015. "A simple statistics-based nearest neighbor cluster detection algorithm." Pattern Recognition 48, no. 3: 918-932.
This research introduces an automatic technique designed for the digital restoration of the damaged parts in historical documents. For this purpose an imaging spectrometer is used to acquire a set of images in the wavelength interval from 400 to 1000 nm. Assuming the presence of linearly mixed spectral pixels registered from the multispectral image, our technique uses two lattice autoassociative memories to extract the set of pure pigments conforming a given document. Through an spectral unmixing analysis, our method produces fractional abundance maps indicating the distributions of each pigment in the scene. These maps are then used to locate cracks and holes in the document under study. The restoration process is performed by the application of a region filling algorithm, based on morphological dilation, followed by a color interpolation to restore the original appearance of the filled areas. This procedure has been successfully applied to the analysis and restoration of three multispectral data sets: two corresponding to artificially superimposed scripts and a real data acquired from a Mexican pre-Hispanic codex, whose restoration results are presented.
Edwin Lechuga-S.; Juan C. Valdiviezo-N.; Gonzalo Urcid. Multispectral image restoration of historical documents based on LAAMs and mathematical morphology. Optical Engineering + Applications 2014, 9216, 921604 .
AMA StyleEdwin Lechuga-S., Juan C. Valdiviezo-N., Gonzalo Urcid. Multispectral image restoration of historical documents based on LAAMs and mathematical morphology. Optical Engineering + Applications. 2014; 9216 ():921604.
Chicago/Turabian StyleEdwin Lechuga-S.; Juan C. Valdiviezo-N.; Gonzalo Urcid. 2014. "Multispectral image restoration of historical documents based on LAAMs and mathematical morphology." Optical Engineering + Applications 9216, no. : 921604.
An artificial neural network model based on dendritic computation using two lattice metrics is introduced in this paper. A description of the mathematical framework of the proposed model is provided and its corresponding learning algorithm is presented in mathematical pseudocode. Computational experiments are given to demonstrate the effectiveness and performance of the learning algorithm as well as its application to some illustrative pattern recognition problems.
Gerhard X. Ritter; Gonzalo Urcid; Juan-Carlos Valdiviezo-N.. Two lattice metrics dendritic computing for pattern recognition. 2014 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE) 2014, 45 -52.
AMA StyleGerhard X. Ritter, Gonzalo Urcid, Juan-Carlos Valdiviezo-N.. Two lattice metrics dendritic computing for pattern recognition. 2014 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE). 2014; ():45-52.
Chicago/Turabian StyleGerhard X. Ritter; Gonzalo Urcid; Juan-Carlos Valdiviezo-N.. 2014. "Two lattice metrics dendritic computing for pattern recognition." 2014 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE) , no. : 45-52.
Gerhard X. Ritter; Gonzalo Urcid. Lattice Based Dendritic Computing: A Biomimetic Approach to ANNs. Transactions on Petri Nets and Other Models of Concurrency XV 2014, 730 -744.
AMA StyleGerhard X. Ritter, Gonzalo Urcid. Lattice Based Dendritic Computing: A Biomimetic Approach to ANNs. Transactions on Petri Nets and Other Models of Concurrency XV. 2014; ():730-744.
Chicago/Turabian StyleGerhard X. Ritter; Gonzalo Urcid. 2014. "Lattice Based Dendritic Computing: A Biomimetic Approach to ANNs." Transactions on Petri Nets and Other Models of Concurrency XV , no. : 730-744.
We present an autonomous technique for the detection and extraction of all potential endmembers from hyperspectral imagery. The proposed technique is based on the convex polyhedral model. The computation of the vertices of a minimal polyhedron is accomplished using lattice auto-associave memories as well as other lattice algebra theoretic concepts. A novel statistical data clustering algorithm is used to select final endmembers.
Gerhard X Ritter; Gonzalo Urcid; Jose Angel Nieves-V; Nieves-V. Jose Angel. An autonomousendmember detection technique based on lattice associative memories and statistical clustering. 2013 5th Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing (WHISPERS) 2013, 1 -4.
AMA StyleGerhard X Ritter, Gonzalo Urcid, Jose Angel Nieves-V, Nieves-V. Jose Angel. An autonomousendmember detection technique based on lattice associative memories and statistical clustering. 2013 5th Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing (WHISPERS). 2013; ():1-4.
Chicago/Turabian StyleGerhard X Ritter; Gonzalo Urcid; Jose Angel Nieves-V; Nieves-V. Jose Angel. 2013. "An autonomousendmember detection technique based on lattice associative memories and statistical clustering." 2013 5th Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing (WHISPERS) , no. : 1-4.
Juan C. Valdiviezo-N.; Gonzalo Urcid; Carina Toxqui; Alfonso Padilla; Cesar Santiago. An efficient algorithm for food quality control based on multispectral signatures. IS&T/SPIE Electronic Imaging 2013, 86610X -86610X-9.
AMA StyleJuan C. Valdiviezo-N., Gonzalo Urcid, Carina Toxqui, Alfonso Padilla, Cesar Santiago. An efficient algorithm for food quality control based on multispectral signatures. IS&T/SPIE Electronic Imaging. 2013; ():86610X-86610X-9.
Chicago/Turabian StyleJuan C. Valdiviezo-N.; Gonzalo Urcid; Carina Toxqui; Alfonso Padilla; Cesar Santiago. 2013. "An efficient algorithm for food quality control based on multispectral signatures." IS&T/SPIE Electronic Imaging , no. : 86610X-86610X-9.
This paper introduces a lattice algebra procedure that can be used for the multispectral analysis of historical documents and artworks. Assuming the presence of linearly mixed spectral pixels captured in a multispectral scene, the proposed method computes the scaled min- and max-lattice associative memories to determine the purest pixels that best represent the spectra of single pigments. The estimation of fractional proportions of pure spectra at each image pixel is used to build pigment abundance maps that can be used for subsequent restoration of damaged parts. Application examples include multispectral images acquired from the Archimedes Palimpsest and a Mexican pre-Hispanic codex.
Juan C. Valdiviezo-N; Gonzalo Urcid. Lattice algebra approach to multispectral analysis of ancient documents. Applied Optics 2013, 52, 674 -682.
AMA StyleJuan C. Valdiviezo-N, Gonzalo Urcid. Lattice algebra approach to multispectral analysis of ancient documents. Applied Optics. 2013; 52 (4):674-682.
Chicago/Turabian StyleJuan C. Valdiviezo-N; Gonzalo Urcid. 2013. "Lattice algebra approach to multispectral analysis of ancient documents." Applied Optics 52, no. 4: 674-682.
We present a two layer dendritic hetero-associative memory that gives high percentages of correct classification for typical pattern recognition problems. The memory is a feedforward dendritic network based on lattice algebra operations and can be used with multivalued real inputs. A major consequence of this approach shows the inherent capability of prototype-class pattern associations to realize classification tasks in a direct and fast way without any convergence problems.
Gonzalo Urcid; Gerhard X. Ritter; Juan-Carlos Valdiviezo-N. Dendritic lattice associative memories for pattern classification. 2012 Fourth World Congress on Nature and Biologically Inspired Computing (NaBIC) 2012, 181 -187.
AMA StyleGonzalo Urcid, Gerhard X. Ritter, Juan-Carlos Valdiviezo-N. Dendritic lattice associative memories for pattern classification. 2012 Fourth World Congress on Nature and Biologically Inspired Computing (NaBIC). 2012; ():181-187.
Chicago/Turabian StyleGonzalo Urcid; Gerhard X. Ritter; Juan-Carlos Valdiviezo-N. 2012. "Dendritic lattice associative memories for pattern classification." 2012 Fourth World Congress on Nature and Biologically Inspired Computing (NaBIC) , no. : 181-187.
Juan C. Valdiviezo-N.; Gonzalo Urcid; Carina Toxqui-Quitl; Alfonso Padilla-Vivanco. A comparison of autonomous techniques for multispectral image analysis and classification. Optical Engineering + Applications 2012, 849920 -849920-10.
AMA StyleJuan C. Valdiviezo-N., Gonzalo Urcid, Carina Toxqui-Quitl, Alfonso Padilla-Vivanco. A comparison of autonomous techniques for multispectral image analysis and classification. Optical Engineering + Applications. 2012; ():849920-849920-10.
Chicago/Turabian StyleJuan C. Valdiviezo-N.; Gonzalo Urcid; Carina Toxqui-Quitl; Alfonso Padilla-Vivanco. 2012. "A comparison of autonomous techniques for multispectral image analysis and classification." Optical Engineering + Applications , no. : 849920-849920-10.
We present a novel hetero-associative memory based on dendritic neural computation. The computations in this model are based on lattice group operations. The proposed model does not suffer from the usual storage capacity problem and is extremely robust in the presence of various types of noise and data corruption.
Gerhard X. Ritter; Darya Chyzhyk; Gonzalo Urcid; Manuel Graña. A Novel Lattice Associative Memory Based on Dendritic Computing. Transactions on Petri Nets and Other Models of Concurrency XV 2012, 7209, 491 -502.
AMA StyleGerhard X. Ritter, Darya Chyzhyk, Gonzalo Urcid, Manuel Graña. A Novel Lattice Associative Memory Based on Dendritic Computing. Transactions on Petri Nets and Other Models of Concurrency XV. 2012; 7209 ():491-502.
Chicago/Turabian StyleGerhard X. Ritter; Darya Chyzhyk; Gonzalo Urcid; Manuel Graña. 2012. "A Novel Lattice Associative Memory Based on Dendritic Computing." Transactions on Petri Nets and Other Models of Concurrency XV 7209, no. : 491-502.
Lattice associative memories are artificial neural networks for which the storage and recall stages, given a finite set X of exemplar images, are defined with lattice algebra operations. Two dual canonical auto-associative memories have been introduced, the min-memory W xx and the max-memory M xx , capable to recall approximations to exemplars from corrupted inputs. It turns out that the min-memory is robust to erosive noise and the max-memory is robust to dilative noise; however, neither one of these memories is able to cope with images degraded by random noise represented as a mixture of erosive and dilative noise. A hybrid procedure based on noise masking and two measures is developed here to endow lattice auto-associative memories with color image recall capability for inputs distorted by additive random noise.
Gonzalo Urcid; José-Angel Nieves Vázquez. Lattice masking and auto-association for recalling color images in the presence of noise. 2011 Third World Congress on Nature and Biologically Inspired Computing 2011, 267 -272.
AMA StyleGonzalo Urcid, José-Angel Nieves Vázquez. Lattice masking and auto-association for recalling color images in the presence of noise. 2011 Third World Congress on Nature and Biologically Inspired Computing. 2011; ():267-272.
Chicago/Turabian StyleGonzalo Urcid; José-Angel Nieves Vázquez. 2011. "Lattice masking and auto-association for recalling color images in the presence of noise." 2011 Third World Congress on Nature and Biologically Inspired Computing , no. : 267-272.