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] | กราฟ (คณิตศาสตร์)
กราฟ "G" = ("V","E") จะเป็นกราฟจำกัด (finite graph) ก็ต่อเมื่อ "V" และ "E" เป็นเซตจำกัด
ในทางตรงกันข้าม หากมี "V" หรือ "E" อย่างใดอย่างหนึ่งที่เป็นเซตอนันต์ ก็จะได้ว่า "G" เป็นกราฟอนันต์ (infinite graph) |
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] | กราฟ (คณิตศาสตร์)
กราฟถ่วงน้ำหนัก (weighted graph) คือ กราฟที่มีการกำหนดค่าให้กับเส้นเชื่อมแต่ละเส้น ซึ่งอาจเป็น "ค่าใช้จ่าย", "น้ำหนัก", "ความยาว" หรืออื่นๆขึ้นกับการใช้งาน บางคนเรียกกราฟประเภทนี้ว่าเครือข่าย กราฟถ่วงน้ำหนักนำไปใช้ในการแก้ปัญหาหลายๆอย่าง เช่น ปัญหาวิถีสั้นสุด เป็นต้น โดยทั่วไปน้ำหนักที่ถ่วงจะถือว่าเป็นจำนวนจริงบวก ในกรณีที่น้ำหนักเส้นเชื่อมเป็นลบได้จะมีการระบุเพิ่มเติม เนื่องจากการจัดการกับกรณีทั้งสองในหลายๆปัญหานั้นต่างกัน |
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โดยทั่วไปหากกล่าวถึงกราฟจะหมายถึงกราฟไม่ถ่วงน้ำหนัก (unweighted graph) ซึ่งไม่มีน้ำหนักถ่วงที่เส้นเชื่อม |
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เราจะกล่าวว่า |
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กราฟที่มีจุดยอดเพียงจุดเดียวและไม่มีเส้นเชื่อมใดๆ เรียกว่า กราฟชัด (trivial graph) กราฟที่มีแต่จุดยอดแต่ไม่มีเส้นเชื่อมใดๆ เรียกว่า กราฟว่าง (empty graph) ส่วนกราฟที่ไม่มีทั้งจุดยอดและเส้นเชื่อม เรียกว่า กราฟศูนย์ (null graph) แต่นิยามนี้ไม่เป็นที่นิยมนัก |
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] | กราฟ (คณิตศาสตร์)
โดยทั่วไปแล้วจุดยอดของกราฟนั้นจะไม่สามารถถูกแยกแยะ หรือพิจารณาว่าแตกต่างกันได้ (ยกเว้นในบางกรณีเช่นมีจำนวนเส้นเชื่อมที่แตกต่างกันเป็นต้น) อย่างไรก็ตาม บางสาขาของทฤษฎีกราฟต้องการให้ระบุจุดยอดที่ชัดเจนได้ ถ้าแต่ละจุดยอดมีการระบุชื่อที่ชัดเจน กล่าวคือมีป้ายชื่อกำกับ เราจะเรียกกราฟเหล่านั้นนั้นว่า "กราฟจุดยอดระบุชื่อ" (vertex-labeled graph) นอกจากนี้ เส้นเชื่อมก็ยังสามารถมีป้ายชื่อกำกับได้เช่นกัน เรียกกราฟลักษณะนี้ว่า "กราฟเส้นเชื่อมระบุชื่อ" (edge-labeled graph) ในกรณีที่ไม่มีการระบุชื่อจะเรียกกราฟว่า "กราฟไม่ระบุชื่อ" (unlabeled graph) |
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] | กราฟ (คณิตศาสตร์)
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] | กราฟ (คณิตศาสตร์)
ในทฤษฎีโมเดล กราฟเป็นแค่โครงสร้าง ในกรณีนั้นจะไม่มีข้อจำกัดในจำนวนของเส้นเชื่อม นั่นคือจะมีเส้นเชื่อมเป็นจำนวนเชิงการนับใด ๆ ก็ได้ |
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] | วิศวกรรมคอมพิวเตอร์
วิศวกรรมคอมพิวเตอร์ () เป็นศาสตร์ที่เกี่ยวข้องกับการออกแบบและสร้างเครื่องหรือระบบคอมพิวเตอร์ และ ระบบที่ใช้คอมพิวเตอร์ ศาสตร์นี้เกี่ยวข้องกับการศึกษาทางด้านฮาร์ดแวร์ ซอฟต์แวร์ การสื่อสาร และความเกี่ยวเนื่องระหว่างเรื่องทั้งสาม หลักสูตรการเรียนมุ่งเน้นทางด้าน ทฤษฎี กฎ และ การฝึกฝนปฏิบัติของทางด้านวิศวกรรมไฟฟ้า และ คณิตศาสตร์ และวิทยาศาสตร์รวมถึงการประยุกต์เข้ากับปัญหาทางด้านการออกแบบคอมพิวเตอร์ และ อุปกรณ์ที่ใช้คอมพิวเตอร์ |
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วิศวกรคอมพิวเตอร์ ศึกษาการออกแบบระบบฮาร์ดแวร์ดิจิทัล ซึ่งรวมถึงระบบการสื่อสาร องค์ประกอบของคอมพิวเตอร์ และอุปกรณ์ที่ประกอบด้วยคอมพิวเตอร์ วิศวกรคอมพิวเตอร์จะเรียนการพัฒนาซอฟต์แวร์ โดยมุ่งเน้นเกี่ยวกับซอฟต์แวร์สำหรับอุปกรณ์ดิจิทัล และ การสร้างส่วนต่อประสานระหว่างผู้ใช้งานซอฟต์แวร์ และ ระหว่างอุปกรณ์ต่าง ๆ รวมทั้งความรู้ทางด้านวิศวกรรมที่ดีด้วย |
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ปัจจุบันสาขาวิชาที่สำคัญในด้านวิศวกรรมคอมพิวเตอร์คือ ระบบฝังตัว การพัฒนาอุปกรณ์ที่มีซอฟต์แวร์และฮาร์ดแวร์ฝังตัวภายใน เช่น อุปกรณ์สื่อสารอย่าง โทรศัพท์มือถือ เครื่องเล่นวิทยุระบบดิจิทัล เครื่องบันทึกวีดิทัศน์ระบบดิจิทัล ระบบเตือนภัย เครื่องถ่ายรังสีเอกซ์ และ เครื่องมือผ่าตัดด้วยแสงเลเซอร์เป็นต้น ซึ่งล้วนแล้วแต่ต้องการการผนวกรวมฮาร์ดแวร์และซอฟต์แวร์ฝังตัวหรือของอื่น ๆ ที่เป็นผลจากการวิศวกรรมคอมพิวเตอร์เข้าด้วยกัน |
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ในแง่ของศาสตร์เกี่ยวกับคอมพิวเตอร์นั้น วิศวกรรมคอมพิวเตอร์ เป็นหนึ่งในห้าสาขาวิชาคอมพิวเตอร์ ซึ่งประกอบด้วย สาขาวิทยาการคอมพิวเตอร์ หรือวิทยาศาสตรคอมพิวเตอร์ สาขาวิศวกรรมคอมพิวเตอร์ สาขาวิศวกรรมซอฟต์แวร์ สาขาเทคโนโลยีสารสนเทศ หรือเทคโนโลยีสารสนเทศและการสือสาร และ สาขาคอมพิวเตอร์ธุรกิจ หรือ ระบบสารสนเทศทางธุรกิจ. |
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] | วิศวกรรมคอมพิวเตอร์
ประวัติวิศวกรรมคอมพิวเตอร์ ในอเมริกาเริ่มจากแต่เดิมเป็นสาขาวิชาเฉพาะทางในวิศวกรรมไฟฟ้า ที่มุ่งศึกษาเกี่ยวกับการวิศวกรรมฮาร์ดแวร์คอมพิวเตอร์ แต่ต่อมาช่วงหลังปี ค.ศ. 1990 จึงมีการเพิ่มเติมเนื้อหาการศึกษาทางด้านซอฟต์แวร์ หรืออาจมองได้ว่าเกิดจากการรวมกันของวิศวกรรมไฟฟ้าและวิทยาการคอมพิวเตอร์ ถ้าพิจารณาจากสาขาวิศวกรรมไฟฟ้าแล้ว วิศวกรคอมพิวเตอร์คือวิศวกรไฟฟ้าที่มุ่งเน้นไปที่ระบบฮาร์ดแวร์เชิงดิจิทัล และไม่เน้นทางด้านความถี่วิทยุ หรือไฟฟ้ากำลัง และถ้ามองจากทางวิทยาการคอมพิวเตอร์แล้ว วิศวกรคอมพิวเตอร์จะเป็นผู้เชี่ยวชาญด้านการต่อประสานระหว่างซอฟต์แวร์และระบบฮาร์ดแวร์ ในยุคหลังมีทฤษฏีหลายอย่างที่เกิดขึ้นในสาขาวิศวกรรมคอมพิวเตอร์ เช่น ระบบเครือข่าย การรักษาความปลอดภัยคอมพิวเตอร์ การประมวลผลภาษาธรรมชาติ หรือ การรู้จำด้วยคอมพิวเตอร์ เป็นต้น |
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ภาควิชาวิศวกรรมคอมพิวเตอร์ในอเมริกาส่วนมาก เริ่มก่อตั้งขึ้นภายใต้หรือควบคู่กับภาควิชาวิศวกรรมไฟฟ้า ตามมหาวิทยาลัยต่าง ๆ ตั้งแต่ต้นคริสต์ทศวรรษ 1990 บางมหาวิทยาลัยเลือกที่จะผนวกสาขาวิศวกรรมคอมพิวเตอร์และวิศวกรรมซอฟต์แวร์เข้ากับภาควิชาวิศวกรรมไฟฟ้า ในขณะที่บางที่เช่น สถาบันเทคโนโลยีแมสซาชูเซตส์ เลือกที่จะรวมภาควิชาวิศวกรรมไฟฟ้าเข้ากับภาควิชาวิทยาการคอมพิวเตอร์แทน |
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] | วิศวกรรมคอมพิวเตอร์
งานด้านวิศวกรรมคอมพิวเตอร์ แบ่งเป็น 2 สาขาหลัก คือ ด้านซอฟต์แวร์ และ ฮาร์ดแวร์ |
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บทความหลัก: วิศวกรรมซอฟต์แวร์ |
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วิศวกรซอฟต์แวร์คอมพิวเตอร์จะพัฒนา, ออกแบบและทดสอบซอฟต์แวร์ บางวิศวกรซอฟต์แวร์ ออกแบบ, สร้างและบำรุงรักษาโปรแกรมคอมพิวเตอร์สำหรับบริษัททั่วไป บางคนจัดตั้งเครือข่ายเช่น "อินทราเน็ต"สำหรับบริษัททั่วไป หลายตนทำหรือติดตั้งซอฟต์แวร์ใหม่หรืออัพเกรดระบบคอมพิวเตอร์ วิศวกรซอฟต์แวร์คอมพิวเตอร์ยังสามารถทำงานออกแบบแอปพลิเคชัน งานนี้เกี่ยวข้องกับการออกแบบหรือการเข้ารหัสโปรแกรมและแอปพลิเคชันใหม่ เพื่อตอบสนองความต้องการของธุรกิจหรือบุคคล |
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] | วิศวกรรมคอมพิวเตอร์
วิศวกรฮาร์ดแวร์คอมพิวเตอร์ส่วนใหญ่จะวิจัย, พัฒนา, ออกแบบและทดสอบอุปกรณ์คอมพิวเตอร์ต่าง ๆ งานนี้สามารถมีช่วงจากแผงวงจรและไมโครโปรเซสเซอร์ จนถึงเราเตอร์ บางคนปรับปรุงอุปกรณ์คอมพิวเตอร์ที่มีอยู่ให้มีประสิทธิภาพมากขึ้นและสามารถทำงานร่วมกับซอฟต์แวร์ใหม่ได้ วิศวกรฮาร์ดแวร์คอมพิวเตอร์ส่วนใหญ่ทำงานในห้องปฏิบัติการวิจัยและบริษัท ผลิตเทคโนโลยีชั้นสูง บางคนยังทำงานให้กับรัฐบาลกลาง ตามข้อมูลของสำนักสถิติแรงงานของสหรัฐฯ, 95% ของวิศวกรฮาร์ดแวร์คอมพิวเตอร์ทำงานในพื้นที่นครบาล พวกเขามักจะทำงานเต็มเวลา ประมาณ 25% ของการทำงานของพวกเขาต้องทำงานมากกว่า 40 ชั่วโมงต่อสัปดาห์ เงินเดือนเฉลี่ยของลูกจ้างวิศวกรคอมพิวเตอร์ฮาร์ดแวร์ที่มีคุณสมบัติ (2012) เป็น $ 100,920 ต่อปี หรือ $48.52 ต่อชั่วโมง วิศวกรคอมพิวเตอร์ฮาร์ดแวร์ทำงาน 83,300 งานในปี 2012 . |
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วิศวกรรมคอมพิวเตอร์ มีสาขาหลัก ได้แก่ |
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บทความหลัก: Information security |
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วิศวกรคอมพิวเตอร์ทำงานในการเข้ารหัส, การถอดรหัส และการคุ้มครองข้อมูล เพื่อพัฒนาวิธีการปกป้องข้อมูลต่าง ๆ ใหม่ เช่น ภาพและเพลงดิจิทัล, กระจายข้อมูลดิบในเมมโมรี, การละเมิดลิขสิทธิ์ และการแก้ไขดัดแปลงรูปแบบอื่น ตัวอย่างรวมถึงการทำงานเกี่ยวกับการสื่อสารไร้สาย, ระบบหลายสายอากาศ, การส่งผ่านด้วยแสง และ ลายน้ำดิจิทัล |
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บทความหลัก : Communications networks and Wireless network |
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มุ่งเน้น การสื่อสารและ เครือข่ายไร้สาย, ความก้าวหน้าในระบบการสื่อสารโทรคมนาคมและเครือข่าย, modultion และการเข้ารหัสควบคุมความผิดพลาด, และทฤษฎีสารสนเทศ การออกแบบเครือข่ายความเร็วสูง, การปราบปรามการรบกวน, การออกแบบและการวิเคราะห์ของระบบอดทนต่อความผิดพลาด () และ การจัดเก็บและรูปแบบการส่งผ่าน ทั้งหมดนี้เป็นส่วนหนึ่งของพื้นที่ พิเศษ |
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บทความหลัก : Compiler and Operating system |
688#16 | [
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] | วิศวกรรมคอมพิวเตอร์
พืนที่พิเศษนี้ มุ่งเน้นไปที่การออกแบบและพัฒนาคอมไพเลอร์และระบบปฏิบัติการ วิศวกรในสาขานี้พัฒนาสถาปัตยกรรมใหม่ของระบบปฏิบัติการ, เทคนิคการวิเคราะห์โปรแกรม และเทคนิค ใหม่ในการรับประกันคุณภาพ ตัวอย่างของการทำงานในด้านนี้รวมถึง การแปลงรหัสโพสต์-ลิงก์-เวลา, การพัฒนา algorithm และการพัฒนาระบบปฏิบัติการ ใหม่ |
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บทความหลัก: Computational science and engineering |
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] | วิศวกรรมคอมพิวเตอร์
วิทยาศาสตร์และวิศวกรรมทางการคำนวณเป็นสาขาวิชาที่ค่อนข้างใหม่ สอดคล้องกับศูนย์ Sloan Career Cornerstone, บุคคลที่ทำงานในพื้นที่นี้ "วิธีการคำนวณจะถูกนำไปใช้ในการกำหนดรูปแบบและการแก้ปัญหาทางคณิตศาสตร์ที่ซับซ้อนด้านวิศวกรรมและด้านฟิสิกข์และสังคมศาสตร์ . ตัวอย่าง รวมถึงการออกแบบอากาศยาน, การประมวลผลแบบพลาสม่าของคุณสมบัตินาโนเมตร บนเวเฟอร์เซมิคอนดักเตอร์, การออกแบบวงจร VLSI, ระบบตรวจจับเรดาร์, การขนส่งไอออนผ่านช่องทางชีวภาพและอื่น ๆ อีกมาก" |
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บทความหลัก : Computer Network, Mobile computing, and Distributed computing |
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ในพื้นที่พิเศษนี้ วิศวกรสร้างสภาพแวดล้อมที่ครบวงจรสำหรับการคอมพิวเตอร์, การสื่อสาร และการเข้าถึงข้อมูลสารสนเทศ ตัวอย่าง เช่น เครือข่ายไร้สายที่ใช้ช่องทางร่วมกัน, การจัดการทรัพยากรแบบปรับตัวในระบบต่าง ๆ และการปรับปรุงคุณภาพของการบริการในสภาพแวดล้อมที่ มือถือและสภาพแวดล้อม ATM ตัวอย่างอื่น ๆ บางอย่าง รวมถึงการทำงานในระบบเครือข่ายไร้สาย และระบบใช้สายกลุ่มแบบอีเธอร์เน็ตความเร็วสูง |
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] | วิศวกรรมคอมพิวเตอร์
บทความหลัก : Computer Architecture, Parallel Processing, and Dependability |
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วิศวกรที่ทำงานในระบบคอมพิวเตอร์จะทำงานในโครงการวิจัยที่ช่วยในการสร้างระบบคอมพิวเตอร์ที่มีประสิทธิภาพสูง, เชื่อถือได้และปลอดภัย โครงการเช่นการออกแบบหน่วยประมวลผลแบบ multi-threading และการประมวลผลแบบขนานจะรวมอยู่ในสาขานี้ ตัวอย่างอื่น ๆ ของการทำงานในด้านนี้รวมถึง การพัฒนาทฤษฎีใหม่, ขั้นตอนวิธีการและเครื่องมืออื่น ๆ ที่เพิ่ม ประสิทธิภาพให้กับระบบคอมพิวเตอร์ |
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บทความหลัก : Computer Vision and Robotics |
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ในพื้นที่พิเศษนี้ วิศวกรคอมพิวเตอร์มุ่งเน้นการพัฒนาเทคโนโลยีการตรวจวัดการมองเห็น ที่จะรับรู้สภาพแวดล้อม, การเป็นตัวแทนของสภาพแวดล้อมและการจัดการสิ่งแวดล้อม จากนี้น สารสนเทศสามมิติที่ถูกรวบรวมได้จะถูกดำเนินการในงานที่หลากหลาย งานเหล่านี้รวมถึง การสร้างแบบจำลองของมนุษย์, การสื่อสารด้วยภาพ, และการเชื่อมต่อระหว่างคอมพิวเตอร์กับมนุษย์ เช่นเดียวกับอุปกรณ์ เช่นกล้องวัตถุประสงค์พิเศษที่มีเซ็นเซอร์วิสัยทัศน์อเนกประสงค์ |
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บทความหลัก: ระบบฝังตัว |
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บุคคลที่ทำงานในพื้นที่นี้จะออกแบบเทคโนโลยีสำหรับการเพิ่มความเร็ว, ความน่าเชื่อถือและ ประสิทธิภาพการทำงานของระบบ ระบบฝังตัวถูกพบในอุปกรณ์จำนวนมากตั้งแต่วิทยุเอฟเอ็มขนาดเล็กจนถึงกระสวยอวกาศ สอดคล้องกับ ศูนย์อาชีพสโลน แคเรีย, การพัฒนาที่กำลังดำเนินการอยู่ในระบบฝังตัว ได้แก่ "ยานพาหนะและอุปกรณ์อัตโนมัติเพื่อดำเนินการค้นหาและช่วยเหลือ, ระบบการขนส่งโดยอัตโนมัติ และการประสานงานของมนุษย์กับหุ่นยนต์ในการซ่อมแซมอุปกรณ์ในอวกาศ" |
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บทความหลัก : วงจรรวม และ การสร้างวงจรรวมขนาดใหญ่มาก |
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้พื้นที่พิเศษของวิศวกรรมคอมพิวเตอร์นี้ ต้องมีความรู้เพียงพอของระบบอิเล็กทรอนิกส์และไฟฟ้า วิศวกรที่ทำงานในพื้นที่นี้จะทำการเพิ่มความเร็ว, ความน่าเชื่อถือและ การใช้พลังงานอย่างมีประสิทธิภาพของการสร้างวงจรรวมขนาดใหญ่มาก (VLSI) และวงจรระบบไมโครรุ่นต่อไป ตัวอย่างของพื้นที่พิเศษนี้เป็นงานที่ทำในการลดการใช้พลังงานของขั้นตอนวิธีการ VLSI และสถาปัตยกรรม |
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] | วิศวกรรมคอมพิวเตอร์
บทความหลัก : Signal processing, Image processing, and Speech processing |
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] | วิศวกรรมคอมพิวเตอร์
วิศวกรคอมพิวเตอร์ในพิ้นที่นี้พัฒนาการปรับปรุงในการปฏิสัมพันธ์ระหว่างมนุษย์กับคอมพิวเตอร์ รวมทั้งการรู้จำคำพูดและการสังเคราะห์เสียงพูด, การถ่ายภาพทางการแพทย์และทางวิทยาศาสตร์ หรือระบบการสื่อสารอื่น ๆ งานอื่น ๆ ในพื้นที่นี้รวมถึงการพัฒนาวิสัยทัศน์คอมพิวเตอร์ เช่นการรับรู้ใบหน้าของมนุษย์ |
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งานวิศวกรรมคอมพิวเตอร์ระดับขั้นต้นส่วนใหญ่ต้องการอย่างน้อยปริญญาตรีวิศวกรรมคอมพิวเตอร์ บางครั้งปริญญาวิศวกรรมไฟฟ้าก็ได้รับการยอมรับ เนื่องจากความคล้ายคลึงกัน ของทั้งสองสาขา เพราะวิศวกรฮาร์ดแวร์ทั่วไปได้ทำงานกับระบบซอฟต์แวร์คอมพิวเตอร์ พื้นหลัง ในการเขียนโปรแกรมคอมพิวเตอร์มักจะเป็นสิ่งจำเป็น จากสถาบันสถิติแรงงานของสหรัฐฯ "เมเจอร์ของวิศวกรรมคอมพิวเตอร์คล้ายกับวิศวกรรมไฟฟ้า แต่ก็มีบางหลักสูตรวิทยาการคอมพิวเตอร์ถูกเพิ่มเข้าไปในหลักสูตร" บางบริษัทขนาดใหญ่หรืองานที่ต้องใช้ความเชี่ยวชาญพิเศษต้องการระดับปริญญาโท นอกจากนี้ยังเป็นสิ่งที่สำคัญสำหรับวิศวกรคอมพิวเตอร์ ที่จะต้องตามให้ทันกับความก้าวหน้าอย่างรวดเร็วในเทคโนโลยี ดังนั้นจึงต้องเรียนรู้อย่างต่อเนื่องตลอดอาชีพของพวกเขาประกอบด้วยองค์ความรู้ดังนี้ |
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] | ซอฟต์แวร์
ซอฟต์แวร์ () หรือ ส่วนชุดคำสั่ง หรือบางครั้งมีการสะกดว่า ซอฟท์แวร์ เป็นส่วนของระบบคอมพิวเตอร์ที่ใช้ในการจัดเก็บและประมวลผลข้อมูล ซอฟต์แวร์นั้นนอกจากจะสามารถใช้งานบนคอมพิวเตอร์ได้แล้ว ยังสามารถใช้งานบนเครื่องใช้ หรืออุปกรณ์อื่น เช่น โทรศัพท์มือถือ หรือหุ่นยนต์ในโรงงาน หรือเครื่องใช้ไฟฟ้าต่าง ๆ คำว่า "ซอฟต์แวร์" ใช้ครั้งแรกโดย จอห์น ดับเบิลยู. เทอร์กีย์ (John W. Turkey) ในปี พ.ศ. 2500 (ค.ศ. 1957) โดยแนวคิดของซอฟต์แวร์ปรากฏครั้งแรกในเรียงความของแอลัน ทัวริง บิดาของวิทยาการคอมพิวเตอร์ กล่าวกันว่าโปรแกรมคอมพิวเตอร์ชิ้นแรกของโลกเขียนโดยเอดา ไบรอน เป็นโปรแกรมที่ใช้สำหรับเครื่องวิเคราะห์ (analytical engine) ของชาร์ลส แบบเบจ |
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] | ซอฟต์แวร์
ซอฟต์แวร์ เป็นชื่อเรียกเพื่อใช้เปรียบต่างกับฮาร์ดแวร์ ซึ่งเป็นลักษณะทางกายภาพในการเก็บและประมวลผลของซอฟต์แวร์ ในคอมพิวเตอร์ซอฟต์แวร์จะถูกเรียกใช้งานในแรมและประมวลผลผ่านซีพียู |
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การแบ่งประเภทของซอฟต์แวร์แบ่งออกได้เป็นหลายแบบ เช่น |
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ซอฟต์แวร์แตกต่างกับไลบรารี คือซอฟต์แวร์สามารถนำมาประมวลผลได้ด้วยตัวเอง ในขณะที่ไลบรารีเป็นส่วนประกอบของซอฟต์แวร์และไม่สามารถนำมาใช้ประมวผลด้วยตนเองได้ |
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] | แอลัน ทัวริง
แอลัน แมธิสัน ทัวริง (; 23 มิถุนายน พ.ศ. 2455 (ค.ศ. 1912) – 7 มิถุนายน พ.ศ. 2497 (ค.ศ. 1954)) เป็นนักคณิตศาสตร์, นักตรรกศาสตร์, นักรหัสวิทยาและวีรบุรุษสงครามชาวอังกฤษ และเป็นที่ยอมรับว่าเป็นบิดาของวิทยาการคอมพิวเตอร์ |
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] | แอลัน ทัวริง
เขาได้สร้างรูปแบบที่เป็นทางการทางคณิตศาสตร์ของการระบุขั้นตอนวิธีและการคำนวณ โดยใช้เครื่องจักรทัวริง ซึ่งตามข้อปัญหาเชิร์ช-ทัวริงได้กล่าวว่าเป็นรูปแบบของเครื่องจักรคำนวณเชิงกลที่ครอบคลุมทุก ๆ รูปแบบที่เป็นไปได้ในทางปฏิบัติ |
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ในระหว่างสงครามโลกครั้งที่สอง ทัวริงมีส่วนสำคัญในการแกะรหัสลับของฝ่ายเยอรมัน โดยเขาเป็นหัวหน้าของกลุ่ม Hut 8 ที่ทำหน้าที่ในการแกะรหัสของเครื่องอินิกมาที่ใช้ในฝ่ายทหารเรือ |
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] | แอลัน ทัวริง
หลังจากสงครามเขาได้ออกแบบเครื่องคอมพิวเตอร์อิเล็กทรอนิกส์ที่สามารถโปรแกรมได้เครื่องแรกๆ ของโลกที่ห้องปฏิบัติการฟิสิกส์แห่งชาติ และได้สร้างเครื่องคอมพิวเตอร์ขึ้นจริง ๆ ที่มหาวิทยาลัยแมนเชสเตอร์ รางวัลทัวริงถูกก่อตั้งขึ้นเพื่อยกย่องเขาในเรื่องนี้ |
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] | แอลัน ทัวริง
นอกจากนั้นแล้ว การทดสอบของทัวริงที่เขาได้เสนอนั้นมีผลอย่างสูงต่อการศึกษาเรื่องปัญญาประดิษฐ์ ซึ่งในขณะมีถกเถียงที่สำคัญว่า "เป็นไปได้หรือไม่ที่จะกล่าวว่าเครื่องจักรนั้นมีสำนึกและสามารถคิดได้" |
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] | แอลัน ทัวริง
แอลัน ทัวริงเป็นชาวอังกฤษ เกิดเมื่อปี พ.ศ. 2455 (ค.ศ. 1912) ที่ลอนดอน และอาศัยอยู่กับพี่ชาย บิดาและมารดาของทัวริงพบกันและทำงานที่ประเทศอินเดีย |
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] | แอลัน ทัวริง
ในสมัยมัธยม ทัวริงสนิทและนับถือรุ่นพี่คนหนึ่งชื่อ คริสโตเฟอร์ มอร์คอม (Christopher Morcom) ซึ่งเสียชีวิตไปเสียก่อน ทัวริงเศร้ามาก เลยตั้งใจสานต่อสิ่งที่รุ่นพี่เขาอยากทำให้สำเร็จ ตลอดสามปีหลังจากนั้น เขาเขียนจดหมายอย่างสม่ำเสมอให้คุณแม่ของมอร์คอม ว่าเขาคิดและสงสัยเรื่องความคิดของคนว่าไปจับจดอยู่ในเรื่องหนึ่ง ๆ ได้อย่างไร (how the human mind was embodied in matter) และปล่อยเรื่องนั้น ๆ ออกไปได้อย่างไร (whether accordingly it could be released from matter) แล้ววันหนึ่งเขาก็ไปเจอหนังสือดังในยุคนั้นชื่อ "The Nature of the Physical World" อ่านไปก็เกิดนึกไปเองว่าทฤษฏีกลศาสตร์ควอนตัมมันต้องเกี่ยวกับปัญหาเรื่อง mind and matter ที่เขาคิดอยู่ |
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] | แอลัน ทัวริง
ปี พ.ศ. 2474 เขาเข้าเรียนคณิตศาสตร์ที่คิงส์คอลเลจ มหาวิทยาลัยเคมบริดจ์ (หมายเหตุ: ยุคนั้นคิงส์คอลเลจเป็นที่พักชายล้วน ซึ่งทัวริงก็อยู่อย่างเปิดเผยว่าเขาเป็นเกย์ และเข้าร่วมกิจกรรมชมรม) ทัวริงมีความสุขกับชีวิตที่นี่มากและทำกิจกรรมหลายอย่าง เช่น พายเรือ, เรือใบเล็ก และ วิ่งแข่ง. ทัวริงพูดเสมอว่า "งานของผมนั้นเครียดมาก และทางเดียวที่ผมจะเอามันออกไปจากหัวได้ก็คือ วิ่งให้เต็มที่" และเขาก็วิ่งอย่างจริงจัง โดยที่ผลการวิ่งมาราธอนของเขา ชนะเลิศการแข่งขันของสมาคมนักกรีฑาสมัครเล่น ด้วยเวลา 2 ชั่วโมง 43 นาที 3 วินาที ในปี พ.ศ. 2489 ซึ่งในการแข่งขันวิ่งมาราธอนโอลิมปิก เมื่อ พ.ศ. 2491 (ค.ศ. 1948) คนที่ได้เหรียญทอง ทำเวลาได้เร็วกว่าเขาเพียง 11 นาที |
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] | แอลัน ทัวริง
ส่วนในเรื่องวิชาการในวงการคณิตศาสตร์ยุคนั้น รัสเซลล์ (Russell) เสนอเอาไว้ว่า "mathematical truth could be captured by any formalism" แต่ยุคนั้น เกอเดิล (Gödel) โต้ว่า "the incompleteness of mathematics: the existence of true statements about numbers which could not be proved by the formal application of set rules of deduction". พอปี พ.ศ. 2476 ทัวริงก็ได้เจอกับรัสเซลล์แล้วก็ตั้งคำถาม พร้อมถกเรื่องราวเหล่านี้ขึ้นมา ทำให้เขาสนใจ |
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ปี พ.ศ. 2477 ทัวริงก็จบจากมหาวิทยาลัยเคมบริดจ์ ด้วยเกียรตินิยมอันดับหนึ่ง ทางมหาวิทยาลัยก็เลยเชิญเขาอยู่เป็น Fellow ด้านคณิตศาสตร์ต่อ (ส่วนใหญ่ Fellow ของเคมบริดจ์จะเป็นพวกที่จบปริญญาเอก แต่ทัวริงจบเพียงปริญญาตรี) ปี พ.ศ. 2478 ทัวริงไปเรียนกับจอห์น ฟอน นอยมันน์ เรื่อง ปัญหาของการตัดสินใจ (Entscheidungs problem) ที่ถามว่า "Could there exist, at least in principle, a definite method or process by which it could be decided whether any given mathematical assertion was provable?" ทัวริงก็เลยมาคิด ๆ โดยวิเคราะห์ว่า คนเราทำอย่างไรเวลาทำงานที่เป็นกระบวนการที่มีกฎเกณฑ์ (methodical process) แล้วก็นึกต่อว่า วางกรอบว่าให้เป็นอะไรซักอย่างที่สามารถทำได้อย่างเป็นกลไก (mechanically) ล่ะ? เขาก็เลยเสนอทฤษฏีออกมาเป็น "The analysis in terms of a theoretical machine able to perform certain precisely defined elementary operations on symbols on paper tape". โดยยกเรื่องที่เขาคิดมาตั้งแต่เด็กว่า 'สถานะความคิด' (state of mind) ของคน ในการทำกระบวนการทางความคิด มันเกี่ยวกับการเก็บ และเปลี่ยนสถานะจากจุดหนึ่งไปอีกจุดหนี่ง ได้ตามการกระทำทางความคิด โดยทัวริงเรียกสิ่งนี้ว่า คำสั่งตรรกะ (logical instructions) แล้วก็บอกว่าการทำงานต้องมี กฎเกณฑ์ที่แน่นอน (definite method) (ต่อมาเรียกว่า ขั้นตอนวิธี) |
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] | แอลัน ทัวริง
พอปี พ.ศ. 2479 เขาก็เลยเตรียมออกบทความวิชาการที่มืชื่อเสียง "On Computable Numbers with an application to the Entscheidungsproblem" แต่ก่อนเขาออกบทความนี้ มีอีกงานของฝั่งอเมริกาของ Church ออกมาทำนองคล้าย ๆ กันอย่างบังเอิญ เขาเลยถูกบังคับให้เขียนอิงงาน Church ไปด้วย (เพราะบทความเขาออกทีหลัง) แต่พอบทความเขาออกมาจริง ๆ คนอ่านก็เห็นว่าเป็นคนละทฤษฏีกันและของเขามีเนื้อหา relied upon an assumption internal to mathematics แม่นกว่า การเน้นเรื่อง operation ใน physical world (ยุคต่อมาคนก็เลยนำ concept เขาไปประยุกต์ใช้และให้เกียรติว่า Turing machine จึงเป็นที่มาของการยกย่องให้ทัวริงเป็นบิดาของวิทยาการคอมพิวเตอร์) ปลายปีนั้นเองเขาก็ได้รับรางวัลสมิธ (Smith's Prize) ไปครอง |
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แล้วเขาก็ไปทำปริญญาโทและปริญญาเอกต่อที่ศูนย์วิจัยของมหาวิทยาลัยปรินซ์ตัน ซึ่งสงบเงียบตัดห่างจากผู้คน แล้วก็ออกบทความว่า โลกทางความคิดกับโลกทางกายมันเชื่อมถึงกันได้ ผ่านออกมาด้วยการกระทำ (ในยุคนั้นคนยังไม่คิดแบบนี้กัน) แล้วก็เสนอความคิดออกมาเป็น Universal Turing Machine (เครื่องจักรทัวริง) ในยุคนั้นยังไม่เรียกว่าคอมพิวเตอร์ แต่เรียกว่าเป็นเครื่องคำนวณที่สามารถป้อนข้อมูลได้ ต่อมาทัวริงก็สร้างเครื่องเข้ารหัส (cipher machine) โดยใช้รีเลย์คลื่นแม่เหล็กไฟฟ้า สำหรับการคูณเลขฐานสอง หลังจากเขาสำเร็จการศึกษา มหาวิทยาลัยปรินซ์ตันก็เสนอตำแหน่งให้เขา แต่เขาตัดสินใจกลับเคมบริดจ์ เลยทิ้งทีมเพื่อน ๆ ไว้และจอห์น ฟอน นอยมันน์ก็เข้ามาสานต่อพอดี |
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] | แอลัน ทัวริง
ส่วนตัวทัวริง ก็เลือกไปทำงานด้าน 'ordinal logic' ต่อแทน เพราะเขาบอกว่าเป็น "my most difficult and deepest mathematical work, was an attempt to bring some kind of order to the realm of the uncomputable" เพราะทัวริงเชื่อว่าคนเรา โดยสัญชาตญาณสามารถตอบโต้ต่อเหตุการณ์ได้โดยไม่ต้องคำนวณ ("Human 'intuition' could correspond to uncomputable steps in an argument") แต่งานยังไม่เสร็จ ก็มีสงครามโลกครั้งที่สองเสียก่อน คือก่อนหน้านั้นเขาก็ทำงาน (อย่างเป็นความลับ) ให้กับ British Cryptanalytic department (หรือเรียกกันว่า Government code & cypher school) พอสงครามเริ่มเขาเลยเปิดเผยตัวเอง (ปกติจะทำเป็น fellow ที่คิงส์คอลเลจ เคมบริดจ์ อยู่หน้าฉากงานเดียว) เลยออกย้ายไปทำงานที่ the wartime cryptanalytic headquaters, Bletchley Park เป้าหมายคือเจาะรหัสของเครื่องเข้ารหัสอินิกมา (Enigma Cipher Machine) ของเยอรมันให้ได้ |
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] | แอลัน ทัวริง
ช่วงนั้น ทัวริงทำงานกับ W.G. Welchman นักคณิตศาสตร์ชื่อดังของเคมบริดจ์อีกคน (คนนี้ทำ critical factors, ทัวริงทำ machanisation of subtle logical deduction) ทัวริงบอกว่าเขาเจาะรหัสได้แล้วคร่าว ๆ ในปี ค.ศ. 1939 แต่ต้องได้เครื่องอินิกมา มาวิเคราะห์การคำนวณทางสถิติเป็นขั้นสุดท้ายก่อน แล้วทุกอย่างจะออกหมด แต่ต้องรอถึงปี ค.ศ. 1942 ที่เรือดำน้ำ U-boat ของสหรัฐไปยึดมาได้ และแล้วหลังจากนั้นอีนิกมาก็ไม่มีความหมายอีกต่อไป |
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] | แอลัน ทัวริง
พอสงครามโลกครั้งที่สองเริ่มสงบปี ค.ศ. 1944 ทัวริงก็เริ่มสานต่อโครงการเก่าตั้งชื่อ "Buiding the Brain" แต่ตัดสินใจล้มโครงการไปในปี ค.ศ. 1945 พอได้ข่าวว่าจอห์น ฟอน นอยมันน์ออกบทความเรื่อง EDVAC ออกมาจากฝั่งอเมริกา |
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] | แอลัน ทัวริง
ปี ค.ศ. 1946 ทัวริงกลับมาดูงานใหม่ ก็พบว่าเป็นงานคนละแนวคิดกัน ทางอเมริกาเน้นด้านอิเลกทรอนิกส์ แต่ทัวริงคิดแบบคณิตศาสตร์ ("I would like to implement arithmetical functions by programming rather than by building in electronic components, a concept different from that of the American-derived designs). โครงการตอนนั้นของทัวริงคือเครื่องคำนวณ (computation machine) ที่สามารถเปลี่ยนได้ตามใจชอบจาก numerical work เป็น algebra เป็น code breaking เป็น file handling หรือแม้กระทั่งเกมส์. ปี ค.ศ. 1947 ทัวริงเสนอว่า ต้องมีระบบจัดเก็บข้อมูล และ ชุดคำสั่งคอมพิวเตอร์ต้องขยายตัวเองออกเป็น ชุดคำสั่งย่อย ๆ ได้ โดยการใช้รูปย่อแบบ รหัสย่อ (คำสั่ง ซึ่งเป็นจุดเริ่มต้นของภาษาโปรแกรม) แต่ปรากฏว่าไม่ได้รับการสนันสนุน |
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] | แอลัน ทัวริง
มหาวิทยาลัยเคมบริดจ์ ยังคงเสนอตำแหน่งให้เขา แต่ทัวริงตัดสินใจเปลี่ยนสายขอพัก ไม่ทำด้านคณิตศาสตร์ ไม่ทำด้านเทคโนโลยี แต่ไปทำเรื่อง neurology กับ physiology sciences แทน แล้วก็ออกบทความเรื่องเครือข่ายประสาท ขึ้นมาว่า "a sufficiently complex mechanical system could exhibit learning ability" แล้วส่งบทความไปตีพิมพ์กับ NPL แต่ NPL ก็ทำงานช้า... อยู่ ๆ ทีมนักวิจัยที่เคมบริดจ์เอง (สมัยนั้นยังชื่อ Mathematical Laboratory อยู่ ยังไม่ได้เปลี่ยนเป็น Computer Laboratory) ก็ผลิตเครื่อง EDSAC ขึ้นมา (เป็นเครื่อง storage computer machine เครื่องแรก) โดยใช้หลักของชาร์ล แบบเบจ พร้อมๆ กับ มหาวิทยาลัยแมนเชสเตอร์ ได้ทีมของทัวริงไปทำเครื่องในแนวทัวริงได้สำเร็จ |
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] | แอลัน ทัวริง
ทัวริงเลยขี้เกียจยุ่งเรื่องการแข่งขันผลงานทางวิทยาศาสตร์ (ช่วงนั้นผลิตกันเร็วมาก) เลยไปวิ่งแข่งแทน เพราะเวลาที่เขาวิ่งในปี ค.ศ. 1946 นั้น ทำให้เขามีสิทธิ์ลุ้นเหรียญทองวิ่งมาราธอนโอลิมปิก แต่โชคร้ายเขาประสบอุบัติเหตุรถยนต์ก่อน เลยไม่สามารถไปแข่งโอลิมปิกในปี ค.ศ. 1948 ได้ (ในปีนั้นคนที่ได้เหรียญเงินเวลารวมก็แพ้ทัวริง) สุดท้ายทัวริงก็เลยตัดสินใจกลับเคมบริดจ์ ผ่านไประยะนึง ทีมงานเก่าเขาที่ย้ายไปมหาวิทยาลัยแมนเชสเตอร์ ก็เชิญเขาไปเป็นหัวหน้าภาควิชาใหม่ (ภาควิชาคอมพิวเตอร์) ทัวริงเลยตัดสินใจย้ายไป คราวนี้ไปเน้นด้านซอฟต์แวร์ ออกบทความวิชาการชื่อดังอีกอันในยุคนั้น "Computer Machine and Intelligence" ในปี ค.ศ. 1950 ซึ่งเป็นรากฐานของแนวคิดพัฒนา ปัญญาประดิษฐ์ ในวงการคอมพิวเตอร์ |
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] | แอลัน ทัวริง
ปี ค.ศ. 1951 เขาก็จับงานใหม่อีกเล่นอีกแนว morphogenetic theory ออกบทความเรื่อง "The Chemical Basis of Morphogenesis" ซึ่งต่อมาเป็น founding paper of modern non-linear dynamical theory (พวก pattern formation of instability into the realm of spherical objects, e.g. radiolaria, cylinder, model of plant stems) |
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] | แอลัน ทัวริง
ในปี ค.ศ. 1952 เขาถูกจับ โทษฐานมีเพศสัมพันธ์กับผู้ชาย ทัวริงไม่ปฏิเสธและยอมรับโทษแต่โดยดี มีทางเลือกให้เขาสองทางคือ จำคุกกับการฉีดฮอร์โมนเอสโตรเจนเป็นเวลาหนึ่งปีเพื่อลดความต้องการทางเพศ ซึ่งเขาเลือกที่จะรับการฉีดยา และแล้วปี ค.ศ. 1954 ร่างของทัวริงก็ถูกพบโดยพนักงานทำความสะอาด ในสภาพมีแอปเปิลครึ่งลูกหล่นอยู่ข้าง ๆ และมีร่องรอยการทำการทดลองทางเคมีอยู่ใกล้ ๆ ในที่สุดเมื่อวันที่ 10 กันยายน ค.ศ. 2009 หลังจากการรณรงค์ทางอินเทอร์เน็ต กอร์ดอน บราวน์นายกรัฐมนตรีแห่งสหราชอาณาจักรก็ทำการขอโทษอย่างเป็นทางการในนามของรัฐบาลบริติชต่อวิธีอันไม่ถูกต้องที่รัฐบาลปฏิบัติต่อทัวริงหลังสงคราม |
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] | แอลัน ทัวริง
หลายปีต่อมา มีการเปิดเผยขึ้นมาว่า ตั้งแต่สงครามโลกครั้งที่สองสงบลง เขายังคงทำงานให้กับองค์การ 'รหัสลับ' แบบลับ ๆ ของรัฐบาลอยู่ อยู่ในสภาพที่ไม่สามารถบอกเพื่อน ๆ ได้ว่าทำอะไรบ้าง และปิดบังมาตลอด ช่วงนั้นกำลังมีสงครามเย็น สหราชอาณาจักรกับสหรัฐอเมริกาเป็นพันธมิตรกัน สู้กับยุโรปตะวันออก, แต่เพื่อนชาวยุโรปตะวันออก ที่เคยร่วมงานกันมาก่อนพยายามติดต่อตัวเขา เช่นในปี ค.ศ. 1953 เพื่อนเขาชาวนอร์เวย์ (เป็นสังคมนิยม) ถึงกับมาเยี่ยม ขณะที่เขากำลังพักผ่อนอยู่ที่ประเทศกรีซ ทำให้พอเขากลับมาถึงอังกฤษ ก็ถูกเรียกไปคุยกับเจ้าหน้าที่ความมั่นคง แต่ก็ไม่มีใครรู้ว่าจริง ๆ แล้วมันเกิดเรื่องอะไรและมีเบื้องหลังอย่างไร |
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สำหรับผลงานที่เด่น ๆ ของทัวริง เช่น การคิดโมเดลที่สามารถทำงานได้เทียบเท่ากับคอมพิวเตอร์ (แต่อาจมีความเร็วต่ำกว่า) โดยใช้คำสั่งพื้นฐานง่าย ๆ เพียง เดินหน้า ถอยหลัง เขียน ลบ |
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คอมพิวเตอร์วิทัศน์ () เป็นสาขาหนึ่งของวิทยาการคอมพิวเตอร์ ว่าด้วยเรื่องเกี่ยวกับการดึงสารสนเทศจากรูปภาพหรือวีดิทัศน์ เครื่องมือที่ใช้ในคอมพิวเตอร์วิทัศน์ได้แก่ คณิตศาสตร์โดยเฉพาะ เรขาคณิต พีชคณิตเชิงเส้น สถิติ และ การวิจัยดำเนินงาน (การหาค่าเหมาะที่สุด) และการวิเคราะห์เชิงฟังก์ชัน โดยเครื่องมือเหล่านี้ใช้ในการสร้างขั้นตอนวิธีหรือ ขั้นตอนวิธี ในการแยกส่วนภาพ และ การจัดกลุ่มภาพเพือให้คอมพิวเตอร์สามารถ "เข้าใจ" ทัศนียภาพ หรือคุณลักษณะต่าง ๆ ในภาพ |
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เป้าหมายโดยทั่วไปของคอมพิวเตอร์วิทัศน์ได้แก่ |
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เพื่อที่จะบรรลุซึ่งเป้าหมายเหล่านี้ ระบบคอมพิวเตอร์วิทัศน์ จะต้องใช้กระบวนการต่างๆ เช่น การรู้จำแบบ การเรียนรู้เชิงสถิติ เรขาคณิตเชิงภาพฉาย การประมวลผลภาพ ทฤษฎีกราฟ และอื่น ๆ |
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คอมพิวเตอร์วิทัศน์การรับรู้ นั้น เกี่ยวข้องอย่างใกล้ชิดกับ จิตวิทยาการรับรู้ และ การคำนวณทางชีวภาพ |
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การประยุกต์ใช้คอมพิวเตอร์วิชั่นอันหนึ่งที่น่าสนใจ ได้แก่ การสร้างปรากฏการลวงตาต่าง ๆ ในภาพยนตร์ ปัจจุบัน เราจะพบการประยุกต์ใช้ คอมพิวเตอร์วิทัศน์ในสาขาต่าง ๆ เช่น การแพทย์ การทหาร ระบบตรวจตราและรักษาความปลอดภัย การตรวจสอบและควบคุมคุณภาพ ระบบหุ่นยนต์ รถยนต์ และอื่น ๆ |
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ในปัจจุบัน เครื่องจักรวิทัศน์ และ การจัดการรูปภาพทางการแพทย์ ที่ใช้วิธีการต่าง ๆ ทางคอมพิวเตอร์วิทัศน์ ได้รับการพัฒนา และ จัดจำหน่าย ในตลาดโลก คิดรวมเป็นมูลค่า หลายหมื่นล้านบาทต่อปี |
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] | ภาพลีนา
ภาพลีนา เป็นส่วนของภาพหน้ากลาง ของ Lena Soderberg ที่รู้จักกันดี และ ใช้กันอย่างกว้างขวาง เรียกได้ว่าเป็นภาพมาตรฐานในวงการการประมวลผลภาพดิจิทัล เลยก็ว่าได้ ผู้ใช้รูปนี้เป็นส่วนใหญ่ก็ไม่ได้รับรู้ที่มาของรูปนี้แต่อย่างใด รูปนี้ได้ถูกใช้และตีพิมพ์ ในผลงานทางวิชาการอย่างกว้างขวาง อยู่เป็นเวลานาน |
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] | ภาพลีนา
ที่มาของรูปนี้เป็นรูปของ Lena Soderberg (ne Sjööblom) ชาวสวีเดน ซึ่งปรากฏ ในหน้ากลางของ นิตยสารเพลย์บอย ในปี 1972 และภาพนี้ได้ถูก ดิจิไตซ์ ที่ Signal and Image Processing Institute (SIPI) มหาวิทยาลัยเซาเทิร์นแคลิฟอร์เนีย โดย Alexander Sawchuk ซึ่งเป็น ผู้ช่วยศาสตราจารย์ในขณะนั้น |
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] | ภาพลีนา
จาก บทความ ของ Jamie Hutchinson ใน Newsletter ของ IEEE Professional Communication Society :
" ในปี 1973 นั้น ในขณะที่ Alexander Sawchuk กับนักเรียนในระดับบัณฑิตศึกษาของเขา กำลังง่วนหาภาพดี ๆ เพื่อที่จะ สแกนไปใช้ลงในงานตีพิมพ์สัมนาของเพื่อนร่วมงาน หลังจากที่ได้พยายามหาจากภาพที่มีอยู่ ก็มีแต่ภาพที่ไม่เร้าใจ ภาพที่เค้ามองหาอยู่นั้น จะเป็นภาพหน้าคน สี กระดาษผิวมัน เพื่อให้เห็นความแตกต่างของระดับแสงสีที่ดี ก็พอดีมีคนเดินถือ นิตยสารเพลย์บอยฉบับใหม่เข้ามาพอดี พวกเขาก็เลยตัดเอาภาพท่อนบนจากหน้ากลาง เนื่องจากเขาต้องการภาพขนาด 512*512 และขึดความสามารถของ สแกนเนอร์ ทีใช้นั้นซึ่งสแกนได้ 100 เส้นต่อนิ้ว จึงตัดได้ภาพขนาด 5.12 นิ้ว ลงมาถึงหัวไหล่ของคนในภาพ. หลังจากได้สแกนเสร็จก็ปรากฏว่าภาพไม่สมบูรณ์ ขาดหายไป 1 เส้น แต่เนื่องจากมีเวลาจำกัด จีงตัดสินใจใช้ภาพนั้นโดยทำการเพิ่มเส้นให้ครบโดยการคัดลอกเอาจากเส้นถัดไป หลังจากเสร็จ ก็ไม่ได้มีความคิดใดๆว่าภาพที่ได้จะกลายมาเป็น หนึ่งในภาพมาตรฐานที่ใช้ในการทดสอบ. Sawchuk จำได้ว่า ทางกลุ่มได้แจกจ่ายรูปให้กับผู้ที่มาเยี่ยมเยือนที่ขอไป เพื่อจุดประสงค์ที่จะได้ทำการเปรียบเทียบผลลัพธ์ของขั้นตอนวิธีในการประมวลผลภาพได้ ซึ่งในที่สุดภาพนี้ก็ได้แพร่หลายเป็นที่นิยมใช้อย่างกว้างขวาง " |
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จนในภายหลังที่ได้รู้ถึงที่มาของภาพกันอย่างกว้างขวาง ก็เกิดเป็นกรณีโต้แย้ง ว่าไม่เหมาะสมที่จะใช้ภาพนี้เนื่องจากที่มาของภาพ และ การที่เพลย์บอย ก็ได้มีความพยายามจะฟ้องร้องเรื่องสิทธิการใช้ภาพ |
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] | ภาพลีนา
คุณลีนา (ตัวจริง เสียงจริง) ได้ไปร่วม the 50th Anniversary IS&T conference ใน Boston จัดขึ้นในเดือน พฤษภาคม 1997
ชื่อลีนา ในภาษาสวีเดน ใช้คำว่า Lena แต่ในภาษาอังกฤษที่ลงในหนังสือเพลย์บอยใช้คำว่า Lenna |
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การประมวลผลภาพ () คือ เป็นการประยุกต์ใช้งานการประมวลผลสัญญาณบนสัญญาณ 2 มิติ เช่น ภาพนิ่ง (ภาพถ่าย) หรือภาพวีดิทัศน์ (วิดีโอ) และยังรวมถึงสัญญาณ 2 มิติอื่น ๆ ที่ไม่ใช่ภาพด้วย |
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] | การประมวลผลภาพ
แนวความคิดและเทคนิค ในการประมวลผลสัญญาณ สำหรับสัญญาณ 1 มิตินั้น สามารถปรับมาใช้กับภาพได้ไม่ยาก แต่นอกเหนือจาก เทคนิคจากการประมวลผลสัญญาณแล้ว การประมวลผลภาพก็มีเทคนิคและแนวความคิดที่เฉพาะ (เช่น connectivity และ rotation invariance) ซึ่งจะมีความหมายกับสัญญาณ 2 มิติเท่านั้น แต่อย่างไรก็ตามเทคนิคบางอย่าง จากการประมวลผลสัญญาณใน 1 มิติ จะค่อนข้างซับซ้อนเมื่อนำมาใช้กับ 2 มิติ |
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เมื่อหลายสิบปีมาแล้ว การประมวลผลภาพนั้น จะอยู่ในรูปของการประมวลผลสัญญาณแอนะล็อก (analog) โดยใช้อุปกรณ์ปรับแต่งแสง (optics) ซึ่งวิธีเหล่านั้นก็ไม่ได้หายสาบสูญ หรือเลิกใช้ไป ยังมีใช้เป็นส่วนสำคัญ สำหรับการประยุกต์ใช้งานบางอย่าง เช่น ฮอโลกราฟี (holography) แต่เนื่องจากอุปกรณ์คอมพิวเตอร์ในปัจจุบัน ราคาถูกลง และเร็วขึ้นมาก การประมวลผลภาพดิจิทัล (digital image processing) จึงได้รับความนิยมมากกว่า เพราะการประมวลผลที่ทำได้ซับซ้อนขึ้น แม่นยำ และง่ายในการลงมือปฏิบัติ |
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การประมวลผลภาพดิจิทัล () เป็นสาขาที่กล่าวถึงเทคนิคและขั้นตอนวิธีต่าง ๆ ที่ใช้การประมวลผลภาพที่อยู่ในรูปแบบดิจิทัล (ภาพดิจิทัล) |
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ภาพในที่นี้ รวมความหมายถึงสัญญาณดิจิทัลใน 2 มิติอื่น ๆ โดยทั่วไปคำนี้เมื่อใช้อย่างกว้าง ๆ จะครอบคลุมถึงสัญญาณวิดีโอ (video) หรือภาพเคลื่อนไหว ซึ่งจะเป็นชุดของภาพนิ่ง เรียกว่า เฟรม (frame) หลาย ๆ ภาพต่อกันไปตามเวลา |
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ซึ่งก็คือสัญญาณ 3 มิติ เมื่อนับเวลาเป็นมิติที่ 3 หรือ อาจจะครอบคลุมถึงสัญญาณ 3 มิติอื่น ๆ เช่น ภาพ 3 มิติทางการแพทย์ หรือ อาจจะมากกว่านั้น เช่น ภาพ 3 มิติ และ หลายชนิด (multimodal image) |
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0.02659556455910206
] | กราฟบริบูรณ์
กราฟบริบูรณ์ (complete graph) เป็น กราฟ ที่ทุกคู่ของ จุดยอด ถูกเชื่อมต่อด้วย เส้นเชื่อม เป็น กราฟสม่ำเสมอ ที่มีระดับขั้น formula_1 กราฟบริบูรณ์บนจุดยอด formula_2 จุด ใช้สัญลักษณ์ formula_3, มี formula_2 จุดยอด, และ formula_5 เส้นเชื่อม |
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ไดกราฟบริบูรณ์ (complete digraph) ก็เป็นลักษณะเดียวกับกราฟ ต่างกันที่เส้นเชื่อมแต่ละเส้น จะถูกแทนด้วยเป็นเส้นเชื่อมระบุทิศทาง 2 เส้น ในทิศทางตรงข้ามกัน |
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] | จอห์น ฟอน นอยมันน์
จอห์น ฟอน นอยมันน์ (John von Neumann, Neumann János, 28 ธ.ค. ค.ศ. 1903 - 8 ก.พ. ค.ศ. 1957) เป็นนักคณิตศาสตร์ชาวอเมริกันเชื้อสายฮังการี มีผลงานสำคัญในหลายสาขา ทั้ง ควอนตัมฟิสิกส์ วิทยาการคอมพิวเตอร์ และ จะว่าไปแล้วก็ทุกๆ สาขาในวิชาคณิตศาสตร์ เลยก็ว่าได้ |
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เขาเป็นบุตรชายคนโต ในพี่น้อง 3 คน ชื่อเดิมของนอยมันน์ คือ János Lajos Margittai Neumann เกิดที่เมืองบูดาเปส บิดาคือ Neumann Miksa (Max Neumann) เป็นนักการธนาคาร และ มารดาคือ Kann Margit (Margaret Kann) นอยมันน์มีชื่อเล่น ว่า "Jancsi" เขาเติบโตมาในครอบครัวชาวยิวที่ไม่เคร่งครัด และได้แสดงถึงความจำที่เป็นเลิศ มาตั้งแต่ยังเป็นเด็ก โดยสามารถทำการหารเลข 8 หลักในใจได้ตอนอายุ 6 ปี. ในปี ค.ศ. 1911 ก็เข้าเรียนที่ Lutheran Gymnasium (ในประเทศเยอรมนี, gymnasium หมายถึง โรงเรียนมัธยมปลาย) พอปี ค.ศ. 1913 เนื่องจากคุณพ่อของเขาได้รับตำแหน่ง (ยศ) เขาจึงได้รับชื่อในภาษาเยอรมัน von จึงใช้ชื่อเต็มเป็น János von Neumann |
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เขาเรียนจบปริญญาเอกสาขาคณิตศาสตร์ จาก มหาวิทยาลัยบูดาเปส ประเทศฮังการี ตอนอายุ 23 ปี |
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] | จอห์น ฟอน นอยมันน์
ระหว่างปี ค.ศ. 1926 ถึง 1930 เขาทำงานเป็น "อาจารย์อิสระ" ("Privatdozent" เป็นตำแหน่งในระบบมหาวิทยาลัยยุโรป สำหรับผู้ที่ต้องการจะเป็นศาสตราจารย์มหาวิทยาลัย ตำแหน่งนี้ไม่มีเงินเดือนประจำ) โดยในขณะนั้นเขาเป็นอาจารย์อิสระที่อายุน้อยที่สุดมหาวิทยาลัยเบอร์ลิน ประเทศเยอรมนี |
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] | จอห์น ฟอน นอยมันน์
ในปี ค.ศ. 1930 นอยมันน์ได้รับเชิญให้ไปยังเมืองพรินซ์ตัน, รัฐนิวเจอร์ซีย์ และได้เป็นหนึ่งในหกบุคคล
(J. W. Alexander, อัลเบิร์ต ไอน์สไตน์, Marston Morse, Oswald Veblen, จอห์น ฟอน นอยมันน์ และ Hermann Weyl) ที่ถูกคัดเลือกเพื่อเป็นอาจารย์ประจำชุดแรกของ Institute for Advanced Study เขาเป็นศาสตราจารย์คณิตศาสตร์ที่นั่น ตั้งแต่เริ่มก่อตั้งสาขาวิชาในปี ค.ศ. 1933 จนกระทั่งวาระสุดท้ายของชีวิตเขา |
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] | จอห์น ฟอน นอยมันน์
ในช่วงสงครามโลกครั้งที่สอง นอยมันน์ได้มีส่วนร่วมใน โครงการแมนฮัตตัน (Manhattan Project) ซึ่งเป็นโครงการสร้างระเบิดปรมาณู |
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] | จอห์น ฟอน นอยมันน์
ช่วง ค.ศ. 1936 จนถึง 1938 แอลัน ทัวริง ได้เป็นนักเรียนแลกเปลี่ยนไปที่สถาบัน และเรียนจบปริญญาเอก โดยมีนอยมันน์เป็นอาจารย์ที่ปรึกษา การไปเป็นนักเรียนแลกเปลี่ยนครั้งนี้ของทัวริง เกิดขึ้นหลักจากที่เขาได้ดีพิมพ์บทความวิชาการ "On Computable Numbers with an Application to the Entscheidungs-problem" ในปี ค.ศ. 1934 ได้ไม่นาน. งานตีพิมพ์นี้ เกี่ยวข้องกับ หลักการของ logical design และ universal machine. ถึงแม้จะเป็นที่แน่ชัดว่า นอยแมนรู้ถึงแนวความคิดของทัวริง แต่ก็ไม่เป็นที่แน่ชัดว่า เขาได้ใช้หลักการของทัวริง ในการออกแบบเครื่อง IAS ที่ถูกสร้างในเวลา 10 ปีต่อมา |
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] | จอห์น ฟอน นอยมันน์
นอยมันน์นั้น ได้รับการขนานนามว่าเป็น บิดาของทฤษฎีเกม (game theory). เขาได้ตีพิมพ์หนังสือ "Theory of Games and Economic Behavior" โดยร่วมเขียนกับ Oskar Morgenstern ในปี ค.ศ. 1944 เขาได้คิดหลักการ "MAD" (mutually assured destruction) ซึ่งเทียบเท่าสำนวนจีนว่า "หยกกระเบื้องล้วนแหลกราญ" หรืออาจแปลไทยได้เป็น "รับรองได้ว่าเจ๊งไปด้วยกันทั้งคู่แน่" ซึ่งเป็นหลักการซึ่งใช้เป็นหลักสำคัญ ในการวางแผนกลยุทธ์ทางด้านอาวุธนิวเคลียร์ของอเมริกา ในช่วงสงครามเย็น |
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นอยมันน์เป็นคนคิด สถาปัตยกรรมแบบ ฟอน นอยมันน์ ซึ่งใช้กันในคอมพิวเตอร์ (แบบที่ไม่ได้ประมวลผลแบบขนาน) ส่วนใหญ่ พูดได้ว่า คอมพิวเตอร์เกือบทั้งหมดในโลกนี้ เป็นเครื่องจักรแบบ ฟอน นอยมันน์ เขาเป็นผู้ริเริ่มสาขา cellular automata และได้สร้างตัวอย่างชุดแรกของ self-replicating automata โดยใช้แค่กระดาษกราฟ กับ ดินสอธรรมดาๆ (ไม่มีคอมพิวเตอร์ช่วยเลย) คำว่า เครื่องจักรแบบ ฟอน นอยมันน์ ยังหมายความถึง เครื่องจักรที่สร้างตนเองซ้ำได้ (self-replicating machine) |
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นอยมันน์ได้พิสูจน์ว่า การใช้เครื่องจักรที่สร้างตนเองซ้ำได้ เป็นวิธีที่มีประสิทธิภาพที่สุด ในการทำเหมืองขนาดใหญ่มากๆ อย่างการทำเหมืองบนดวงจันทร์ หรือ แถบดาวเคราะห์น้อย เนื่องจากกลไกแบบนี้จะมีการเติบโตเป็นแบบเลขชี้กำลัง |
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นอยมันน์นับเป็นบุคคลที่ฉลาดล้ำลึก และความจำที่เป็นเลิศเกือบจะเรียกได้ว่า จำได้ทุกอย่าง ในระดับรายละเอียดเลยก็ว่าได้ เขาเป็นคนชอบออกสังคมไม่เก็บตัว ชอบดื่มเหล้า เต้นรำและการเริงรมย์ เป็นคนสนุกสนาน และขบขัน เสียชีวิตที่กรุงวอชิงตัน ดี.ซี. |
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] | จอห์น ฟอน นอยมันน์
จาก การโปรแกรมเชิงเส้น ที่เขียนโดย George B. Dantzig ซึ่งเป็นผู้ที่คิดค้น simplex method ที่ใช้แก้ปัญหาการโปรแกรมเชิงเส้น เขาได้เขียนถึงนอยมันน์ จากประสบการณ์ที่ได้ไปพบและขอคำแนะนำจากนอยมันน์ และยังได้สะท้อนถึงบุคลิกของนอยมันน์ และได้เล่าถึงตอนที่นอยมันน์ได้ช่วยเหลือ โดยการตอบคำถามของ Hotelling (ผู้คิดค้น Principal components analysis) ระหว่างการนำเสนอผลงานการโปรแกรมเชิงเส้นของเขา |
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] | การสร้างภาพเชิง 3 มิติ
การสร้างภาพเชิง 3 มิติ () คือ การหารูปร่างและขนาดของวัตถุใน 3 มิติ โดยเทคนิคของการวัดรูปร่างนี้ จะมีเงื่อนไขจำกัดอยู่ เนื่องจากสิ่งที่ต้องการวัดคือ ขนาดสัมบูรณ์ของวัตถุ เพราะฉะนั้นขนาดของวัตถุที่วัดได้ จะต้องไม่ขึ้นกับชนิดผิวและการสะท้อนของวัตถุ ระยะห่างจากอุปกรณ์เก็บภาพ 3 มิติ และ สภาพแสงและการส่องสว่าง |
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] | การสร้างภาพเชิง 3 มิติ
เทคนิคในการเก็บภาพ 3 มิตินี้ มีอยู่หลายวิธีด้วยกัน ซึ่งแต่ละวิธีก็มีข้อจำกัดที่แตกต่างกันไป อุปกรณ์รับรู้ที่ใช้ในการเก็บภาพ 3 มิตินี้ สามารถแยกกว้างๆ ได้เป็น 3 กลุ่ม คือ |
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] | การสร้างภาพเชิง 3 มิติ
การสามเหลี่ยม เป็นการวัดหาระยะความลึก (depth) ของภาพโดยในการวัดจะมีพื้นฐานมาจาก การตัดกันของแกนอะไรบางอย่างเป็นรูปสามเหลี่ยม เมื่อรวมกับข้อมูลของอุปกรณ์วัด จะทำให้สามารถหาระยะลึกได้ |
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