Fast Oriented Line Integral Convolution for Vector Field Visualization via the Internet
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regular convolution学术语言-回复什么是常规卷积(regular convolution)?常规卷积是一种在信号处理和图像处理领域广泛使用的数学运算。
它被用于处理和分析数据,尤其是在卷积神经网络(CNN)中,起到了至关重要的作用。
常规卷积基于滤波器(也称为卷积核)与输入信号之间的运算,用来提取输入信号的特征。
常规卷积的过程可以概括为以下几个步骤:1. 输入信号(也称为输入图像):常规卷积的第一个步骤是选择一个输入信号或图像。
输入信号可以是一个二维矩阵(即灰度图像)或一个三维矩阵(即彩色图像)。
例如,在处理图像时,我们可以选择一张大小为28x28像素的灰度图像作为输入信号。
2. 卷积核(滤波器)的选择:常规卷积的下一步是选择一个卷积核(也称为滤波器)。
卷积核是一个小的二维矩阵,其大小通常小于输入信号的大小。
卷积核包含了一组权重,这些权重将作为卷积操作的参数。
例如,我们可以选择一个3x3的卷积核来对输入信号进行卷积操作。
3. 卷积操作:在常规卷积中,卷积核与输入信号进行逐元素乘法,然后将乘积相加。
具体而言,卷积核的每个元素与输入信号的对应元素相乘,然后将所有乘积相加得到一个新的值。
这个值将作为输出信号的一个元素。
通过将卷积核在输入信号上按步长(stride)滑动,将整个输入信号进行遍历,就可以得到输出信号的所有元素。
卷积操作的结果可以看作是将卷积核的某种局部特征应用于输入信号的结果。
4. 边界处理:在进行卷积操作时,可能会遇到输入信号的边界问题。
边界处理可以采用多种方法,例如,可以使用填充(padding)来扩展输入信号的边界,或者可以使用截断(truncate)来处理边界问题。
5. 输出信号:最终,卷积操作的结果将得到一个输出信号。
输出信号的大小通常会因为卷积核的大小、步长和边界处理方式而不同。
输出信号可能会被用作下一层的输入信号,或者作为最终的输出结果。
总结起来,常规卷积是通过将选择的卷积核在输入信号上滑动进行逐元素乘法和求和操作来提取输入信号的特征。
惯导拟合路径惯导(Inertial navigation)是一种常见的导航技术,通过专用设备和传感器测量车辆、飞行器、船舶等对象的加速度和角速度,从而实现对其运动状态的实时监测和估计。
惯导有着广泛的应用,比如飞行器导航、船舶导航、自动驾驶等领域。
在这篇文章中,我们将探讨惯导在路径规划与导航中的应用,重点讨论惯导拟合路径的原理和技术。
首先,让我们来了解一下惯导拟合路径的基本原理。
惯性导航系统通过测量车辆的加速度和角速度,在给定的初始条件下,可以通过积分计算车辆相对于初始位置的位移和旋转角度。
基于这些测量值和计算结果,我们可以构建车辆或飞行器的运动轨迹,并且通过惯导拟合路径的技术来实现相对准确的路径规划和导航。
具体来说,惯导拟合路径的过程可以分为几个步骤。
首先,需要获取车辆或飞行器的初始位置和姿态信息,这可以通过GPS、惯性测量单元(IMU)或其他传感器来实现。
然后,我们需要对车辆的运动状态进行估计,这可以通过对加速度、角速度的测量数据进行数学模型的建立和参数估计来实现。
接下来,我们可以通过对测量数据和模型之间的比较,实现对车辆的位置和姿态进行估计和预测。
最后,通过对估计结果进行路径规划和导航引导,实现对车辆轨迹的有效控制和调整。
惯导拟合路径的优势在于其具有较高的实时性和精度。
与传统的导航方法相比,惯导拟合路径可以实时监测车辆的位置和姿态,在短时间内对运动状态进行估计和预测。
这使得惯导拟合路径在应对实时变化的环境和需求时具有明显的优势。
此外,惯导拟合路径还可以通过与其他导航系统(如GPS)的组合使用,进一步提高导航的准确性和稳定性。
当然,惯导拟合路径也存在一些挑战和限制。
首先,由于惯性传感器本身的误差、漂移等问题,惯导拟合路径存在着累积误差的问题。
这意味着随着时间的增加,惯导拟合路径的精度会逐渐下降。
其次,惯导拟合路径对初始条件具有较高的敏感性。
初始位置和姿态的不准确性会导致拟合路径的偏移和误差。
此外,由于惯导系统无法感知和纠正地球自转等因素的影响,惯导拟合路径在长时间和长距离的导航中可能出现明显的漂移。
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Combine flexibility in Remote I/O configurationwith the speed and determinism of EtherCAT.•The EtherCAT Coupler Unit is the link between the EtherCAT MachineControl network and the NX-series I/O Units. With I/O Units ranging frombasic I/O's to high-speed synchronous models, the NX-series is the perfectmatch for the Sysmac Machine Automation Controllers.Features•Up to 63 NX-IO Units can be connected to one EtherCAT Coupler Unit. Standard and high-performance units can be mixed.*1•High-speed remote I/O control is possible at the fastest communication cycle of 125 μs.*2•Each Coupler plus its I/O form just a single EtherCAT node on the network.•I/O control and safety control can be integrated by connecting Units for safety.•The Coupler supports the EtherCAT Distributed Clock (DC) and propagates this to synchronous I/O units.•The node address can be fixed by rotary switches, or set by software. Choose the method that best suits your way of engineering.•Slave configuration by Sysmac Studio can be done centrally via the controller, or on-the-spot using the Coupler's built-in USB port.*1Input per Coupler Unit: Maximum 1024 bytes, Output per Coupler Unit: Maximum 1024 bytes*2NX7-@@@@ and NX-ECC203 combinedSysmac is a trademark or registered trademark of OMRON Corporation in Japan and other countries for OMRON factory automation products. EtherCAT is a registered trademark of Beckhoff Automation GmbH for their patented technology. EtherNet/IP TM is the trademarks of ODVA. Other company names and product names in this document are the trademarks or registered trademarks of their respective companies.System ConfigurationSystem Configuration of Slave TerminalsThe following figure shows an example of the system configuration when an EtherCAT Coupler Unit is used as a Communications Coupler Unit.*1.The connection method for the Sysmac Studio depends on the model of the CPU Unit or Industrial PC.*2.An EtherCAT Slave Terminal cannot be connected to any of the OMRON CJ1W-NC @81/@82 Position Control Units even though they canoperate as EtherCAT masters.*3.For whether NX Units can be connected to the CPU Unit or Communications Coupler Unit to be used, refer to the user's manual for the CPUUnit or Communications Coupler Unit to be used.EtherCAT master *2Sysmac Studio Support SoftwareOrdering InformationApplicable standardsRefer to the OMRON website () or ask your OMRON representative for the most recent applicable standards for each model.*1.This depends on the specifications of the EtherCAT master. For example, the values are as follows when the EtherCAT Coupler Unit isconnected to the built-in EtherCAT port on an NJ5-series CPU Unit: 500 μs, 1,000 μs, 2,000 μs, and 4,000 μs. Refer to the NJ/NX-series CPU Unit Built-in EtherCAT Port User’s Manual (Cat. No. W505) for the specifications of the built-in EtherCAT ports on NJ/NX-series CPU Units.*2.This depends on the Unit configuration.Recommended EtherCAT Communications CableUse a straight STP (shielded twisted-pair) cable of category 5 or higher with double shielding (braiding and aluminum foil tape) for EtherCAT.Cable with Connectors*1.Standard type cables length 0.2, 0.3, 0.5, 1, 1.5, 2, 3, 5, 7.5, 10, 15 and 20 m are available.Rugged type cables length 0.3, 0.5, 1, 2, 3, 5, 10 and 15 m are available.For details, refer to Cat.No.G019.*2.The lineup features Low Smoke Zero Halogen cables for in-cabinet use and PUR cables for out-of-cabinet use. Although the LSZH cable issingle shielded, its communications and noise characteristics meet the standards.*3.Cables colors are available in blue, yellow, or Green.*4.For details, contact your OMRON representative.Product nameCommunications cycle inDC Mode *1 *2Current consumptionMaximum I/O power supply current Model EtherCAT Coupler Unit250 to 4,000 μs 1.45 W or lower4 ANX-ECC20110 ANX-ECC202125 to 10,000 μs 1.25 W or lower NX-ECC203ItemAppearanceRecommended manufacturerCable length [m] *1ModelCable with Connectors on Both Ends (RJ45/RJ45)Standard RJ45 plugs type *1Wire gauge and number of pairs: AWG26, 4-pair cable Cable sheath material: LSZH *2Cable color: Yellow *3OMRON0.3XS6W-6LSZH8SS30CM-Y 0.5XS6W-6LSZH8SS50CM-Y 1XS6W-6LSZH8SS100CM-Y 2XS6W-6LSZH8SS200CM-Y 3XS6W-6LSZH8SS300CM-Y 5XS6W-6LSZH8SS500CM-Y Cable with Connectors on Both Ends (RJ45/RJ45)Rugged RJ45 plugs type *1Wire gauge and number of pairs: AWG22, 2-pair cable Cable color: Light blueOMRON0.3XS5W-T421-AMD-K 0.5XS5W-T421-BMD-K 1XS5W-T421-CMD-K 2XS5W-T421-DMD-K 5XS5W-T421-GMD-K 10XS5W-T421-JMD-K Cable with Connectors on Both Ends (M12 Straight/M12 Straight)Shield Strengthening Connector cable *4M12/Smartclick ConnectorsWire Gauge and Number of Pairs: AWG22, 2-pair Cable Cable color: BlackOMRON0.5XS5W-T421-BM2-SS 1XS5W-T421-CM2-SS 2XS5W-T421-DM2-SS 3XS5W-T421-EM2-SS 5XS5W-T421-GM2-SS 10XS5W-T421-JM2-SS Cable with Connectors on Both Ends (M12 Straight/RJ45)Shield Strengthening Connector cable *4M12/Smartclick Connectors Rugged RJ45 plugs typeWire Gauge and Number of Pairs: AWG22, 2-pair Cable Cable color: BlackOMRON0.5XS5W-T421-BMC-SS 1XS5W-T421-CMC-SS 2XS5W-T421-DMC-SS 3XS5W-T421-EMC-SS 5XS5W-T421-GMC-SS 10XS5W-T421-JMC-SSCables / ConnectorsWire Gauge and Number of Pairs: AWG24, 4-pair Cable*We recommend you to use above cable and connector together.Wire Gauge and Number of Pairs: AWG22, 2-pair Cable*We recommend you to use above cable and connector together.Note:Connect both ends of cable shielded wires to the connector hoods.Optional ProductsAccessoriesEnd Cover (NX-END01)An End Cover is connected to the end of the EtherCAT Slave Terminal.One End Cover is provided together with the EtherCAT Coupler Unit.ItemAppearanceRecommended manufacturerModelCables-Hitachi Metals, STAR-C5E SAB 0.5 × 4P CP *-Kuramo Electric Co.KETH-SB *-SWCC Showa Cable Systems Co.FAE-5004 *RJ45 Connectors-Panduit CorporationMPS588-C *ItemAppearanceRecommended manufacturer ModelCables-Kuramo Electric Co.KETH-PSB-OMR *-JMACS Japan Co., Ltd.PNET/B *RJ45 Assembly ConnectorOMRONXS6G-T421-1 *Product nameSpecificationModelUnit/Terminal Block Coding PinsPins for 10 Units(30 terminal block pins and 30 Unit pins)NX-AUX02Product NameSpecificationModelNo. of terminals Ground terminal mark Terminal current capacity Terminal Block8Present10 ANX-TBC082General Specification*Refer to the OMRON website (/) or consult your OMRON representative for the most recent applicable standards for each model.SpecificationsEtherCAT Coupler Unit NX-ECC201/NX-ECC202/NX-ECC203*1.Refer to the NX-series Safety Control Units User’s Manual (Cat. No. Z930) for the number of Safety Control Units that can be connected.*2.This function was added or improved for a version upgrade. Refer to the NX-series EtherCAT Coupler Unit User’s Manual (Cat. No. W519) forinformation on version upgrades.*3.The range of node addresses that can be set depends on the model of the built-in EtherCAT port. For the node address ranges that can beset for a built-in EtherCAT port, refer to the user's manual for the built-in EtherCAT port on the connected CPU Unit or Industrial PC.*4.This depends on the specifications of the EtherCAT master. For example, the values are as follows when the EtherCAT Coupler Unit isconnected to the built-in EtherCAT port on an NJ5-series CPU Unit: 500 μs, 1,000 μs, 2,000 μs, and 4,000 μs. For the specifications of the built-in EtherCAT port, refer to the user's manual for the built-in EtherCAT port on the connected CPU Unit or the Industrial PC.*5.This depends on the Unit configuration.*6.There are restrictions in the communications cycles that you can set for some of the NX Units. If you use any of those NX Units, set acommunications cycle that will satisfy the specifications for the refresh cycles that can be executed by the NX Unit. Refer to the appendix of the NX-series Data Reference Manual (Cat. No. W525-E1-07 or later) to see if there are restrictions on any specific NX Units. For information on the communications cycles that you can set, refer to the user’s manuals for the NX Units.*7.Refer to the NX-series EtherCAT Coupler Unit User’s Manual (Cat. No. W519) for procedures for designing the Unit power supply system andI/O power supply system.*e a voltage that is appropriate for the I/O circuits of the NX Units and the connected external devices.ItemSpecificationEnclosureMounted in a panel Grounding methodGround to 100 Ω or less Operating environmentAmbient operating temperature 0 to 55°CAmbient operating humidity 10% to 95% (with no condensation or icing)AtmosphereMust be free from corrosive gases.Ambient storage temperature −25 to 70°C (with no condensation or icing)Altitude2,000 m max.Pollution degree Pollution degree 2 or less: Meets IEC 61010-2-201.Noise immunity Conforms to IEC61000-4-4. 2 kV (power supply line)Overvoltage category Category II: Meets IEC 61010-2-201.EMC immunity level Zone BVibration resistance Conforms to IEC 60068-2-6.5 to 8.4 Hz with 3.5-mm amplitude, 8.4 to 150 Hz, acceleration of 9.8 m/s 2, 100 min each in X, Y, and Z directions (10 sweeps of 10 min each = 100 min total)Shock resistanceConforms to IEC 60068-2-27. 147 m/s 2, 3 times each in X, Y, and Z directions Applicable standards *cULus: Listed (UL 508 or UL61010-2-201), ANSI/ISA 12.12.01,EU: EN 61131-2, C-Tick or RCM, KC Registration, NK, and LRItemSpecificationNX-ECC201NX-ECC202NX-ECC203Number of connectable NX Units 63 Units max.*1Send/receive PDO data sizes Input: 1,024 bytes max. (including input data, status, and unused areas)Output: 1,024 bytes max. (including output data and unused areas)Mailbox data size Input: 256 bytes Output: 256 bytesMailboxEmergency messages and SDO requestsRefreshing methods *2•Free-Run refreshing •Synchronous I/O refreshing •Time stamp refreshing•Free-Run refreshing•Synchronous I/O refreshing •Time stamp refreshing •Task period prioritized refreshingNode address setting rangeWhen the settable node address range for the built-in EtherCAT port is 1 to 512*3•Set on switches: 1 to 199•Set with the Sysmac Studio: 1 to 512When the settable node address range for the built-in EtherCAT port is 1 to 192*3•Set on switches: 1 to 192•Set with the Sysmac Studio: 1 to 192I/O jitter performanceInputs: 1 μs max.Outputs: 1 μs munications cycle in DC Mode250 to 4,000 μs *4 *5125 to 10,000 μs *3 *4 *6Unit power supply *7Power supply voltage24 VDC (20.4 to 28.8 VDC)NX Unit power supply capacity10 W max.Refer to Installation orientation and restrictions for details.NX Unit power supply efficiency 70%Isolation methodNo isolation between NX Unit power supply and Unit power supply terminals Current capacity of power supply terminals4 A max.I/O powersupply *7Power supply voltage5 to 24 VDC (4.5 to 28.8 VDC) *8Maximum I/O power supply current4 A 10 A Current capacity of power supply terminals4 A max.10 A max.NX Unit power consumption1.45 W max. 1.25 W max.Current consumption from I/O power supply 10 mA max. (for 24 VDC)Dielectric strength 510 VAC for 1 min, leakage current: 5 mA max. (between isolated circuits)Insulation resistance100 VDC, 20 M Ω min. (between isolated circuits)EtherCAT Communications Specifications*The EtherCAT Coupler Unit conforms to EtherCAT standards. Check the specifications of the EtherCAT master being connected for the configurable topology. However, note that only NX-ECC203 EtherCAT Coupler Units (Ver. 1.5 or later) is compatible with a ring topology.Version InformationNote:Some Units do not have all of the versions given in the above table. If a Unit does not have the specified version, support is provided by theoldest available version after the specified version. Refer to the user's manuals for the specific Units for the relation between models and versions.*1For the NX-ECC202, there is no unit version of 1.1 or earlier.*2For the NX-ECC203, there is no unit version of 1.2 or earlier.ItemSpecificationCommunications standard IEC 61158 Type 12Physical layer 100BASE-TX (IEEE 802.3)Modulation Baseband Baud rate 100 MbpsTopologyDepends on the specifications of the EtherCAT master. *Transmission mediaCategory 5 or higher twisted-pair cable (Recommended cable: double-shielded cable with aluminum tape and braiding)Transmission distance Distance between nodes: 100 m or lessModel number of EtherCAT Coupler UnitUnit version Corresponding versionsUsing an NX-series CPU Unit Using an NJ-series CPU Unit Using an NY-series Industrial PC Unit version of CPU UnitSysmac StudioversionUnit version of CPU Unit Sysmac Studioversion Unit version of Industrial PCSysmac StudioversionNX-ECC201Ver. 1.2Ver. 1.10Ver. 1.13Ver. 1.07Ver. 1.08Ver. 1.12Ver. 1.17Ver. 1.1Ver. 1.06Ver. 1.07Ver. 1.0Ver. 1.05Ver. 1.06NX-ECC202Ver. 1.2*1Ver. 1.07Ver. 1.08NX-ECC203Ver. 1.7Ver. 1.41Ver. 1.41Ver. 1.41Ver. 1.6Ver. 1.25Ver. 1.25Ver. 1.25Ver. 1.5Ver. 1.19Ver. 1.19Ver. 1.19Ver. 1.4Ver. 1.16Ver. 1.16Ver. 1.17Ver. 1.3*2Ver. 1.13Ver. 1.13External InterfaceEtherCAT Coupler Unit NX-ECC20@Terminal BlockApplicable Terminal Blocks for Each Unit ModelSymbol NameFunction(A)NX bus connectorThis connector is used to connect each Unit.(B)IndicatorsThe indicators show the current operating status of the Unit.(C)Communications connectors These connectors are connected to the communications cables of the EtherCAT network.There are two connectors, one for the input port and one for the output port.(D)Peripheral USB port This port is used to connect to the Sysmac Studio Support Software.(E)Terminal block The terminal block is used to connect external devices.The number of terminals depends on the type of Unit.(F)Rotary switches These rotary switches are used to set the 1s digit and 10s digit of the node address of the EtherCAT Coupler Unit as an EtherCAT slave. The address is set in decimal.(G)DIP switchThe DIP switch is used to set the 100s digit of the node address of the EtherCAT Coupler Unit as an EtherCAT slave.Symbol NameFunction(A)Terminal number indications The terminal numbers (A1 to A8 and B1 to B8) are displayed.The terminal number indicators are the same regardless of the number of terminals on the terminal block, as shown above.(B)Release holes Insert a flat-blade screwdriver into these holes to connect and remove the wires.(C)Terminal holes The wires are inserted into these holes.(D)Ground terminal markThis mark indicates the ground terminals. Only the NX-TBC082 has this mark.Unit modelCurrent capacity ofUnit's power supply terminals Terminal BlocksUnit power supplyI/O power supplyModelNo. of terminalsGround terminalmark Terminal currentcapacity NX-ECC201 4 A NX-TBC0828Present 10 A NX-ECC202 or NX-ECC2034 A10 ANX-TBC0828Present10 A(B)(D)(E)Eight-terminal Block(A)NX-TBC082Applicable WiresUsing FerrulesIf you use ferrules, attach the twisted wires to them.Observe the application instructions for your ferrules for the wire stripping length when attaching ferrules.Always use plated one-pin ferrules. Do not use unplated ferrules or two-pin ferrules.The applicable ferrules, wires, and crimping tool are given in the following table.*1.Some AWG 14 wires exceed 2.0 mm 2 and cannot be used in the screwless clamping terminal block.When you use any ferrules other than those in the above table, crimp them to the twisted wires so that the following processed dimensions are achieved.Using Twisted Wires/Solid WiresIf you use the twisted wires or the solid wires, use the following table to determine the correct wire specifications.*1Secure wires to the screwless clamping terminal block. Refer to the Securing Wires in the USER'S MANUAL for how to secure wires.*2With the NX-TB @@@1 Terminal Block, use twisted wires to connect the ground terminal. Do not use a solid wire.<Additional Information> If more than 2 A will flow on the wires, use plated wires or use ferrules.Terminal typesManufacturerFerrule model Applicable wire (mm 2 (AWG))Crimping toolTerminals other than ground terminalsPhoenix Contact AI0,34-80.34 (#22)Phoenix Contact (The figure in parentheses is the applicable wire size.)CRIMPFOX 6 (0.25 to 6 mm 2, AWG 24 to 10)AI0,5-80.5 (#20)AI0,5-10AI0,75-80.75 (#18)AI0,75-10AI1,0-8 1.0 (#18)AI1,0-10AI1,5-8 1.5 (#16)AI1,5-10Ground terminalsAI2,5-102.0 *1Terminals other than ground terminalsWeidmuller H0.14/120.14 (#26)Weidmueller (The figure in parentheses is the applicable wire size.)PZ6 Roto (0.14 to 6 mm 2, AWG 26 to 10)H0.25/120.25 (#24)H0.34/120.34 (#22)H0.5/140.5 (#20)H0.5/16H0.75/140.75 (#18)H0.75/16H1.0/14 1.0 (#18)H1.0/16H1.5/14 1.5 (#16)H1.5/16TerminalsWire typeWire sizeConductor length(stripping length)Twisted wires Solid wire Classification Current capacity Plated Unplated Plated UnplatedAll terminals except ground terminals2 A max.Possible Possible Possible Possible0.08 to 1.5 mm 2AWG28 to 168 to 10 mmGreater than2 A and 4 A or less Not Possible Possible*1NotPossible Greater than 4 A Possible *1NotPossibleGround terminals ---Possible PossiblePossible *2Possible*22.0 mm 29 to 10 mm1.6 mm max.2.0 mm max.(Ground terminals)(Ground terminals)Conductor length (stripping length)Dimensions(Unit: mm)EtherCAT Coupler Unit● EtherCAT Coupler Unit Only*The dimension is 1.35 mm for Units with lot numbers through December 2014.● With Cables Connected*1.*2.•• 1.5NX-ECC 11End Cover*This is the shape for Units with lot numbers through December 2014.Related Manuals Man. No Model Manual ApplicationDescription W519NX-ECC20@NX-series EtherCAT Coupler Unit User’s ManualLeaning how to use anNX-series EtherCATCoupler Unit andEther-CAT Slave Terminals The following items are described: the overall system and configuration methods of an EtherCAT Slave Terminal (which consists of an NX-series EtherCAT Coupler Unit and NX Units), and information on hardware, setup, and functions to setup, control, and monitor NX Units through EtherCAT.2020.6In the interest of product improvement, specifications are subject to change without notice. OMRON CorporationIndustrial Automation Company/(c)Copyright OMRON Corporation 2020 All Right Reserved.。
FeaturesBack to back gate-source Zener diodes Guaranteed R DS(ON) at 4.0V gate drive Low threshold Low on-resistanceIndependent N- and P-channelsElectrically isolated N- and P-channels Low input capacitance Fast switching speedsFree from secondary breakdowns Low input and output leakageApplicationsHigh voltage pulsers Amplifiers BuffersPiezoelectric transducer drivers General purpose line drivers Logic level interfaces►►►►►►►►►►►►►►►►General DescriptionThe Supertex TC6215 consists of high voltage, low threshold N-channel and P-channel MOSFETs in an 8-Lead SOIC (TG) package. Both MOSFETs have integrated back to back gate-source Zener diode clamps and guaranteed R DS(ON) ratings down to 4.0V gate drive allowing them to be driven directly with standard 5.0V CMOS logic.These low threshold enhancement-mode (normally-off) transistors utilize an advanced vertical DMOS structure and Supertex’s well-proven silicon-gate manufacturing process. This combination produces devices with the power handling capabilities of bipolar transistors and with the high input impedance and positive temperature coefficient inherent in MOS devices. Characteristic of all MOS structures, these devices are free from thermal runaway and thermally-induced secondary breakdown.Supertex’s vertical DMOS FETs are ideally suitedto a wide range of switching and amplifying applications where very low threshold voltage, high breakdown voltage, high input impedance, low input capacitance, and fast switching speeds are desired.N- and P-ChannelEnhancement-Mode Dual MOSFET-G indicates package is RoHS compliant (‘Green’)GP SP GN SNDP DP DN DNYY = Year Sealed WW = Week Sealed L = Lot Number= “Green” Packaging 8-Lead SOIC (TG)(top view)Absolute Maximum Ratings are those values beyond which damage to the device may occur. Functional operation under these conditions is not implied. Continuous operation of the device at the absolute rating level may affect device reliability. All voltages are referenced to device ground.* Distance of 1.6mm from case for 10 seconds.8-Lead SOIC (TG)Package may or may not include the following marks: Si orPin ConfigurationN-Channel Switching Waveforms and Test CircuitVOUTPUT 10V0V0VVDDInputOutputNotes:All DC parameters 100% tested at 25°C unless otherwise stated. (Pulsed test: 300µs pulse at 2% duty cycle.)All AC parameters sample tested.1.2.DD0V -10V0V V DDInputOutputNotes:All DC parameters 100% tested at 25°C unless otherwise stated. (Pulsed test: 300µs pulse at 2% duty cycle.)All AC parameters sample tested.1.2.Block DiagramSN GN SPGPDPDPDN DN 8-Lead SOIC(top view)P-Channel Output Characteristics-4.0-3.5-3.0-2.5-2.0-1.5-1.0-0.50.0-50-45-40-35-30-25-20-15-10-5V DS (volts)I D (a m p e r e s )V =-10VV =-8V V =-7VV =-6VV =-5VV =-4VV =-3VV =-2VP-Channel Saturation Characteristics-2.2-2.0-1.8-1.6-1.4-1.2-1.0-0.8-0.6-0.4-0.20.0-10-9-8-7-6-5-4-3-2-1V DS (volts)I D (a m p e r e s )V GS =-10V V GS =-8V V GS =-6V V GS =-5VV GS =-4VV GS =-3VV GS =-2VN-Channel Output Characteristics0.00.51.01.52.02.53.03.54.04.505101520253035404550V DS (volts)I D (a m p e r e s )V GS =10V V GS =8V V GS =7VV GS =6VV GS =5VV GS =4VV GS =3VV GS =2VN-Channel Saturation Characteristics0.00.51.01.52.02.53.03.54.012345678910V DS (volts)I D (a m p e r e s )V GS =10V V GS =8V V GS =6VV GS =5VV GS =4VV GS =3VV GS =2VTypical Performance CurvesSupertex inc. does not recommend the use of its products in life support applications, and will not knowingly sell them for use in such applications unless it receives an adequate “product liability indemnification insurance agreement.” Supertex inc. does not assume responsibility for use of devices described, and limits its liability to the replacement of the devices determined defective due to workmanship. No responsibility is assumed for possible omissions and inaccuracies. Circuitry and specifications are subject to change without notice. For the latest product specifications refer to the Supertex inc. website: http//.©2008 All rights reserved. Unauthorized use or reproduction is prohibited.1235 Bordeaux Drive, Sunnyvale, CA 94089(The package drawing(s) in this data sheet may not reflect the most current specifications. For the latest package outline information go to /packaging.html .)8-Lead SOIC (Narrow Body) Package Outline (TG)4.90x3.90mm body, 1.75mm height (max), 1.27mm pitchSide ViewView A-AJEDEC Registration MS-012, Variation AA, Issue E, Sept. 2005.* This dimension is not specified in the original JEDEC drawing. The value listed is for reference only.Drawings are not to scale.Supertex Doc. #: DSPD-8SOLGTG, Version H101708.Note:This chamfer feature is optional. A Pin 1 identifier must be located in the index area indicated. The Pin 1 identifier can be: a molded mark/identifier;an embedded metal marker; or a printed indicator.1.。
现代电子技术Modern Electronics Technique2024年3月1日第47卷第5期Mar. 2024Vol. 47 No. 50 引 言汽车智能化是汽车产业一直在追寻的目标,而自动驾驶是汽车智能化不可或缺的一环。
要实现自动驾驶,必须为汽车加上一双眼睛和配套的处理系统,这套处理系统需要像人一样识别交通标志。
交通标志检测的实现方案主要有两大类:一类是基于计算机图形学的方案,比如依据颜色直方图、尺度不变特征变换特征、方向基于双向嵌套级联残差的交通标志检测方法江金懋, 钟国韵(东华理工大学 信息工程学院, 江西 南昌 330013)摘 要: 交通标志检测是自动驾驶领域的一个重要课题,其对于检测系统的实时性和精度都有非常高的要求。
目标检测领域中的YOLOv3算法是业界公认在精度和速度上都处于前列的一种算法。
文中以YOLOv3检测算法作为基础网络,提出一种双向嵌套级联残差单元(bid⁃NCR ),替换掉原网络中顺序堆叠的标准残差块。
双向嵌套级联残差单元的两条残差边采用相同的结构,都是一次卷积操作加上一次级联残差处理,两条边上级联的标准残差块的数量可以调节,从而形成不同的深度差。
然后将两条边的结果逐像素相加,最后再做一次卷积操作。
相较于标准残差块,双向嵌套级联残差单元拥有更强的特征提取能力和特征融合能力。
文中还提出跨区域压缩模块(CRC ),它是对2倍率下采样卷积操作的替代,旨在融合跨区域的通道数据,进一步加强主干网络输入特征图所包含的信息。
实验结果表明:提出的模型在CCTSDB 数据集上mAP (0.5)、mAP (0.5∶0.95)分别达到96.86%、68.66%,FPS 达到66.09帧。
相比于YOLOv3算法,3个指标分别提升1.23%、10.35%、127.90%。
关键词: 交通标志检测; 双向嵌套级联残差单元; 跨区域压缩模块; YOLOv3; 长沙理工大学中国交通标志检测数据集; 特征提取; 特征融合中图分类号: TN911.73⁃34; TP391 文献标识码: A 文章编号: 1004⁃373X (2024)05⁃0176⁃06Traffic sign detection method based on bi⁃directional nested cascading residualsJIANG Jinmao, ZHONG Guoyun(School of Information Engineering, East China University of Technology, Nanchang 330013, China)Abstract : Traffic sign detection is an important topic in the field of autonomous driving, which has very high requirements for real ⁃time performance and accuracy of the detection system. The YOLOv3 algorithm in the field of target detection is recognized as one of the leading algorithms in terms of accuracy and speed. In this paper, by taking YOLOv3 detection algorithm as the base network, a bi⁃directional nested cascaded residual (bid⁃NCR) unit is proposed to replace the standard residual blocks sequentially stacked in the original network. The two residual edges of the bid⁃NCR unit is of the same structure, both of which are one convolutional operation plus one cascaded residual processing, and the number of cascaded standard residual blocks on the two edges can be adjusted to form different depth differences. The results of the two edges are then added pixel by pixel, and another convolutional operation is performed, finally. In comparison with the standard residual blocks, the bid ⁃NCR unit has stronger feature extraction capability and feature fusion capability. The cross ⁃region compression (CRC) module, which is an alternative to the 2⁃fold downsampling convolutional operation, is proposed. It aims to fuse the channel data across regions to further enhance the information contained in the input feature map of the backbone network. The experimental results show thatthe model proposed in this paper achieves mAP(0.5) and mAP(0.5∶0.95) of 96.86% and 68.66%, respectively, and FPS of 66.09 frames on the dataset CCTSDB. In comparison with YOLOv3 algorithm, the three indicators are improved by 1.23%, 10.35% and 127.90%, respectively.Keywords : traffic sign detection; bid⁃NCR unit; CRC module; YOLOv3; CSUST Chinese traffic sign detection benchmark(CCTSDB); feature extraction; feature fusionDOI :10.16652/j.issn.1004⁃373x.2024.05.031引用格式:江金懋,钟国韵.基于双向嵌套级联残差的交通标志检测方法[J].现代电子技术,2024,47(5):176⁃181.收稿日期:2023⁃09⁃13 修回日期:2023⁃10⁃11176第5期梯度直方图特征[1]等,以上方法最大的问题在于这些人工提取的特征高度依赖于特定的场景,泛化能力很差;另一类是基于深度学习的方案,比如文献[2]提出的基于多尺度卷积神经网络的方案,设计了一个多尺度空洞卷积池化金字塔模块用于采样。
AS1 SERIESINSTRUCTION MANUALCONTROLSOUT LED on receiver (RX)The yellow LED ON indicates the presence of the object into controlled area.POWER ON LED on receiver (RX)The green LED ON indicates the optimal device functioning.The fast blinking of the green LED indicates a critical device alignment. Please refer to “DIAGNOSTICS” paragraph for other indications.POWER ON LED on emitter (TX)The green LED ON indicates the correct device functioning.Please refer to “DIAGNOSTICS” paragraph for other indications.INSTALLATION MODEGeneral information on device positioning• Align the two receiver (RX) and emitter (TX) units, verifying that their distance is inside the device operating distance, in a parallel manner placing the sensitive sides one in front of the other, with the connectors oriented on the same side. The critical alignmentof the unit will be signalled by the fast blinking of the green receiver LED.• Mount the two receiver and emitter units on rigid supports which are not subject to strong vibrations, using specific fixing brackets and /or the holes present on the device lids.Precautions to respect when choosing and installing the device• Choose the device according to the minimum object to detect and the maximum controlled area requested.• In agro-industrial applications, the compatibility of light grid housing material and any chemical agents used in the production process has to be verified with the assistance of the DATASENSOR technical sales support department.• The AREA scan TM light grids are NOT safety devices, and so MUST NOT be used in the safety control of the machines where installed. Moreover the following points have to be considered:- Avoid installation near very intense and / or blinking light sources, in particular near to the receiver unit.- The presence of strong electromagnetic disturbances can jeopardise the correct functioning of the device. This condition has to be carefully evaluated and checked with the DATASENSOR technical sales support department;- The presence of smoke, fog and suspended dust in the working environment can reduce the device’s operating distance.- Strong and frequent temperature variations, with very low peak temperatures, can generate a thin condensation layer on the optics surfaces, compromising the correct functioning of the device.- Reflecting surfaces near the luminous beam of the AREA scan TM device (above, under or lateral) can cause passive reflections able to compromise object detection inside the controlled area.- if different devices have to be installed in adjacent areas, the emitter of one unit must not interfere with the receiver of the other unit.General information relative to object detection and measurement• For a correct object detection and / or measurement, the object has to pass completely through the controlled area. Testing the correct detection before beginning the process is suggested. The resolution is non uniform inside the entire controlled area. For example the resolution in the AS1-HR model depends on the scanning program chosen.CONNECTIONSAS1-HR AS1-SR AS1-HR AS1-SR1 – brown: +24 VDC +24 VDC 1 – brown: +24 VDC+24 VDC2 – white:SEL_RXNot used2 – white:SEL_TX Not used3 – blue: 0 V0 V3 – blue: 0 V 0 V4 – black: Switching output Switching output 4 – black:SYNC SYNCRECEIVER (RX):M12 5-pole connector5 – grey: SYNC SYNCEMITTER (TX):M12 4-pole connectorShielded cables are not foreseen in the standard connection.Ground connection of the two units is not necessary. If desired, this connection can be obtained replacing the screw provided in the packaging with the one indicated in the drawing, which blocks the lid of the connector side of each unit.The respect of the connection shown in the drawing, is necessary if ground connection of the entire system is requested.FUNCTIONING AND PERFORMANCESThe beam interruption due to the passage of an object inside the controlled area causes the closing of the switching output and the variation of the device analogue output signal. Small objects can be detected (reaching dimensions of only 0.5 mm) and with a reduced surface area.In particular:The switching output is always activated when at least one beam is obscured. The status variation is signalled by the yellow receiver LED that turns on.The device presents inputs (both on TX and Rx units) that consent the selection of the resolution and response time.Low response times correspond to worser resolutions and viceversa.The device does not require calibration; periodical checks of the resolution and / or measurement are however suggested.The blinking of the green receiver LED (stability function ) signals the critical alignment of the units and / or the functioning outside or near the maximum operating distance. In optimal conditions the LED remains on continuously.The two units are synchronised via cable (SYNC wire).Precarious connections or induced disturbances on the synchronism line can cause device malfunctioning or a temporary blocking.DIAGNOSTICSRECEIVER UNIT:Segnal StatusCauseActionONSwitching output.Presence of the object in the controlled area.OUT LEDOFFSwitching output.Controlled area free of objects.ONOptimal functioning. Fast blinkingCritical alignment of the unit or/and functioning closed to maximum operating distance.Slow blinkingWrong connections and/or malfunctioning.- Verify the output connections and any short-circuits.- Switch OFF and switch ON the device.- If condition persists, contact Datasensor.POWER ONLEDOFFDevice is not powered.- Verify the connections.- If condition persists, contact Datasensor.EMITTER UNIT:POWER ONLEDPROG. N°SEL_RXSEL_TXRESOLUTIONRESPONSE TIME (msec )1 0V or FLOAT 0V or FLOAT LOW 2.752 0V or FLOAT +24Vdc M/L3 3 +24Vdc 0V or FLOAT M/H 7.754 +24Vdc +24Vdc HIGH 8Resolution figure : the box indicated the area with highest resolutionPROGRAM 1PROGRAM 2PROGRAM 3 - 4Ideal for fast detection on entire controlled area, with low resolution.Ideal for fast detection on entire contolled area, with constant resolution onlimited area.Ideal for detection with high resolution on entirecontrolled area.DIMENSIONS 800-262-4332-------------------------------------------------------------------------------------------------------------------------------------------- DECLARATION OF CONFORMITYIDEC and DATASENSOR jointly declare under their sole responsibility that these products conform to the 2004/108/CE, 2006/95/CE Directives, and successive amendments.-------------------------------------------------------------------------------------------------------------------------------------------- IDEC and DATASENSOR reserve the right to make modifications and improvements without prior notification.826003450 Rev.00。
Fast Oriented Line Integral Convolution for Vector Field Visualization viathe InternetRainer Wegenkittl and Eduard Gr¨o llerInstitute of Computer Graphics,Vienna University of TechnologyAbstractOriented Line Integral Convolution(OLIC)illustratesflowfields by convolving a sparse texture with an anisotropic convolution ker-nel.The kernel is aligned to the underlyingflow of the vectorfield. OLIC does not only show the direction of theflow but also its ori-entation.This paper presents Fast Rendering of Oriented Line In-tegral Convolution(FROLIC),which is approximately two orders of magnitude faster than OLIC.Costly convolution operations as done in OLIC are replaced in FROLIC by approximating a stream-let through a set of disks with varying intensity.The issue of over-lapping streamlets is discussed.Two efficient animation techniques for animating FROLIC images are described.FROLIC has been implemented as a Java applet.This allows researchers from various disciplines(typically with inhomogenous hardware environments) to conveniently explore and investigate analytically defined2D vec-torfields.CR Categories and Subject Descriptors:I.3.3[Computer Graph-ics]:Picture/Image Generation-Viewing Algorithms;I.3.6[Com-puter Graphics]:Methodology and Techniques-Interaction Tech-niques.1IntroductionTexture based techniques for the visualization offlowfields have been investigated in detail in recent years.Examples are,e.g.,[1], [9],[11]and[17].Van Wijk[17]explores stochastic texture synthesis to visualize scalar and vectorfields.A spot noise texture is constructed by adding randomly weighted and positioned spots.Spot noise is a versatile technique where characteristics of the spot are intuitively transfered to characteristics of the spot noise texture.Varying the shape and features of the spot locally enables a local control of the texture.Aflowfield can be visualized by taking elongated ellipses as spots.The larger axes of these spots are,for example,aligned with the locally varyingflow direction.The result is an anisotropic texture which depicts the entireflowfield and does not distract the viewer with larger geometric features.The anisotropy of the tex-ture manifests itself by a high correlation along the direction of theflow and a low correlation perpendicular to theflow.The spot noise technique can be thought of asfiltering an isotropic texture (e.g.,white noise)with a locally varyingfilter kernel.The shape and properties of thefilter kernel encode local features,e.g.,direc-tion and velocity magnitude,of the underlyingflowfield.This is typically achieved by aligning the convolution kernel to the tangen-tial direction of theflow.Four improvements and extensions to the spot noise technique are discussed in[4].Spots are bent to bet-ter approximate the underlyingflow.Filtering is done to eliminate undesired low frequency components from the spot noise texture.Institute of Computer Graphics,Vienna University of Technol-ogy,Karlsplatz13/186/2,A-1040Vienna,Austria email:wegenkittl, groeller@cg.tuwien.ac.at Graphics hardware methods for the acceleration of the spot noise texture generation are discussed.Furthermore the synthesis of spot noise on grids with irregular cell sizes is presented.Spot noise has also been utilized to visualize turbulentflow patterns[3].Cabral and Leedom[1]introduced the Line Integral Convolu-tion(LIC)method.In their approachfiltering of a white noise input texture takes place along(curved)streamline segments.LIC uses one-dimensionalfilter kernels which are determined by integrating the underlying vectorfield.The intensity at an arbitrary po-sition of the output image is calculated bywhere T is the input texture,is the parameterized streamline through)and k()describes the convolution kernel.specifies the length of the streamline segment used in thefilter operation.The texture values along the streamline segment,,are weighted with the corresponding kernel values.They are accumulated to give the intensity at position.Various kernel functions can be used in thefilter operation.For single images a constantfilter kernel gives a good impression of theflow direction.Taking periodic low-pass filter kernels and phase shifting these kernels in successive images allows to animate theflowfield.The animation showsflowing rip-ples which also encode the orientation of theflow.Forssell[6]extended the Line Integral Convolution method to curvilinear grid surfaces.Calculations are done on a regular carte-sian grid in computational space,whereas the results are displayed on curvilinear grids in physical space.Animating(i.e.,phase shift-ing)the convolution kernel with constant kernel length in computa-tional space produces distorted and misleadingflow visualizations in physical space.This is due to a usually nonlinear mapping be-tween computational space and physical space.The problem is overcome by adapting the length of the convolution kernel locally. Speed encoding is achieved by changing the amount of the phase shift of the convolutionfilter according to the locally varying ve-locity of the vectorfield.Calculating a LIC image is a rather time consuming task. Stalling and Hege[14]reduced calculation times considerably by exploiting coherence properties.Given a simple(constant)convo-lution kernel k(),the difference in intensity of two ad-jacent positions on the same streamline can be calculated by an easy incremental update operation.The computation order is not pixel-per-pixel as in[1]but streamline oriented.This gives an order of magnitude speed-up with the drawback of allowing only simple convolution kernels.Additionally Stalling and Hege’s method al-lows to zoom into a specific area of the input texture.Thus the input texture and the resulting image do not have to be of the same resolution.Kiu and Banks[8]use Line Integral Convolution with multi-frequency noise texture.The locally varying magnitude of the vec-torfield determines which frequency components are selected and integrated into a multi-frequency noise image.Areas with high ve-locities are represented by a noise function with lower spatial fre-quency.Further texture based techniques are described,e.g.,in[2], [10],and[13].The variations of the Line Integral Convolution method pre-sented so far do not encode the orientation of aflow within a still image.In section2Oriented Line Integral Convolution(OLIC) [16]is described,which overcomes this disadvantage.Section 3discusses a new technique for Fast Rendering of OLIC images (FROLIC).Section4investigates the design of sparse textures for FROLIC.Animation aspects are described in section5.The internet offers great potential of allowing various users in a heterogeneous setup to use the same visualization software.Section6deals with a Java implementation of the FROLIC algorithm.Finally in section 7some conclusions are given and future work is outlined.2Oriented Line Integral Convolution(OLIC)Figure1:Two streamlines with equal direction but opposite orientationLIC images encodeflow direction and velocity magnitude,but they do not show the orientation of theflow in still images.Figure1 shows two streamlines with equal direction but opposite orientation. LIC does not distinguish between these two cases.Flow orientation can be illustrated through animation.But there are cases where only still images are available or necessary,e.g.,reproduction of vector fields in books or journals.Furthermore LIC images are characterized by high spatial fre-quencies normal to theflow.This gives a good impression of the overall vectorfield,but is susceptible to aliasing problems in case an image has to be manipulated like,e.g.,resized or printed.Ori-ented Line Integral convolution(OLIC)[16]was designed to show the orientation of aflow even in still images and it is not as much prone to aliasing effects as LIC.There are two major differences between LIC and OLIC.LIC images typically use dense noise tex-tures wheras OLIC utilizes only sparse textures.A sparse texture can be thought of as a set of ink droplets which are thinly distributed on a sheet of paper.The vectorfield smears these ink droplets but the ink droplets are so far apart from each other that blurred traces of droplets usually do not overlap.The second difference between LIC and OLIC is that OLIC uses asymmetric convolution kernels (figure2).A ramp-like kernel as infigure2produces traces of droplets with intensity variation along the streamline.As a sparse texture is taken traces do not overlap very much and the orientation of theflow is visible in still images.Infigure3the difference between LIC and OLIC is clearly visi-ble.Figure3(a)shows the LIC image of a circularflow but it is not recognizable if theflow is in clockwise or counterclockwise orien-tation.Figure3(b)shows the OLIC image of a circular clockwise flow andfigure3(c)shows the OLIC image of a circular counter-clockwiseflow.The additional information in the OLIC image is gained at the expense of spatial resolution.The initial positions of the droplets in the sparse texture must be selected carefully to avoid the formation of undesirable patterns in the OLIC image.In[16]the droplets are positioned on a regular grid.Additionally these positions are slightly jittered.If the dis-tance between droplets is too large a lot offlow information isnot(a)(b)(c)Figure3:LIC image(a),OLIC images for twoflows with opposite orientation(b), (c)depicted in the result image.On the other hand if the droplets are too close to each other,many traces will overlap.If the overlap-ping is too extensive the orientation is not clearly visible any more. Section4investigates the placement of droplets in the input texture.OLIC allows to encodeflow velocity by the length of the traces of individual droplets.The animation of OLICs can be achieved by simply phase shifting the convolution kernel for each frame of the animation sequence.The phase shift is adapted to the length of the trace of a droplet.Short traces have small phase shifts and long traces have large phase shifts.Initially each droplet is assigned a random phase shift(offset)to avoid synchronization artefacts.In [16]OLIC images are calculated pixel by pixel.In a precalcula-tion step areas of the result image which are not affected by any of the droplets can be determined and skipped in the following convo-convolution kernelconvolutionink dropletsstreamlinesresulting trace Figure2:Sparse texture and ramp-like kernel-function for OLIClution process.Despite this optimization the calculation of OLIC images is quite slow and comparable to the cost of calculating LIC images.In section3a fast approximative calculation of OLIC is presented.3Fast Rendering of OLIC(FROLIC)One characteristic feature of OLIC is the usage of sparse textures. Usually a sparse texture is made up of constant intensity droplets although one can think of droplets with a different,e.g.,gaussiandistributed,intensity function.The distance between droplets is large enough so that traces of neighboring droplets typically do not overlap too much.This allows,in combination with the asymmetric convolution kernel,to illustrate the orientation of theflow.Convo-lution with a sparse texture is not as difficult as convolution with a dense texture.This will be now used for Fast Rendering of OLIC images(FROLIC).FROLIC calculates an approximate solution to the exact con-volution result of OLIC thereby achieving a considerable speed-up. With a sparse texture the convolution at a specific point of the result image involves at most one single droplet.Each droplet produces a trace with intensity increasing from tail to head.Due to the circu-lar shape of a droplet the intensity varies slightly along the breadth of a trace as well(figure4(a)).As a trace is rather small FROLIC approximates the shape of a trace by a set of small,possibly over-lapping disks(figure4(b)).The disks are positioned along a short portion of a streamline.Each disk has constant intensity,but the intensity varies between adjacent disks.If n disks are taken to ap-proximate a trace then intensity increases in n discrete steps from tail to head of the trace.The intensity of adjacent disks is increas-ing to simulate the continuous ramp kernel of the OLIC method. Although being an approximative variant of a LIC-type algorithm, FROLIC is also somewhat in the spirit of iconic vectorfield rep-resentations.Such approaches are,e.g.,spot noise[17],surface particles[18],and particle traces on2D surfaces[11].The FROLIC calculation is done as follows:for each droplet a short streamline portion is calculated by integrating the underlying flowfield.The length of a streamlet indicates localflow velocity. The smallest and largest velocities in the vectorfield are assigned specific streamlet lengths,intermediate velocity values are linearly interpolated.A prefixed number of disks is positioned in regular intervals along a streamlet.The processing order is from tail to head of the trace,i.e.,darker disks are drawnfirst and might be(a)(b)Figure4:Exact trace of a droplet with OLIC(a)and approximatedtrace of a droplet with FROLIC(b)partially occluded by brighter disks which are drawn later on.In our approach the number of disks positioned along a streamlet is independent from the length of the streamlet.This allows an easy animation algorithm as described in section5.The main advantage of FROLIC as compared to OLIC is that drawing disks is much faster than doing a costly convolution cal-culation.Instead of calculating the result image pixel per pixel as OLIC does,only the rather small set of droplets has to be processed. In an image with resolution of600x600about1000droplets are suf-ficient.Furthermore drawing simple geometric primitives like disks can be done with hardware support.During experiments we found that the approximation error introduced by the FROLIC method is well justified by the efficiency gain.The calculation time for the FROLIC images infigures5(b)and6(b)is about two seconds ona Pentium100Mhz PC.Investigations show that FROLIC(without hardware supported rendering)is approximately two orders of mag-nitude faster than OLIC.Figures5and6give a comparison between OLIC and FROLIC images.The images were calculated with a res-olution of600x600.The calculation of the FROLIC image infigure 5was295times faster than the corresponding OLIC image.Infig-ure6the speed-up was170.The difference in the speed-up factors is mainly due to the longer streamlets infigure5which are more costly to calculate with OLIC than with FROLIC.OLIC is independent from the specific texture,whereas the cost of FROLIC depends on the number of droplets.Increasing the ker-nel length increases the cost of both methods.In this case OLIC has to convolve the texture with a larger streamline portion and FROLIC has to draw more disks for each streamlet.The radius of the droplets has no effect on the OLIC calculation,while it slightly influences the FROLIC performance.This is due to the fact that larger disks have to be drawn in this case.A slight performance degradation happens with FROLIC when the resolution of the out-put image is increased.A larger image resolution,on the other hand,slows down the OLIC calculation considerably.Speed en-coding influences the OLIC performance,as the length of stream-lets(and therefore the convolution cost)may vary to a great degree between differentflowfields.This is not the case with FROLIC as the number of disks drawn for each streamlet is independent from its length.4Droplet Texture DesignThis section deals with the placement of droplets on a sparse input texture.There are two criteria which should be optimized but which are opposed to each other.One criterion calls for a densefilling of the output image with streamlets.This ensures that most of the vectorfield information is represented in the output image.The second criterion is that overlapping streamlets should be avoided as far as possible in order to clearly illustrateflow orientation.Finding an optimal droplet distribution in the input texture so that a tight packing of streamlets results in the output image is quite intricate.The optimal texture depends on the underlying vec-torfield as well as on the chosen minimal and maximal streamlet lengths.Furthermore changing the position of a droplet has non-trivial consequences concerning the induced streamlet.The stream-let may change its length or shape.This complicatesfilling algo-rithms which are based on distributing and moving droplets in the input texture.Another consideration is that the arrangement of the streamlets should not produce macro structures which are easily perveived by the human visual system and which disturb the inter-pretation of theflow data.Such macro structures might result for example if streamlets are exactly aligned along a specific stream-line or the alignment of streamlets is such that they form wavefront patterns.There has already been work on optimal streamline placement [7],[15].Turk and Banks[15]use an energy function to guide the placement of streamlines.An image with an uneven distribution of streamlines(in certain areas streamlines are either too crowded or too sparse)has higher energy than an image with a more even streamline density.The optimization process decreases the energy function which approaches a local minimum.The resulting images look somewhat like elegant hand-designed streamline drawings but the optimization process itself is quite costly.Our task deals only with the placement of short streamlets and is therefore inherently simpler than the streamline placement in[15]. Simple approaches for droplet placement are random distribution and placement of droplets on a regular or jittered grid.If the dis-tance of adjacent grid points is in the same order as the maximal streamlet length then overlapping may occur but is usually not a severe problem.If overlapping of streamlets shall be avoideden-(a)(b)Figure5:Econometric data with OLIC(a)and FROLIC(b) tirely,a distance image is used which has the same resolution as the final output image.For each pixel the distance image contains the distance to the closest streamlet drawn so far(figure7(b),(c)).A new streamlet candidate is calculated and if it is too close to a pre-viously drawn streamlet it is discarded.Otherwise the streamlet is drawn into the output image as a set of disks and the distance image is updated.The update operation is based on a rasterized template of the disk(figure7(a)).Pixels within the disk have the distance value zero,other pixels of the template contain the distance to the disk up to a certain threshold value d.For each disk of the streamlet the template is pasted into the distance image in a z-buffer fashion. If a pixel of the output image is now closer to the currently drawn disk its distance value is modified to the corresponding template value otherwise it remains unchanged.This approach ensures that streamlets are not closer to each other than the predefined threshold value d.The threshold value d determines the density of streamlets in the output image.Experiments have shown that a small value of d pro-duces a dense output image but undesirable macro structures might occur.If only pixel positions on,e.g.,a jittered grid are tested for possible streamlet placement and overlapping streamlets are dis-(a)(b)Figure6:Circularflow with OLIC(a)and FROLIC(b)carded there could be some thinly populated areas in the output image.In a second pass additional pixel positions are tested for streamlet placement.The search order in the second pass can be random,circular starting from the image center,or according to a Peano curve.The search order should not be too regular,e.g.,in scanline order,so that the danger of macro structures is reduced.Doing thefill operation in one step without initially placing streamlets globally,e.g.,on a grid,is prone to generating macro structures.By choosing the threshold value d to be at least three to four times the perimeter of the streamlets generally avoids the macro structures.Figure8gives a comparison between a FROLIC with and without overlapping streamlets respectively.The thresh-old d infigure8is small as compared to the streamlet perimeter. Therefore some macro structures are recognizeable.5Animation of FROLICAnimation of OLIC images is realized by phase shifting the convo-lution kernel in consecutive frames of the animation sequence(see section2).This approach can also be adapted to FROLIC.With FROLIC a streamlet consists of a set of disks with varying intensity. These intensities are cycled to convey to the viewer theimpression(a)(b)(c)Figure7:Rasterized template of a disk(a),two streamlets(b),distance image(c) of motion.The spatial position of streamlets is not changed.The starting points of streamlets can be thought of as nozzles which pe-riodically introduce dye into theflow.This is an Eulerian approach [12]as opposed to using moving particles,which would be a La-grangian approach.Moving particles have the disadvantage that de-pending on theflowfield an uneven particle distribution may evolve quite rapidly.In the following we will discuss two algorithms how to realize animation of FROLIC images.Thefirst algorithm was implemented as a Java applet[5]which will be described in more detail in section6.The second algorithm realizes FROLIC anima-tion by color-table animation.Thefirst algorithm is based on the fact that a linearly increas-ing intensity function has to be cycled.Each streamlet is again assigned a random initial phase shift to avoid synchronization ef-fects.For each streamlet the current position c indicates the disk with highest intensity.Given frame i of the animation sequence the following frame i+1is constructed by reducing the intensity of all pixels of frame i by afixed amount.This amount is equal to the intensity difference between adjacent disks.Frame i+1is built from the intensity-reduced frame i by drawing a single disk for each streamlet.These disks have highest intensity and are positioned at location(c+1)mod n.n is the number of disks used to represent a streamlet.Both operations(i.e.,intensity reduction and disk draw-(a)(b)Figure8:FROLIC image(a)with,(b)without overlapping streamlets ing)together cycle the intensity ramp one disk along theflow.The human visual system is very sensitive to appearing or disap-pearing bright spots.This can be a problem for cycling an intensity ramp along afixed streamlet,as a bright disk disappears at the end of a streamline and reappears at the start of the streamline.The impression of a pulsating effect can be,however,avoided by using afilter(e.g.,Gaussian)which attenuates the intensity at the begin-ning and the end of a streamlet.As a streamlet is typically made up of a small number of disks we use in our implementation a simple filter which initially increases linearly,is constant in the middle por-tion,andfinally decreases linearly.Whenever a new disk is drawn its intensity is modified with the abovefilter according to the disk position.Color-table animation is the second approach for efficiently an-imating FROLIC images.With a color table the intensity value of a pixel is specified indirectly.Each pixel is assigned a short color-table index which points to a specific entry in the color table. Available intensities or colors are stored in the color table itself. Color-table animation changes the entries of the color table instead of changing the corresponding image.As the color table is only small in size,e.g.,256entries,this can be done very fast.The pos-sibilities of color-table animation are rather limited but sufficient for animating FROLIC images.Figure9illustrates the principle.A streamlet is initially built by drawing a set of disks.Adjacentdisks are represented by consecutive color-table indices.The color table holds the intensity ramp,i.e.,successive color-table entriescontain increasing intensity values.After this initialization step the assignment of indices to pixels is not changed anymore.Animationis achieved by cycling the intensity values in the color table itself (seefigure9).The random initial phase shift(offset)is realized bystarting each streamlet with a randomly selected color-table index.There is a problem if the intensity of a streamlet should be ad-ditionally attenuated at the beginning and end of the streamline.Inthis case the intensity of a disk does not only depend on the offset within the intensity ramp but is also dependent on the spatial po-sition.This means that a color-table index can not simultaneouslyrepresent a disk in the middle of one streamlet and a disk at the beginning or end of another streamlet.This situation is handledby subdividing the color table into non overlapping equal-sized re-gions.Each region represents all the streamlets with the same initialphase shift.If,for example,there are256color-table entries and each streamlet is represented by32disks then8(256/32)differentinitial phase shifts can be realized.We have currently included thefirst algorithm into our prototype implementation(see section6)as successive intensity reductions ofentire images are easily realized in Java.As we can not manipulate color-table entries within our Java applet,we are currently imple-menting the color-table animation approach under another softwareenvironment.Figure9:Color-table animation for FROLIC,two consecutive frames6FROLIC via the InternetThis section describes a prototype implementation ofFROLIC and some other vectorfield visualization techniques within a Java applet[5].The applet can be accessed at http://www.cg.tuwien.ac.at/research/vis/dynsys/frolic/. Over the last years we have been collaborating with researchersworking on analytically defined dynamical systems.Depending on the professional background,e.g.,mathematicians,economists, the scientists typically have a quite inhomogenous hardware equipment.Most of these scientists do not have high-end graphics hardware at their disposal.Therefore it can be difficult to provide them with visualization tools that are specifically tailored to their needs.Internet computing provides a mechanism to offer peoplehardware-independent visualization capabilities.The same tech-niques can be used in different setups without the need to modify the implementation.Software maintainance and update is no prob-lem as the latest version is available over the internet.The Java applet provides some methods to experiment with and investigate analytically defined2D vectorfields.This gives researchers thepossibility to easily visualize their analytical vector data without having to use any complex visualization tool.A2D vectorfield is defined by a system of two differential equa-tions.A fast rendering of theflow behavior of such a system is crucial to efficiently explore different parameter settings and varia-tions of a given vectorfield.As LIC and OLIC produce high qual-ity images at a high computational cost,FROLIC was developed to provide an approximative but fast representation of the system behavior.The user submits among other parameters:the vector field equations,the area of interest and the resolution of the output image.During the calculation of a FROLIC image a numerical sim-ulation of the vectorfield is done by applying,e.g,Euler or Runge-Kutta methods.FROLIC images can be calculated with or without the avoidance of overlapping streamlets.Animations of FROLIC images are also possible.Other techniques included in the applet are the following:The speed of the vectorfield is encoded in an intensity image.High intensity areas correspond to high velocity regions of the vector field.A hedge-hog representation of the vectorfield illustrates the flow with arrow glyphs positioned on a regular grid.Isoclines,i.e., curves where theflow is either horizontal or vertical,may also be calculated.LIC and OLIC images are determined by doing exact (and costly)convolution operations.Particles may be introduced into theflow as well.As particles change their location usually an uneven particle distribution results very soon.7ConclusionThis paper describes various extensions to Oriented Line Inte-gral Convolution(OLIC).As opposed to Line Integral Convolu-tion(LIC)OLIC images depict the orientation of aflowfield even within a still image.Calculating an OLIC image involves expensive convolution operations.FROLIC is presented in this paper which accelerates the calculation of OLIC images by about two orders of magnitude.This is achieved by approximating a streamlet by a set of disks with varying intensity.Two algorithms are discussed to efficiently animate FROLIC im-ages.FROLIC is implemented as a Java applet to allow researchers with different hardware resources to easily explore2D analytical dynamical systems through internet computing.Future work will include variations of streamlet approximation. For example streamlets in strongly converging or diverging areas will be represented by disks with varying radii.Instead of approx-imating a streamlet by a set of(usually overlapping)disks one can also think of using predefined footprints.For each streamlet the best suited representation in a footprint table is selected.Visualization over the internet is a promising new area of re-search.We plan to extend the implemented Java applet and adapt its functionality according to user reactions. 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