Generating an Eigen Matrix Genotype From Aggregated Imagery
\nor, the \u201cEigen Variant\u201d
\nBy Kevin M. Cowan and Steve Harris
\nOctober 10, 2017
\nAbstract:
\nA familiar theme in facial recognition technology is \u201cFacial recognition is hard, and remains far from an exact science at this point in its evolution.\u201d Currently, the technology used to create useful, precise biometric representations and associate these representations to their human counterparts (a.k.a. Facial Recognition), is a hit-or-miss \u201cbest guess\u201d science. A second weakness of this approach is that it exclusively considers the world from a static, two-dimensional perspective.
\nWe propose a shift from the static, two-dimensional perspective into a dynamic, multidimensional paradigm, by hybridizing the disciplines of forensic anthropology, 3-D modeling, object-oriented remote sensing and digital imaging; and then combining this approach with the low-power footprint, high-scale searchability of modern \u201cbig data\u201d search engine(s?) capabilities. The resulting process will harness the methodology of forensic anthropology to reverse engineer a model of an object \u2014 not only limited to faces \u2014 but taking into account a variety of distinctive scalar vectors associated with an individual. This would include, but would not be limited to: Cranial Topography, Cephalic Index, Functional Craniology, Machine Learning and Pattern Matching. This would be accomplished utilizing both static and stochastic variant vectors aggregated into a single matrix, or what we call an \u2018Eigen Variant\u2019. What sets this model apart from contemporary biometric and\/or facial recognition gathering is that while most models only deal with a single, or limited, number of images, the Eigen Variant encourages image data aggregation. The more data to aggregate, the more distinctive the variant becomes. Thus to incorporate not only traditional biometric recognition strategies, but morphological, mathematical and contextual aspects as well.
\nThe \u2018Eigen Variant\u2019
\nDefinition
\nIn the simplest terms, an Eigen Variant is an object containing a multidimensional set of Eigen Matrices, which in turn contain a set of Eigenvectors, the scalar values of which may be either simple or complex. The Eigenvectors contains (n) sets of scalar values that are stored for analytics and retrieval in the form of multidimensional arrays. These multidimensional arrays constitute a genotype extrapolated from a phenotype, derived from (n) sources of digital imaging which, in essence, comprise a mathematical fingerprint.
\nAn Eigen Variant is ultimately derived, then, from the aggregation of (n) images that are a) mined for singular objects in the form of patterns and gradient variants, mathematical distinctiveness (spatial, geometric, spectral, etc); and then b) reduced to a set of scalar arrays and converted to Eigenvectors; which are then; c) matched and merged into a Eigen Matrix contained in the Eigen Variant that constitutes a genotype of the target object. This object may be anything having distinguishing characteristics that can be reduced to its scalar designations, which is to say, any physical object. Beyond the mathematical aspect, though, the Eigen Variant is an object-oriented class hierarchy capable of applying functional Machine Learning in the context of a procedural container in real-time.
\nProposed Methodology
\nDigital Image Acquisition and Aggregation
\nComposite imagery would be acquired and processed from a variety of sources. The more sources, the more distinctive the genotype; thus the more sources, the better the result. The key to this process would be associating the given image with a known Eigen Variant. Rather than focusing specifically on Eigenface biometrics, the process would isolate distinct objects (E.g. jewelry, clothing, prosthetics, etc) as well as facial, cranial, and other distinctly identifiable objects (E.g. Eigenface vectors, ear shape vectors, etc). These objects would be analyzed by a Support Vector Machine for future reference, and the distinctive objects would be packaged as a set and passed along a set of microservices as follows.
\nEigen Matrix Application
\nEach distinct object produced from the composite analysis is re-parsed with the proprietary purpose of identifying distinctive static and stochastic (random) elements in the form of crestlines, ridges and troughs that are then reduced into an Eigen Matrix. In \u201creal world\u201d terms, this would be something like the shape of an ear, or a particular piece of jewelry, and so on.
\nEigen Variant Instantiation
\nThe resulting Eigen Matrix is then sent along for analysis and comparison to existing matrices stored in the data engine. Here is where modern \u201cbig data\u201d technology holds the critical advantage. Utilizing \u2018big data\u2019 indexing and querying techniques, it is possible to compare objects to billions of other objects in a matter of milliseconds, not only in standard mathematical terms, but also in terms of applied morphology. The matrix is thus analyzed from mathematical, morphological and contextual relevance and matched to an Eigen Matrix where it is then merged into the current variant, where in each evolution, its distinctiveness is enhanced resulting in a phenologically distinct object. If no suitable match is found, a new Eigen Matrix is instantiated, and categorized by similarity.
\nIngestion and Analysis
\nOnce a suitable Eigen Matrix has been found for the incoming data, a process will consider the most accurate way of incorporating this new information into the existing variant. This will utilize object-oriented remote sensing techniques coupled with a proprietary mathematical \u2018image stitching\u2019 process that will integrate the data into the existing paradigm. In \u201creal world\u201d terms think of this as merging two or more pictures of an ear, taken at different angles, distances, times-of-day, etc, into a single image \u2014 after removing all the extraneous information and normalizing the distinctive objects captured therein \u2014 and then further amalgamating this information into the larger whole. Because our Eigen Variant is multidimensional, it is possible to incorporate virtually any type of information (E.g. skeletal information from X-Ray\/MRI, etc; spectral information from ultraviolet\/infrared information, and so on). All such data can be normalized and reduced to an Eigen Matrix, which is then ingested into the larger Eigen Variant.
\nPersistence and Retrieval
\nOnce the data has been analyzed and ingested into a relevant variant, it becomes persistent and retrievable via query. Using an inverted index database like Solr, a portable, clustered neural network could be established that could query and retrieve from a cross-referenced dataset of billions of documents in a matter of milliseconds, incorporating complex\/compound query elements to retrieve highly-relevant results. This approach has the advantage of requiring less computational power than massive proprietary data centers.
\nProof of Concept
\nSolr and Machine Vision: Solr Revolution 2017
\nhttps:\/\/lucenesolrrevolution2017.sched.com\/event\/BAwM\/solr-and-machine-vision?iframe=yes&w=100%&sidebar=yes&bg=no#
\nII. Case Study: Machine Learning with \u201cLabeled Faces in the Wild (LFW)\u201d
\nSummary
\nThe advantage of the Eigen Variant is that it is founded in well-understood concepts, including modern big data engine scalability and object-oriented software utilization. The combination of these technologies creates a powerful tool that requires minimal computational power. The resultant system is powerful, compact, portable, extensible and capable of artificial intelligence in the form of real time machine learning. The paradigm differs from contemporary models in that data aggregation is requisite, rather than anathema; and acquisition from a wide variety of sources increases the distinctiveness of the genotype, rather than detracting from it. This allows for highly relevant matching from a broad swath of angles, distances, and other conditions that are not possible with the conventional approach.
\nReferences:
\nApache Solr
\nhttp:\/\/lucene.apache.org\/solr\/
\nThe Genotype Vs. Phenotype
\nhttps:\/\/pged.org\/what-is-genotype-what-is-phenotype\/
\nThree-dimensional Eigenmatrix Example
\nhttps:\/\/en.wikipedia.org\/wiki\/Eigenvalues_and_eigenvectors#Three-dimensional_matrix_example
\nEigenface definition
\nhttps:\/\/en.wikipedia.org\/wiki\/Eigenface
\nAn Introduction to Facial Recognition
\nhttp:\/\/www.cedar.buffalo.edu\/~govind\/CSE717\/papers\/IntroductionToBiometricRecognition.pdf
\nFacial Recognition Patent Abstract
\nhttps:\/\/www.google.com\/patents\/US5787186
\nIllumination invariant face recognition using convolutional neural networks
\nhttp:\/\/ieeexplore.ieee.org\/abstract\/document\/7091490\/
\nPushing the Frontiers of Unconstrained Face Detection and Recognition: IARPA
\nhttps:\/\/www.cv-foundation.org\/openaccess\/content_cvpr_2015\/papers\/Klare_Pushing_the_Frontiers_2015_CVPR_paper.pdf
\nFace Recognition on Consumer Devices: Reflections on Replay Attacks
\nhttp:\/\/ieeexplore.ieee.org\/abstract\/document\/7029643\/
\nCranial Topography
\nhttp:\/\/www.mccc.edu\/~kerrs\/documents\/Morphsinus_fall14.pdf
\nNIR-VIS Heterogeneous Face Recognition via Cross-Spectral Joint Dictionary Learning and Reconstruction
\nhttps:\/\/www.cv-foundation.org\/openaccess\/content_cvpr_workshops_2015\/W05\/papers\/Juefei-Xu_NIR-VIS_Heterogeneous_Face_2015_CVPR_paper.pdf
\nShared representation learning for heterogenous face recognition
\nhttp:\/\/ieeexplore.ieee.org\/abstract\/document\/7163093\/
\nCustomized Orthogonal Locality Preserving Projections With Soft-Margin Maximization for Face Recognition
\nhttp:\/\/ieeexplore.ieee.org\/abstract\/document\/7078936\/
\nSuperimposition and reconstruction in forensic facial identification: a survey
\nhttps:\/\/ac.els-cdn.com\/0379073895017704\/1-s2.0-0379073895017704-main.pdf?_tid=ee862b54-ae96-11e7-a1e1-00000aab0f01&acdnat=1507735072_9e1b5e4095e3a9a7ca07ff9ad55c8a48
\nWho is this person? A comparison study of current three-dimensional facial approximation methods
\nhttp:\/\/www.sciencedirect.com\/science\/article\/pii\/S0379073813001849
\nThree-dimensional Cranio-Facial Reconstruction in Forensic Identification: Latest Progress and New Tendencies in the 21st Century
\nhttps:\/\/www.astm.org\/DIGITAL_LIBRARY\/JOURNALS\/FORENSIC\/PAGES\/JFS2004117.htm
\nFacial reconstruction: utilization of computerized tomography to measure facial tissue thickness in a mixed racial population
\nhttps:\/\/ac.els-cdn.com\/0379073896020105\/1-s2.0-0379073896020105-main.pdf?_tid=b4745f52-ae97-11e7-89b7-00000aacb361&acdnat=1507735405_4320d655d3608a4629d831b79eefadd7
\nForensic Three-Dimensional Facial Reconstruction: Historical Review and Contemporary Developments
\nhttps:\/\/www.astm.org\/DIGITAL_LIBRARY\/JOURNALS\/FORENSIC\/PAGES\/JFS14176J.htm
\nA Fully Three-Dimensional Method for Facial Reconstruction Based on Deformable Models
\nhttps:\/\/www.astm.org\/DIGITAL_LIBRARY\/JOURNALS\/FORENSIC\/PAGES\/JFS14175J.htm
\nThe geometrical precision of virtual bone models derived from clinical computed tomography data for forensic anthropology
\nhttps:\/\/link.springer.com\/article\/10.1007\/s00414-017-1548-z
\nCephalic index
\nhttps:\/\/en.wikipedia.org\/wiki\/Cephalic_index
\nCranial morphology and facial type: Is it appropriate to describe the face using skull terminology?
\nhttp:\/\/www.sciencedirect.com\/science\/article\/pii\/S2212443814000034
\nCranial shape and size variation in human evolution: structural and functional perspective
\nhttps:\/\/link.springer.com\/article\/10.1007\/s00381-007-0434-2
\n\u201cFunctional craniology
\nThe evolution of the human cranium is consequently considered in terms of functional and structural relationships between its components, largely influenced by the allometric variations associated with the increase in the relative cranial capacity. In the human genus, the changes in the face, base, and neurocranium are characterised by a mosaic variation, in which adaptations, secondary consequences, and stochastic factors concur to generate a set of anatomical possibilities and constraints.
\n\u201d
\nImage Stitching
\nhttps:\/\/en.wikipedia.org\/wiki\/Image_stitching
\nAnaglyph 3D
\nhttps:\/\/en.wikipedia.org\/wiki\/Anaglyph_3D
\nStereoscopy
\nhttps:\/\/en.wikipedia.org\/wiki\/Stereoscopy
\nEuclidean Vector
\nhttps:\/\/en.wikipedia.org\/wiki\/Euclidean_vector
\nDarboux Vector
\nhttps:\/\/en.wikipedia.org\/wiki\/Darboux_vector
\nVector_(mathematics_and_physics)
\nhttps:\/\/en.wikipedia.org\/wiki\/Vector_(mathematics_and_physics)
\nLabled Faces in the Wild
\nhttp:\/\/vis-www.cs.umass.edu\/lfw\/
\nAn object\u2010oriented approach for analysing and characterizing urban landscape at the parcel level
\nhttp:\/\/www.tandfonline.com\/doi\/abs\/10.1080\/01431160701469065
\nMachine Learning
\nhttps:\/\/en.wikipedia.org\/wiki\/Machine_learning
\nVector Space
\nhttps:\/\/en.wikipedia.org\/wiki\/Vector_space
\nMathematical Morphology
\nhttps:\/\/en.wikipedia.org\/wiki\/Mathematical_morphology
\nThe Fibonacci Sequence
\nhttps:\/\/www.livescience.com\/37470-fibonacci-sequence.html
\nThe Mandelbrot Set
\nhttp:\/\/mathworld.wolfram.com\/MandelbrotSet.html
\nThe Golden Ratio
\nhttps:\/\/en.wikipedia.org\/wiki\/Golden_ratio
\nMathematical Interpretation between Genotype and Phenotype Spaces and Induced Geometric Crossovers
\nhttps:\/\/arxiv.org\/abs\/0907.3202<\/p>\n<\/body>","protected":false},"excerpt":{"rendered":"
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