Image FormationAcknowledgementsLecture OutlineSlide 4Abstract ImageBasic RadiometryLight and MatterLecture AssumptionsSlide 9StepsFactors in Image FormationSlide 12GeometryBasic OpticsPinhole Camera ModelPinhole camera imageEquivalent GeometryThin Lens ModelCoordinate SystemPerspective ProjectionX-Z ProjectionY-Z ProjectionPerspective EquationsReverse ProjectionStereo GeometrySlide 26RadiometryRadiometry & GeometryRadiometry Final ResultCos a Light FalloffSlide 31PhotometryB&W Video SystemColor Video SystemColor RepresentationDigital Color CamerasHuman Eyes and Color PerceptionSlide 38DigitizationDigitization: Spatial ResolutionSpatial ResolutionEffect of Sampling Interval - 1Effect of Sampling Interval - 2The Missing Fence FoundThe Sampling TheoremSamplingSlide 47Mixed Pixel ProblemSignal QuantizationQuantizationChoice of KSlide 52Choice of Function: UniformLogarithmic QuantizationSlide 55Tesselation PatternsSlide 57Digital GeometryConnected ComponentsFinding Connected ComponentsAlgorithmExampleNeighborAlternate Neighborhood DefinitionsPossible SolutionsDigital DistancesNext3D Computer Visionand Video ComputingImage FormationImage FormationTopic 1 of Part IImage FormationCSc I6716Spring 2008Zhigang Zhu, City College of New York [email protected] Computer Visionand Video ComputingAcknowledgementsAcknowledgementsThe slides in this lecture were kindly provided by Professor Allen HansonUniversity of Massachusetts at Amherst3D Computer Visionand Video ComputingLecture OutlineLecture OutlineImage Formation Basic StepsGeometryPinhole camera model & Thin lens modelPerspective projection & Fundamental equationRadiometryPhotometryColor, human vision, & digital imagingDigitalizationSampling, quantization & tessellationsMore on Digital ImagesNeighbors, connectedness & distances3D Computer Visionand Video ComputingLecture OutlineLecture OutlineImage Formation Basic StepsGeometryPinhole camera model & Thin lens modelPerspective projection & Fundamental equationRadiometryPhotometryColor, human vision, & digital imagingDigitalizationSampling, quantization & tessellationsMore on Digital ImagesNeighbors, connectedness & distances3D Computer Visionand Video ComputingAbstract ImageAbstract ImageAn image can be represented by an image function whose general form is f(x,y).f(x,y) is a vector-valued function whose arguments represent a pixel location.The value of f(x,y) can have different interpretations in different kinds of images.ExamplesIntensity Image - f(x,y) = intensity of the sceneRange Image - f(x,y) = depth of the scene from imaging systemColor Image - f(x,y) = {fr(x,y), fg(x,y), fb(x,y)}Video - f(x,y,t) = temporal image sequence3D Computer Visionand Video ComputingBasic RadiometryBasic RadiometryRadiometry is the part of image formation concerned with the relation among the amounts of light energy emitted from light sources, reflected from surfaces, and registered by sensors.SurfaceOpticsCCD ArrayPLight SourceL(P,d)inpe3D Computer Visionand Video ComputingLight and MatterLight and MatterThe interaction between light and matter can take many forms:ReflectionRefractionDiffractionAbsorptionScattering3D Computer Visionand Video ComputingLecture AssumptionsLecture AssumptionsTypical imaging scenario:visible lightideal lensesstandard sensor (e.g. TV camera)opaque objectsGoalTo create 'digital' images which can be processed to recover some of the characteristics of the 3D world which was imaged.3D Computer Visionand Video ComputingImage FormationImage FormationLight (Energy) SourceSurfacePinhole LensImaging PlaneWorld Optics Sensor SignalB&W FilmColor FilmTV CameraSilver DensitySilver densityin three colorlayersElectrical3D Computer Visionand Video ComputingStepsSteps World Optics Sensor Signal Digitizer Digital RepresentationWorld realityOptics focus {light} from world on sensorSensor converts {light} to {electrical energy}Signal representation of incident light as continuous electrical energyDigitizer converts continuous signal to discrete signalDigital Rep. final representation of reality in computer memory3D Computer Visionand Video ComputingFactors in Image FormationFactors in Image FormationGeometryconcerned with the relationship between points in the three-dimensional world and their imagesRadiometryconcerned with the relationship between the amount of light radiating from a surface and the amount incident at its imagePhotometryconcerned with ways of measuring the intensity of lightDigitizationconcerned with ways of converting continuous signals (in both space and time) to digital approximations3D Computer Visionand Video ComputingLecture OutlineLecture OutlineImage Formation Basic StepsGeometryPinhole camera model & Thin lens modelPerspective projection & Fundamental equationRadiometryPhotometryColor, human vision, & digital imagingDigitalizationSampling, quantization & tessellationsMore on Digital ImagesNeighbors, connectedness & distances3D Computer Visionand Video ComputingGeometryGeometryGeometry describes the projection of:two-dimensional (2D) image plane.three-dimensional (3D) world Typical AssumptionsLight travels in a straight lineOptical Axis: the axis perpendicular to the image plane and passing through the pinhole (also called the central projection ray)Each point in the image corresponds to a particular direction defined by a ray from that point through the pinhole.Various kinds of projections:- perspective - oblique- orthographic - isometric- spherical3D Computer Visionand Video ComputingBasic OpticsBasic OpticsTwo models are commonly used:Pin-hole cameraOptical system composed of lensesPin-hole is the basis for most graphics and visionDerived from physical construction of early camerasMathematics is very straightforwardThin lens model is first of the lens modelsMathematical model for a physical lensLens gathers light over area and focuses on image plane.3D Computer Visionand Video ComputingPinhole Camera ModelPinhole Camera ModelWorld projected to 2D ImageImage invertedSize reducedImage is dimNo direct depth informationf called the focal length of the lensKnown as perspective projectionPinhole lensOptical AxisfImage Plane3D Computer Visionand Video ComputingPinhole camera imagePinhole