Designer-Critiqued Comparison of 2D Vector Visualization Methods A Pilot Study

did平行趋势检验时间范围1. 什么是did平行趋势检验？did平行趋势检验（Difference-in-Differences Parallel trend test）是一种经济学中常用的处理因果推断问题的方法。

也被称为事件研究设计或断点回归设计。

这种方法可以通过比较处理组和对照组在时间上的趋势来评估政策、活动或干预措施对所研究的结果变量的影响。

在一个did设计中，研究对象被分成两组：处理组和对照组。

处理组接受了一项特定政策、活动或干预措施，而对照组没有接受该项措施。

通过比较处理组和对照组之间的差异变化，可以确定该措施的效果是否存在。

在did平行趋势检验中，我们假设在措施实施之前，处理组和对照组的趋势是平行的，即两组在措施实施之前的发展趋势相似。

如果这个假设成立，即处理组和对照组没有系统性的差异，那么任何随后的差异可以归因于措施本身。

2. 如何确定did平行趋势检验的时间范围？确定did平行趋势检验的时间范围需要考虑以下因素：2.1 实验前期趋势首先，我们需要检查处理组和对照组在措施实施之前的趋势是否平行。

这可以通过观察两组在措施实施之前的数据来确定。

如果处理组和对照组的趋势在措施实施之前存在显著差异，那么did平行趋势检验可能不适用。

2.2 措施实施时间点确定了实验前期趋势后，我们需要确定措施的实施时间点。

措施的实施时间点应当尽可能明确，确保处理组和对照组在实施前后不存在混淆。

通常，措施的实施时间点应当在处理组和对照组的趋势发生明显改变的时间之前。

2.3 控制时间段在确定了措施的实施时间点后，我们需要确定控制时间段。

控制时间段是指在实施措施之前和实施之后，没有受到干预的时间范围。

这个时间段用来比较处理组和对照组在实施之前和实施之后的变化。

控制时间段的选择应考虑到数据的可用性和趋势的稳定性。

通常，控制时间段应当包含了足够的时间观察期，以确保我们能够捕捉到可能存在的季节性和周期性变化。

3. did平行趋势检验的实施步骤实施did平行趋势检验的基本步骤如下：3.1 数据收集首先，我们需要收集处理组和对照组在措施实施前后的相关数据。

Leveraging Machine Learning -AdWords Smart-BiddingAnnika Weckner, Display Specialist - Central EuropeDenis Dautaj, Search Audience & Automation Specialist - Central Europe121.What makes AdWords Smart Bidding so powerful2.Different Bidding-Strategies to meet your goals3.Smart Bidding improvements based on your needs4.How to successfully test Smart Bidding312AdWords Smart Bidding1.What makes AdWords Smart Bidding so powerful2.Different Bidding-Strategies to meet your goals3.Smart Bidding improvements based on your needs4.How to successfully test Smart Bidding3 5 key things to remember“From Mobile First toAI First”Sundar PichaiCEO Google Inc.OLD TRANSLATIONEnglishNo problem can be solved from the same consciousness that they have arisen.NEW TRANSLATIONEnglish Problems can never be solved with the same way of thinking thatcaused them.GermanProbleme kann man niemals mit derselben Denkweise lösen, durch die sie entstanden sind.AdWords Auction-Time BiddingRule-based Bidding-AdWords automated rules -AdWords ScriptsManual Bidding3rd Party Platform Automated Bidding(1-2 bid refreshes per day on avg.)AdWords Launches ContentNetworkQualityScoreSeparate Bids forContent NetworkAdWordsEditorConversionOptimizer“Mobile Devices WithFull Internet Browsers”SitelinksPLAsClick ToCallGDNRemarketingDSATabletTargetingEnhancedCampaignsRLSAReviewExtensionsCross-DeviceConversionsShoppingCampaignsLocationExtensionsAdCustomizersCall-OnlyCampaignsStructuredSnippetsGmail AdsETAsPriceExtensionsNo RHSAdsClick ToMessageCampaignRLSASimilarAudiencesCustomerMatchDFSA200020082016 20042012where we can add valueBiddingAttributionUXTargeting (KWs, Audience)MeasurementTargeting (KWs, Audience)BiddingMeasurementTodayTomorrowCreativesCreativesReportingReportingUXAttribution1Why automation is important21.2.Different Bidding-Strategies to meet your goals3.Smart Bidding improvements based on your needs4.How to successfully test Smart Bidding3 5 key things to rememberBidSIGNALS AVAILABLE WITHBID ADJUSTMENTSEXCLUSIVE SIGNALS FOR ADWORDS AUTOMATEDBIDDINGNoon ESTLocationSmartphoneRemarketinglistOS Ad creativeSearch partnerActual queryLanguageAppBrowserCombinations between 2 or more signals2.0% CVR 4.0% CVRbuy jeansExample, on the keywordvs.query-level biddingDynamic Search Ads (DSA)Manual: website-URL/category -levelAutomated: query -levelGoogle ShoppingManual: product -level Automated: query -levelKeywords (Broad, Phrase)Manual: keyword -level Automated: query -levelKeyword jeansQuery*buy jeans jeans wash jeansUser Behavior ➔Sites previouslyvisited by a user ➔Cross-deviceusage➔Interests➔Time of day andday of weekDemographics➔Age and gender➔Geographiclocation➔Device type➔Browser orOperatingSystemContent of theWebpage Viewed➔Website content,structure, andkeywordsAd Characteristics➔Ad format➔Ad performanceOnsite Behavior➔How recently auser left your site➔How many pagesa user viewed onyour site➔Value of theproducts a userhas viewed onyour siteinfinite permutationsMoments thatmatterPlacement Message Formats Bids30+steps in purchase cycleGoogle RTB analyzes 70 million unique signals at the exact moment a webpage loads5+ hours per day with digital2M sites650K apps22 creativeson 3 OSs Infinite permutationscall for Automation ∞1Why automation is important21.What makes AdWords Smart Bidding so powerful2.3.Smart Bidding improvements based on your needs4.How to successfully test Smart Bidding3 5 key things to rememberMaximize Clicks Enhanced CPC Target CPA Target ROASTarget Outranking Share Target Search Page LocationVISIBILITYWEBSITE CLICKS CONVERSIONS /SALESREVENUEA range of automation options, aligned to specific marketing goalsCampaign goalRecommended strategyWhat Automatically sets bids during each auction to get you as many conversions as possible within your target CPA goalWhy Get the most conversions at your target CPA through power of auction-time biddingUse Cases ●Advertisers who would like to automatically optimize bids to maximize conversions●Lead generation and ecommerce businessesWhat Automatically adjusts your manual bid up or down based on each click’s likelihood to result in a conversionWhy Retain control of your core bid but get more conversions through eCPC's automatic real time bid adjustmentsUse Cases ●Advertisers who want to set core bid manually or through 3rd Party Bidding Tools with added layer of real time optimization●Lead generation and ecommerce businessesDoes not offer the full power of Target CPA or Target ROAS, as it only works on a limited portion of traffic and adjusts bids from -100% to +30% based on how likely a click is to lead to a conversion.Full case studyResult:CPA:-75%Approach:●Implemented Target CPA●Used range of targeting options on the Google Display Network , in-market audiences, keyword contextual targeting and similar audiencesCPA: -50%Conversions:+66% Used Target CPATime saved:40% Full case study1Why automation is important21.What makes AdWords Smart Bidding so powerful2.Different Bidding-Strategies to meet your goals3.4.How to successfully test Smart Bidding3 5 key things to rememberMore predictivesignals Better target accuracyBefore AfterOne target CPA Mobile CPA Desktop CPA Tablet CPAMonitor a bid strategy performance and understand its current status Monitor the performance offlexible bid strategies key KPIsand watch how it improves overtimeUnderstand the strategy statusand potential limitations, thentake actionFind the most profitable targets with Target CPA Bid Simulator Determine the optimalTarget CPA and apply thechange directly in theTarget CPA Simulator tooldata-driven attribution: even more Automation!Optimize towards your chosen attribution model in SearchData-drivenmodelRules-basedmodels1Why automation is important21.What makes AdWords Smart Bidding so powerful2.Different Bidding-Strategies to meet your goals3.Smart Bidding improvements based on your needs4.3 5 key things to rememberMaximize Clicks Enhanced CPC Target CPA Target ROASTarget Outranking ShareTarget Search Page LocationVISIBILITYWEBSITE CLICKS CONVERSIONS /SALESREVENUECampaign goalRecommended strategyRecommended conversions*Search Display--<30>30>50--<30>30>8082CURRENT CONVERSIONSCampaign 2100CURRENT CONVERSIONS+30%SIMULATED CONVERSIONUPLIFT %......Campaign 1...+19SIMULATED CONVERSIONUPLIFT+30SIMULATED CONVERSIONUPLIFT 0SIMULATED CPA CHANGE...+23%SIMULATED CONVERSIONUPLIFT %+0%SIMULATED CPA CHANGEWe create estimates using your account’s Bid Simulator data .Bid Simulator looks at the specific auctions your accounts participated in during a recent past week to estimate these performance gains.1.Opt-in Target CPA Bid StrategyCPA Target = 30-day CPA avg.Minimum 30 conversionsControl Period 2+ weeksLearning1+ weekRun Test2-4 weeksEvaluate /Adjust2. Pre-Post evaluation(Ignore “learning” week andmost recent week)3. Potential target adjustment(within +/- 20%)ConversionDelay~1 weekIgnore inevaluation!Ignore inevaluation!Check campaignstatus columnRun well-executed A/B tests with Drafts & ExperimentsEnter a specific date rangeDetermine the portion of trafficyou want to go through theexperimentAssess performance1Why automation is important2AdWords Smart Bidding1.What makes AdWords Smart Bidding so powerful2.Different Bidding-Strategies to meet your goals3.Smart Bidding improvements based on your needs4.How to successfully test Smart Bidding31.T a k e y o u rp h o n e2. G o t o ww w .k a h o o t .i t 3.T y p e i n :01Smart Bidding allows us to shift time to other important tasks02Smart Bidding is the only way to effectively handle infinite data combinations03Get best performance out of your campaigns with Target CPA/ROAS 04Start with targets that align with your historical CPA or ROAS05Successfully test Smart Bidding with clean experimentTHANK YOU! Questions?Find out more at our booth or at:we are Squared .deAre you up for more digital knowledge?Get the full picture with our strategic Digital Marketing and Leadership programThink with Google newsletter.Simply sign up at our booth or at:。

高中英语影视文化阅读理解30题1<背景文章>"Hollywood has produced countless classic movies, and one of them is 'The Godfather'. This film tells the story of the Corleone family, a powerful Mafia clan. The patriarch, Vito Corleone, is a respected and feared figure. His son, Michael, initially reluctant to be involved in the family business, is gradually drawn into the world of crime and power.The plot of the movie is full of twists and turns. It shows the complex relationships within the family, as well as the conflicts between different Mafia families. The theme of the film is about power, family, loyalty, and morality. It explores the dark side of human nature and the consequences of choices.The main characters are vividly portrayed. Vito Corleone is wise and cunning, while Michael is intelligent and determined. The movie also features a cast of supporting characters, each with their own motives and agendas.'The Godfather' has had a profound impact on audiences. It is regarded as one of the greatest movies of all time. It has influenced countless filmmakers and has become a cultural icon."1. The movie 'The Godfather' is mainly about ____.A. love and friendshipB. power, family, loyalty and moralityC. adventure and excitementD. comedy and humor答案：B。

胡小霞，邓丽娟，刘睿婷，等. 基于主成分分析的大蒜药用质量评价[J]. 食品工业科技，2023，44（12）：293−299. doi:10.13386/j.issn1002-0306.2022080237HU Xiaoxia, DENG Lijuan, LIU Ruiting, et al. Evaluation of Medicinal Quality of Garlic Based on Principal Component Analysis[J].Science and Technology of Food Industry, 2023, 44(12): 293−299. (in Chinese with English abstract). doi: 10.13386/j.issn1002-0306.2022080237· 分析检测 ·基于主成分分析的大蒜药用质量评价胡小霞1，邓丽娟2，刘睿婷3,4，史荣梅3,5,*（1.乌鲁木齐海关技术中心，新疆乌鲁木齐 830063；2.天康生物制药有限公司，新疆乌鲁木齐 830026；3.新疆医科大学药学院，新疆乌鲁木齐 830011；4.新疆胡蒜研究院（有限公司），新疆乌鲁木齐 830013；5.新疆大蒜药用研究重点实验室，新疆乌鲁木齐 830013）摘　要：通过比较分析大蒜的药用品质，建立大蒜药用质量评价体系。

以水分、灰分、水溶性浸出物、大蒜素含量、蒜氨酸含量、大蒜辣素含量和蒜酶活力为指标，分析甘肃民乐、江苏邳州、山东金乡、河南郑州、重庆巫溪和新疆且末、拜城、种马场、虎头镇、大有镇、新地乡等11个产地大蒜的药用品质特征及差异，并通过相关性分析、主成分分析和聚类分析对大蒜质量进行综合评价。

结果表明，不同产地大蒜的上述指标都具有显著性差异。

相关性分析表明，蒜酶活力与水分呈极显著正相关性（P <0.01），蒜氨酸含量与灰分和大蒜辣素含量呈显著正相关性（P <0.05）。

英语美文—双语·1. 女人一生中最重要的一双鞋Avery has fallen head over heels for shoes. And not just any shoes. Stilettos are what make her go weak at the knees .艾弗里对于鞋子可谓情有独钟，但并非所有的鞋都能投其所好，细高跟鞋才是她的最爱。

Ms Avery wears "all different types and colours of heels".艾弗里小姐则尝试过“各种款式和颜色的高跟鞋”。

Her favourite is a pair of leopard-print, peep-toe heels from Australian designer Leona Edmiston, but the brand favoured by more than any other of those surveyed was ManoloBlahnik.其中，她最喜欢的是由澳大利亚设计师莉澳娜·爱德米斯顿设计的一双豹纹露趾高跟鞋。

但据调查，最受女性青睐的鞋品牌是莫罗·伯拉尼克。

Favoured by shoe-crazed Carrie Bradshaw of Sex And The City fame, ManoloBlahniks are famous for their sleek lines, not comfort levels.《欲望都市》中“嗜鞋如命”的卡莉·布拉德肖对莫罗·伯拉尼克牌高跟鞋也是钟爱有加。

这个品牌高跟鞋的最大亮点是它优美的弧线，而非舒适度。

The 21-year-old owns "about 30" pairs of heels, but she is by no means a rarity: a survey of more than 450 Australian women found 32 per cent owned between 26 and 50 pairs of heels, while 31 per cent owned between 11 and 25 pairs.21岁的艾弗里有“大约30双”高跟鞋，但她绝对算不上另类。

写一篇关于选择大学专业的英语作文全文共6篇示例，供读者参考篇1Picking My Future CareerHi there! My name is Tommy and I'm 10 years old. I'm in 5th grade and I love learning about all sorts of things at school. My favorite subjects are science, math, and reading. I can't wait until I'm older and get to go to college!College seems like a really fun place to learn. I've heard there are lots of different subjects you can study and pick a major in. A major is kind of like your favorite subject that you want to focus on and learn the most about. Then after college, you can get a job using what you learned in your major. Pretty cool, right?I've been thinking a lot lately about what kind of major I might want to pick when I get to college. I have so many interests that it's hard to choose! I really love science and doing experiments. Maybe I could study something like biology or chemistry. Learning about how things work and making discoveries sounds awesome.Or I could study math and learn all about numbers, equations, and problem-solving. Math can be challenging but I like trying to figure things out. Plus math is used for lots of different jobs like engineering, finance, and computer science. Those all seem interesting too!Then again, I'm a really good reader and enjoy writing stories and essays. Studying English literature or creative writing could allow me to improve my skills and maybe even write books someday. How fun would that be?!No matter what though, I know it's important to pick something that really fascinates me. Because if I find my classes boring, it will be hard to stay focused and do well. And doing well in college is crucial so I can get my dream job after graduating!I have a few ideas of careers that appeal to me right now. Being a scientist and making new discoveries sounds super cool. Or I could be an author or journalist and write books and articles for people to read. Math genius is another option - those people help invent incredible new technologies. Teaching could be neat too, since I'd get to share knowledge with students like how my teachers help me learn.Honestly though, at 10 years old, I'm really not 100% sure yet what I want to be when I grow up. My interests seem tochange every few months! That's okay though, because I have plenty of time to figure it out.For now, I'm just going to keep exploring different topics, trying new activities, and finding what sparks excitement and curiosity in me. If I study hard in school, get good grades, and stay open-minded about options, I'm sure I'll end up finding that perfect college major that fits my skills and passions. Then I can have a career doing something I absolutely love!No matter what though, the most important thing is choosing a path that makes me happy. A job is a huge part of life, so I want to spend my time doing work that is meaningful and fulfilling to me. As long as I follow my heart and keep working hard, I'm confident the right opportunity will come my way.Phew, thinking about majors and careers is exciting but also a little overwhelming! I've got several more years before I need to make any big decisions though. For now, I'm just going to enjoy being a kid. Who knows, maybe I'll change my mind a thousand times before college! I'll stay curious, have fun, and not worry too much about the future just yet. This is just the very start of my journey!篇2Choosing My College MajorHi there! My name is Timmy and I'm 8 years old. I know I'm just a kid, but I've been thinking a lot about what I want to study when I go to college one day. It's never too early to start planning for the future, right?My friends and I have had some great discussions during recess about the different college majors we might want to pursue. It's been really fun fantasizing about all the cool jobs we could have when we grow up. I'm going to tell you about some of the majors I'm most interested in right now.One idea I've been tossing around is studying to become a scientist. I love learning about animals, plants, rocks, stars, and everything else in nature. My favorite subject in school is science because I get to do lots of hands-on experiments and projects. Just the other day, we got to dissect a frog, which was totally awesome and gross at the same time!If I major in science, I could become a marine biologist and study all the amazing creatures that live in the oceans. Can you imagine getting to swim with whales and dolphins every day? That would be a dream job for sure. Or maybe I could be a paleontologist and dig up dinosaur bones. Just thinking about holding a T-Rex skull in my hands gives me goosebumps!Another path I'm considering is majoring in art. I'm a really creative and artistic kid - I love drawing, painting, sculpting with clay, you name it. Whenever we have free time in class, you can usually find me doodling away furiously in my notebook. My teachers are always telling me what a talent I have.If I study art, I could potentially become a world-famous painter or sculptor one day. Can't you see my masterpieces hanging in museums and galleries around the world? Of course, I'd have to get over my fear of putting my work out there for everyone to see and critique. But I figure that by the time I'm an adult, I'll be a lot more confident in myself and my abilities.Then again, the idea of majoring in history is also really appealing to me. You guys know how much I love listening to my grandparents tell stories about what life was like when they were young. Learning about people, cultures, and civilizations from long ago completely fascinates me.As a history major, I could travel all over the world exploring ancient ruins and uncovering artifacts from past eras. Maybe I'd even get to star in my own documentary on the History Channel! How cool would that be? Of course, I'd have to be prepared to spend a lot of time in libraries pouring over old books and records. But honestly, that doesn't sound too bad to me.One major that a lot of my friends seem interested in is business. They all talk about wanting to be wealthy entrepreneurs or CEOs of big companies when they grow up. The idea of majoring in business so I can learn to manage money, market products, and run my own company is kind of intriguing, I have to admit.If I go the business route, I could invent some kind of amazing new product or app and get crazy rich off of it. Then I could spoil myself by buying all the video games, toys, and candy I could ever want! Maybe I'd even be generous enough to share some of my fortune with my family and friends. But who am I kidding? That money would be all mine!I have so many years of school left before I even have to make my final decision on a major. I'm sure my interests and dreams will change and evolve a million times between now and then. But no matter what path I ultimately choose, you can bet I'll put my heart and soul into pursuing it. It's going to be one wild, fun-filled adventure!Well, thanks for letting me share some of my thoughts and aspirations with you all. Now if you'll excuse me, I have a hot date with my Nintendo Switch and a giant bag of gummy worms calling my name. Maybe after demolishing that, I'll feel inspiredto conquer the world as a professional gamer - you never know!A kid can dream, can't he? See ya!篇3Choosing My Future Career: Dreaming Big as a KidHi there! My name is Timmy, and I'm 10 years old. I know it might seem a little early for me to be thinking about college majors and careers, but I'm a pretty ambitious kid with lots of big dreams. My parents always encourage me to start planning for the future, even if my plans might change as I get older.To be honest, I'm not totally sure what career path I want to follow yet. There are just so many cool options out there! But I've been giving it a lot of thought lately, and I think I've narrowed it down to a few top choices.My first idea is to become an astronaut. I've always been fascinated by space and the idea of exploring other planets and galaxies. Can you imagine how amazing it would be to actually travel to Mars or the moon? I could be one of the first humans to set foot on an alien world! Of course, becoming an astronaut is incredibly difficult and competitive. I'd probably need to major in something like aerospace engineering or astrophysics and get really good grades. But hey, a kid can dream, right?Another career that has caught my eye is being a video game designer. I love playing video games, and the idea of actually creating my own games from scratch sounds like a total blast. I could come up with cool new characters, awesome storylines, and mind-blowing graphics. Maybe I'd even get to voice act as one of the characters – how fun would that be? To make it in the gaming industry, I'd likely need to study computer science or something along those lines.My third big idea is to become a marine biologist. The oceans are filled with such incredible and mysterious creatures, and I'd love to dedicate my life to studying and protecting them. Can you imagine getting to swim alongside giant whales or discovering a brand new species of fish? Of course, that would involve a major in marine biology or a related field, and likely a lot of swimming lessons.Those are my top three career paths for now, but who knows – maybe I'll change my mind a hundred times before I actually get to college. For all I know, I could end up wanting to be a chef, an artist, a doctor, or even the president! The world is filled with so many possibilities.No matter what I end up doing, though, I know I'll need to work really hard in school. My parents are always stressing theimportance of getting good grades and applying myself. They want me to choose a career that I'm truly passionate about but that will also allow me to support myself financially. No goofing off or slacking for this kid!I still have plenty of time to figure things out, but it's never too early to start dreaming big. Who knows, maybe in 15 years you'll see me walking on the surface of Mars, or read about the latest smash-hit video game I created, or watch me on TV discussing my latest deep-sea expedition. With hard work and determination, anything is possible.For now, though, I've got to run – my friends and I are going to the park to pretend we're astronauts blasting off into space. Maybe I'll discover some new alien life forms...or at least get some good ideas for that video game I want to make someday. The future is waiting, and I can't wait to make my dreams a reality!篇4Picking My Future Career PathHey there! My name is Timmy and I'm 10 years old. I'm already starting to think about what I want to be when I grow up. There are so many cool jobs out there, it's hard to choose! Myparents and teachers always tell me I should start thinking about potential college majors that could lead to different careers. It's a big decision for a kid like me, but I'm going to share my thought process with you.First off, I really love animals. I can't get enough of watching animal documentaries and reading books about different creatures. I've been begging my parents for a pet dog or cat for years! Because of my love for furry friends, I've thought about maybe becoming a veterinarian when I'm older. That way, I could help sick or injured animals get better. How awesome would it be to cuddle puppies and kittens all day? I could also work at a zoo and get to hangout with exotic animals like lions, zebras and elephants! The potential downside is that I might have to give animals shots, which seems kind of sad. I don't know if I could handle putting them through that pain, even if it's to help them in the long run. So while being a vet sounds fun, I'm not 100% sold on that career yet.Another idea I've had is to become a scientist of some kind. My favorite classes in school are always science-related, especially when we get to do cool experiments. Last year, we made little volcanos out of baking soda and vinegar. It was so much fun watching them erupt! I could definitely see myselfworking in a lab, mixing chemicals and studying interesting phenomena like volcanos, space, animals, you name it. Scientists are always making new discoveries that change the world. However, science seems kind of complicated and math-heavy, which isn't my strongest subject. I struggle with algebra already and I'm only in 4th grade! Maybe I'll feel differently in a few years though.If I'm being totally honest, my biggest passion is sports, especially basketball. I'm always dribbling my ball around the house, much to my parents' annoyance. In my dreams, I become a superstar athlete in the NBA, hitting buzzer-beater shots to win championships. How cool would it be to play professionally and have millions of fans cheering you on? The problem is, not everyone can make it to that elite level. The odds are really stacked against you. Even if I don't go pro, maybe I could still work in sports in some capacity like coaching, training, or sports broadcasting. That way I'd get to be around the game I love every single day. The downside is the pay might not be as high compared to other fields, and I'd have to deal with angry parents if I ever became a coach! It's certainly an appealing option though.Lately, I've also been thinking about politics as a potential path. From watching the news with my parents, it seems like politicians get to make a lot of important decisions that impact millions of people. Just imagine being the President of the United States or a Senator – you'd be one of the most powerful people in the world! If I went into politics, I could try to make the country a better place by improving schools, taking care of the environment, and so on. However, dealing with heated debates and navigating complicated laws doesn't seem very fun at all. Politicians also have to spend a ton of time traveling and being away from family. I'm not sure I'd want that lifestyle. Politics is probably a long shot for me, but maybe I'll change my mind someday.One field I'm almost certainly ruling out is anything in the medical field. I know doctors and nurses help save lives, which is amazing. But whenever I think about blood, needles, or graphic injuries, I start feeling really queasy. I puked the last time I skinned my knee – there's no way I could handle the gross stuff that doctors see on a daily basis! I'll leave that profession to those with stronger stomachs than me.So as you can see, I've got a lot to think about when it comes to choosing a career and college major. I'm just a kid, so mymind still changes constantly. Who knows, maybe I'll discover a new passion in the next few years that puts me on a totally different path. Or I may decide to combine multiple interests by doing something like becoming a scientist who studies animals. The great thing is, I have so many options ahead of me! My parents always tell me to follow my heart and do what makes me happy. As long as I work hard, I'm sure I'll figure out the perfect job for me eventually. I'll just have to wait and see where life takes me. The future is filled with endless possibilities!篇5Choosing My Future College MajorHi, my name is Timmy and I'm in the 5th grade. I may be just a kid, but I've been thinking a lot about what I want to study when I go to college in the future. It's a really big decision that will impact the rest of my life, so I want to make sure I pick the right major!My parents always tell me I should follow my passions and do what makes me happy. Well, I have a lot of interests and things I'm passionate about, so narrowing it down is tough. I love playing video games and I'm really good at them. Maybe I couldstudy computer science or video game design and make my own games one day? That would be awesome!But then again, I'm also obsessed with dinosaurs. I have a huge dino figurine collection and I know all their names and facts about them. Perhaps I could be a paleontologist and study real dinosaur fossils? How cool would it be to discover a new species! Though digging in the dirt all day doesn't sound that fun...Sports are another big passion of mine, especially baseball. I'm the star player on my little league team. Deciding to be a professional baseball player is probably a long shot, but I could major in sports medicine or athletic training. That way I could work with athletes and still be involved with sports. Though I heard you have to take a lot of hard science classes for those majors.My parents want me to be a doctor like my uncle, but I get so squeamish around blood and needles. I don't think I could handle doing surgery or giving shots all day. Yuck! Maybe I'll just skip the medical field entirely to be safe.Then there's my love of art and being creative. Majoring in something like studio art, graphic design, or animation would let me express myself in creative ways. The issue is those careers don't always make a lot of money, and my parents keep saying Ineed to study something "practical" so I can get a good job after college.With so many appealing options, how will I ever decide?! I could try to double major, but that seems like way too much work. I don't want to spend forever in college. Maybe I should just keep an open mind for now and take a bunch of different classes early on to see what I like best.I've got a few years before I need to officially pick a major though. For now, I think I'll focus on trying my best in every subject like math, science, English, history, and so on. Who knows, I might discover a new interest or hidden talent along the way that helps me figure out the perfect major when the time comes.I'll also do lots of research into potential careers and their majors by reading books, watching videos, talking to professionals, and maybe even job shadowing. The more I learn about the options, the easier it will be to determine which path feels right for me.No matter what I choose, I'm sure it will be the right decision as long as I put in the effort to really think it through and pick something I'm genuinely interested in and excited about. Thengetting my degree will be fun instead of hard work. Well, probably still some hard work, but the rewarding kind!I can't wait to start exploring majors and planning for my future career. It's equal parts exciting and scary, but I have plenty of time to figure it all out. For now, I'll keep pursuing all my interests and passions with an open mind. Who knows, maybe I'll event up being a dinosaur video game designer... or a baseball-playing paleontologist! Haha, a kid can dream, right? The possibilities are endless.篇6Picking My Future Career PathHi there! My name is Timmy and I'm 10 years old. I'm in 5th grade and lately I've been thinking a lot about what I want to be when I grow up. It's a really big decision that will shape my whole future! My parents and teachers have been asking me about it, and I know I'll have to pick a major when I go to college someday. There are so many cool options out there, it's hard to choose just one.My best friend Johnny wants to be a doctor. His mom is a nurse and he's been going to the hospital with her since he was little. He loves learning about the human body and how to helppeople get better when they're sick. Johnny is really good at science and math, which I guess you need to be a doctor. I'm not that into those subjects though. I like them okay, but I get bored easily. I'm more of an artsy, creative kid.One career I've thought about is being an author or writer. I love reading stories and getting lost in other worlds. Sometimes I make up my own tales and write them down. My teacher says I have a huge imagination and I'm a great storyteller. Being a writer sounds like a fun job where I could create characters and adventures all day! The downside is that it might be hard to make lots of money. My parents want me to pick a career where I can support myself.Another option could be working with animals. I'm obsessed with my puppy Rufus and all my stuffed animal toys. A few years ago, I really wanted to be a veterinarian when I grew up. That's the doctor for pets, in case you didn't know! I'm not as interested in that anymore though. As much as I love critters, I don't know if I could handle giving them shots or performing surgery. It seems really stressful. Maybe I could work at a pet store or animal shelter instead? That could allow me to play with dogs and cats all day!If I'm being honest, my biggest dream job is becoming a famous actor or singer. How cool would it be to be in movies and on TV shows? Or having my music played on the radio? I could meet celebrities and walk on red carpets. My parents always laugh when I tell them this though. They say it's an extremely competitive field and the odds of "making it big" are very slim. I keep hoping they're wrong because being an entertainer seems like the most fun profession ever!Since I'm pretty athletic, being a professional athlete like a basketball or football player could be an option too. I'd get to play sports for a living and travel around to compete. The potential downside is that sports careers don't last that long compared to other jobs. Players have to retire when they get older due to injuries. Then what would I do after that? Become a coach or commentator maybe? I'm honestly not sure yet.With so many paths to explore, it's overwhelming trying to decide what direction to go in life at such a young age. I know I don't have to figure it all out immediately though. I can keep an open mind and explore different interests over the next few years. Who knows, a career I've never even considered could end up calling my name! Maybe I'll find a way to combine a fewpassions, like being a sports writer or an artist who designs video games.No matter what I choose, I know my parents and teachers will support me. They always say that as long as I work hard and do something I love, they'll be proud of me. I feel really lucky to have so many opportunities ahead. Kids in other countries don't always get the same freedom to pick their own path. I'm going to take advantage of that and have an amazing career...even if I can't decide what that is quite yet! For now, I'll keep dreaming big and see where life takes me.。

Project report about two -dimensional DOA estimation题目：考虑一个20阵元数的双线性均匀线阵，现有三个信源入射，它们的波达方向（DOA ）分别是(10o , 10o ), (20o , 20o ) 和 (30o , 30o )，请用2D -MUSIC 算法，2D -ESPRIT 算法，2D -Capon 算法,2D -PM 算法以及DOA 矩阵方法来估计这些信源的波达方向。

1. 信号接收模型如图1，考虑N 个不同二维DOA (),,1,2,,n n n N θφ=的窄带远场信号()n s t ,在离散时间t 入射有2M 个传感器的双平行均匀线阵时。

x 轴和y 轴上信源的方向矢量分别为：图1()()21sin cos 2sin cos ,1,,,n n n n Tj M d j d x n n e e πθφλπθφθφ-⎡⎤=⎣⎦a （1）()2sin sin ,1n n Tj d y n n e πθφλθφ⎡⎤=⎣⎦a（2）其中λ为波长，d 是阵元间距，x 轴M 个阵元对应方向矩阵为()()()1122,,,,,,x x x x N N θφθφθφ=⎡⎤⎣⎦A a a a ，具体表示为：()()()112211222sin cos 2sin cos 2sin cos 21sin cos 21sin cos 21sin cos 111N NN Nj d j d j d M Nx j M d j M d j M d e e e e e e πθφλπθφλπθφλπθφλπθφλπθφλ⨯---⎡⎤⎢⎥⎢⎥=∈⎢⎥⎢⎥⎢⎥⎣⎦A （3）y 轴2个阵元对应方向矩阵为()()()1122,,,,,,y y y y N N θφθφθφ⎡⎤=⎣⎦A a a a ，具体表示为：112222sin sin 2sin sin 2sin sin 1111N NNy j d j d j d eeeπθφπθφλπθφλ⨯⎡⎤=∈⎢⎥⎣⎦A （4）双平行线阵中子阵列1的接收信号为()()()11x t s t t =+x A n（5）子阵列2的接收信号为()()()22x t t t =+x A Φs n（6）其中()1t n 和()2t n 分别表示子阵列1和2的与信号不相干的加性高斯白噪声，112sin sin 2sin sin ,,N N j d j d diag e e πθφλπθφλ⎡⎤=⎣⎦Φ，()()()11,TN N t s t s t ⨯=∈⎡⎤⎣⎦s 表示信源矢量。

2021年中国研究生数学建模竞赛d题抗乳腺癌候选药物的
优化建模
抗乳腺癌候选药物的优化建模是一个复杂而关键的研究领域。

下面是一些可能用于优化候选药物的建模方法：
1. 分子对接与虚拟筛选：使用计算机模拟技术，预测候选药物与乳腺癌相关靶点之间的结合模式和亲和力。

这有助于筛选出具有潜在抗乳腺癌活性的化合物，并为后续研究提供方向。

2. 三维药物构效关系（3D-QSAR）：通过分析化合物的三维结构与其生物活性之间的关系，建立定量的构效关系模型。

这可以帮助优化候选药物的结构，以提高其针对乳腺癌的活性和选择性。

3. 药物动力学建模：利用数学模型描述候选药物在体内的吸收、分布、代谢和排泄（ADME）过程，预测其在人体内的药物浓度和作用时间。

这有助于设计合适的给药方案，提高药物疗效。

4. 系统生物学建模：将乳腺癌视为一个完整的生物系统，建立数学模型描述其中的分子交互作用、信号传导网络和细胞生理过程。

这可以帮助理解乳腺癌发生和发展的机制，并为优化候选药物的设计提供理论依据。

5. 人工智能和机器学习：利用大数据和机器学习算法，分析乳腺癌患者的临床和基因组学数据，寻找与治疗反应和预后相关的生物标志物。

这可以帮助个体化地选择最佳的抗乳腺癌候选药物。

需要注意的是，以上只是一些常见的优化建模方法，实际研究中可能还会结合其他技术和方法来进行更全面、准确的模拟和优化。

Learning Based Super-Resolution Imaging:Use ofZoom as a CueB.Tech.Project ReportSubmitted in partial fulfillmentof the requirements forB.Tech.DegreeinElectrical EngineeringbyRajkiran Panuganti(99007034)under the guidance ofProf.Subhasis ChaudhuriDepartment of Electrical EngineeringIndian Institute of Technology,BombayApril20032Acceptance CertificateDepartment of Electrical EngineeringIndian Institute of Technology,BombayThe Bachelor of Technology project titled Learning Based Super-Resolution Imaging:Use of Zoom as a Cue and the corresponding report was done by Rajkiran Panuganti(99007034) under my guidance and may be accepted.Date:April16,2003(Prof.Subhasis Chaudhuri)AcknowledgmentI would like to express my sincere gratitude towards Prof.Subhasis Chaudhuri for his invaluable guidance and constant encouragement and Mr.Manjunath Joshi for his help during the course of the project.16th April,2003Rajkiran PanugantiAbstractWe propose a novel technique for super-resolution imaging of a scene from observations at different camera zooms.Given a sequence of images with different zoom factors of a static scene,the problem is to obtain a picture of the entire scene at a resolution corresponding to the most zoomed image in the scene.We not only obtain the super-resolved image for known integer zoom factors,but also for unknown arbitrary zoom factors.In order to achieve that we model the high resolution image as a Markov randomfield(MRF)the parameters of which are learnt from the most zoomed observation.The parameters are estimated using the maximum pseudo-likelihood(MPL)criterion.Assuming that the entire scene can be described by a homogeneous MRF,the learnt model parameters are then used to obtain a maximum aposteriori(MAP)estimate of the high resolutionfield.Since there is no relative motion between the scene and the camera,as is the case with most of the super-resolution techniques, we do away with the correspondence problem.Experimental results on synthetic as well as on real data sets are presented.ContentsAcceptance Certificate iAcknowledgment ii Abstract iii Table of Contents iv 1Introduction1 Introduction1 2Related Work4 Related Work4 3Low Resolution Image Model9 Low Resolution Image Model9 4Super-Resolution Restoration12Super-Resolution Resotoration124.1Image Field Modeling (12)4.2Parameter Learning (14)4.3MAP Restoration (15)4.4Zoom Estimation (16)5Experimental Results19Experimental Results195.1Experimentations with Known,Integer Zoom Factors (19)5.2Experiments with unknown zoom factors (25)5.3Experimental Results when parameters are estimated (28)6Conclusion33 Conclusion33 References34Chapter1IntroductionIn most electronic imaging applications,images with high spatial resolution are desired and often required.A high spatial resolution means that the pixel density in an image is high,and hence there are more details and subtle gray level transitions,which may be critical in various applications.Be it remote sensing,medical imaging,robot vision,industrial inspection or video enhancement(to name a few),operating on high-resolution images leads to a better analysis in the form of lesser misclassification,better fault detection,more true-positives,etc. However,acquisition of high-resolution images is severely constrained by the drawbacks of the limited density sensors.The images acquired through such sensors suffer from aliasing and blurring.The most direct solution to increase the spatial resolution is to reduce the pixel size (i.e.,to increase the number of pixels per unit area)by the sensor manufacturing techniques. But due to the decrease in pixel size,the light available also decreases causing more shot noise [1,2]which degrades the image quality.Thus,there exists limitations on the pixel size and the optimal size is estimated to be about40µm2.The current image sensor technology has almost reached this level.Another approach to increase the resolution is to increase the wafer size which leads to an increase in the capacitance[3].This approach is not effective since an increase in the capacitance causes a decrease in charge transfer rate.Hence,a promising approach is to use image processing methods to construct a high-resolution image from one or more available low-resolution observations.Resolution enhancement from a single observation using image interpolation techniquesis of limited application because of the aliasing present in the low-resolution image.Super-resolution refers to the process of producing a high spatial resolution image from several low-resolution observations.It includes upsampling the image thereby increasing the maximum spatial frequency and removing degradations that arise during image capture,viz.,aliasing and blurring.The amount of aliasing differs with zooming.This is because,when one captures the images with different zoom settings,the least zoomed entire area of the scene is represented by a very limited number of pixels,i.e.,it is sampled with a very low sampling rate and the most zoomed scene with a higher sampling frequency.Therefore,the larger the scene(the lesser zoomed area captured),the lower will be the resolution with more aliasing effect.By varying the zoom level,one observes the scene at different levels of aliasing and blurring. Thus one can use zoom as a cue for generating high-resolution images at the lesser zoomed area of a scene.As discussed in the next chapter,researchers traditionally use the motion cue to super-resolve the image.However this method being a2-D dense feature matching technique,re-quires an accurate registration or preprocessing.This is disadvantageous as the problem of finding the same set of feature points in successive images to establish the correspondence between them is a very difficult task.Errors in registration are reflected on the quality of the super-resolved image.Further,the methods based on the motion cue cannot handle observa-tions at varying levels of spatial resolution.It assumes that all the frames are captured at the same spatial resolution.Previous research work with zoom as a cue to solve computer vision problems include determination of depth[4,5,6],minimization of view degeneracies[7],and zoom tracking[8].We show in this paper that even the super-resolution problem can be solved using zoom as an effective cue by using a simple MAP-MRF formulation.The basic problem can be defined as follows:One continuously zooms in to a scene while capturing its images. The most zoomed-in observation has the highest spatial resolution.We are interested in gen-erating an image of the entire scene(as observed by the most wide angle or the least zoomed view)at the same resolution as the most zoomed-in observation.The details of the method are presented in this thesis.We also discuss various issues and limitations of the proposed technique.The remainder of this thesis is organized as follows.In chapter2we review some of the prior work in super-resolution imaging.We discuss how one can model the formation of low-resolution images using the zoom as a cue in chapter3.The zoom estimation,parameter learning and the MAP-MRF approach to derive a cost function for the super-resolution esti-mation is the subject matter for chapter4.We present typical experimental results in chapter5 and chapter6provides a brief summary,along with the future research issues to be explored.Chapter2Related WorkMany researchers have tackled the super-resolution problem for both still and video images, e.g.,[9,10,11,12](see[13,14]for details).The super-resolution idea wasfirst proposed by Tsai and Huang[12].They used the frequency domain approach to demonstrate the ability to reconstruct a single improved resolution image from several down-sampled noise free versions of it.A frequency domain observation model was defined for this problem which considered only globally shifted versions of the same scene.Kim et al.discuss a recursive algorithm, also in the frequency domain,for the restoration of super-resolution images from noisy and blurred observations[15].They considered the same blur and noise characteristics for all the low-resolution observations.Kim and Su[16]considered different blurs for each low-resolution image and used Tikhonov regularization.A minimum mean squared error approach for multiple image restoration,followed by interpolation of the restored images into a single high-resolution image is presented in[17].Ur and Gross use the Papoulis and Brown[18],[19] generalized sampling theorem to obtain an improved resolution picture from an ensemble of spatially shifted observations[20].These shifts are assumed to be known by the authors. All the above super-resolution restoration methods are restricted either to a global uniform translational displacement between the measured images,or a linear space invariant(LSI) blur,and a homogeneous additive noise.A different approach to the super-resolution restoration problem was suggested by Peleg et al.[10,21,22],based on the iterative back projection(IBP)method adapted from computeraided tomography.This method starts with an initial guess of the output image,projects the temporary result to the measurements(simulating them),and updates the temporary guess according to this simulation error.A set theoretic approach to the super-resolution restoration problem was suggested in[23].The main result there is the ability to define convex sets which represent tight constraints on the image to be restored.Having defined such constraints it is straightforward to apply the projections onto convex sets(POCS)method.These methods are not restricted to a specific motion charactarictics.They use arbitrary smooth motion,linear space variant blur,and non-homogeneous additive noise.Authors in[24]describe a complete model of video acquisition with an arbitrary input sampling lattice and a nonzero exposure time.They use the theory of POCS to reconstruct super-resolution still images or video frames from a low-resolution time sequence of images.They restrict both the sensor blur and the focus blur to be constant during the exposure.Ng et al.develop a regularized constrained total least square(RCTLS)solution to obtain a high-resolution image in[25].They consider the presence of ubiquitous perturbation errors of displacements around the ideal sub-pixel locations in addition to noisy observations.In[26]the authors use a maximum a posteriori(MAP)framework for jointly estimating the registration parameters and the high-resolution image for severely aliased observations. They use iterative,cyclic coordinate-descent optimization to update the registration parame-ters.A MAP estimator with Huber-MRF prior is described by Schultz and Stevenson in[27]. Other approaches include an MAP-MRF based super-resolution technique proposed by Rajan et al[28].Here authors consider an availability of decimated,blurred and noisy versions of a high-resolution image which are used to generate a super-resolved image.A known blur acts as a cue in generating the super-resolution image.They model the super-resolved image as an MRF.In[29]the authors relax the assumption of the known blur and extend it to deal with an arbitrary space-varying defocus blur.They recover both the scene intensity and the depthfields simultaneously.For super-resolution applications they also propose a general-ized interpolation method[30].Here a space containing the original function is decomposed into appropriate subspaces.These subspaces are chosen so that the rescaling operation pre-serves properties of the original function.On combining these rescaled sub-functions,theyget back the original space containing the scaled or zoomed function.Nguyen et al[31] proposed a technique for parametric blur identification and regularization based on the gener-alized cross-validation(GCV)theory.They solve a multivariate nonlinear minimization prob-lem for these unknown parameters.They have also proposed circulant block preconditioners to accelerate the conjugate gradient descent method while solving the Tikhonov-regularized super-resolution problem[32].Elad and Feuer[33]proposed a unified methodology for super-resolution restoration from several geometrically warped,blurred,noisy and down-sampled measured images by combining maximum likelihood(ML),MAP and POCS approaches.An adaptivefiltering approach to super-resolution restoration is described by the same authors in[34].They exploit the properties of the operations involved in their previous work[33] and develop a fast super-resolution algorithm in[35]for pure translational motion and space invariant blur.In[36]authors use a series of short-exposure images taken concurrently with a corresponding set of images of a guidestar and obtain a maximum-likelihood estimate of the undistorted image.The potential of the algorithm is tested for super-resolved astronomic imaging.Chiang and Boult[37]use edge models and a local blur estimate to develop an edge-based super-resolution algorithm.They also applied warping to reconstruct a high-resolution image[38]which is based on a concept called integrating resampler[39]that warps the image subject to some constraints.Altunbasak et al.[40]proposed a motion-compensated,transform domain super-resolution procedure for creating high quality video or still images that directly incorporates the trans-form domain quantization information by working in the compressed bit stream.They apply this new formulation to MPEG-compressed video.In[41]a method for simultaneously es-timating the high-resolution frames and the corresponding motionfield from a compressed low-resolution video sequence is presented.The algorithm incorporates knowledge of the spatio-temporal correlation between low and high-resolution images to estimate the original high-resolution sequence from the degraded low-resolution observation.In[42]authors pro-pose to enhance the resolution using a wavelet domain approach.They assume that the wavelet coefficients scale up proportionately across the resolution pyramid and use this property to go down the pyramid.Shechtman et al.[43]construct a video sequence of high space-time res-olution by combining information from multiple low-resolution video sequences of the same dynamic scene.They used video cameras with complementary properties like low-frame rate but high spatial resolution and high frame rate but low spatial resolution.They show that by increasing the temporal resolution using the information from multiple video sequences spatial artifacts such as motion blur can be handled without the need to separate static and dynamic scene components or to estimate their motion.Authors in[44]propose a high-speed super-resolution algorithm using the generalization of Papoulis’sampling theorem for multi-channel data with applications to super-resolving video sequences.They estimate the point spread function(PSF)for each frame and use the same for super-resolution.Capel and Zisserman[45]have proposed a technique for automated mosaicing with super-resolution zoom in which a region of the mosaic can be viewed at a resolution higher than any of the original frames by fusing information from several views of a planar surface in order to estimate its texture.They have also proposed a super-resolution technique from multiple views using learnt image models[46].Their method uses learnt image models either to di-rectly constrain the ML estimate or as a prior for a MAP estimate.Authors in[47]describe image interpolation algorithms which use a database of training images to create plausible high frequency details in zoomed images.In[48]authors develop a super-resolution algorithm by modifying the prior term in the cost to include the results of a set of recognition decisions,and call it as recognition based super-resolution or hallucination.Their prior enforces the condi-tion that the gradient of the super-resolved image should be equal to the gradient of the best matching training image.We now discuss in brief the previous work on MRF parameter estimation.In[49]au-thors use Metroplis-Hastings algorithm and gradient method to estimate the MRF parameters. Laxshmanan and Derin[50]have developed a iterative algorithm for MAP segmentation using the ML estimates of the MRF parameters.Nadabar and Jain[51]estimate the MRF line pro-cess parameters using geometric CAD models of the objects in the scene.A multiresolution approach to color image restoration and parameter estimation using homotopy continuation method was described by[52]As discussed in[47],the richness of the real world images would be difficult to captureanalytically.This motivates us to use a learning based approach,where the MRF parameters of the super-resolved image can be learnt from the most zoomed observation and hence can be used to estimate the super-resolution image for the least zoomed entire scene.In[53],Joshi et al proposed an approach for super-resolution based on MRF modeling of the intensityfield in which MRF parameters were chosen on an adhoc basis.However,a more practical situation is one in which these parameters are to be estimated.In this thesis, we simultaneously estimate the these uknown parameters and obtain the super-resolution in-tensity map.The Maximum Likelihood(ML)estimate of the parameters are obtained by an approximate version MPL estimation in order to reduce the computations.Our approach gen-erates a super-resolved image of the entire scene although only a part of the observed zoomed image has multiple observations.In effect what we do is as follows.If the wide angle view corresponds to afield of view ofαo,and the most zoomed view corresponds to afield of view ofβo(whereαβ),we generate a picture of theαofield of view at a spatial resolution com-parable toβofield of view by learning the model from the most zoomed view.The details of the method are now presented.Chapter3Low Resolution Image ModelThe zooming based super-resolution problem is cast in a restoration framework.There are p observed images Y i p i1each captured with different zoom settings and of size M1M2 pixels each.Figure3.1illustrates the block schematic of how the low-resolution observations of a same scene at different zoom settings are related to the high-resolution image.Here we consider that the most zoomed observed image of the scene Y p(p3in thefigure)has the highest resolution.A zoom lens camera system has complex optical properties and thus it is difficult to model it.As Lavest et al.[5]point out,the pinhole model is inadequate for a zoom lens,and a thick-lens model has to be used;however,the pinhole model can be used if the object is virtually shifted along the optical axis by the distance equal to the distance between the primary and secondary principal planes of the zoom lens.Since we capture the images with a large distance between the object and the camera and if the depth variation in the scene is not very significant compared to its distance from the lens,it is reasonable to assume that the paraxial shift about the optical axis as the zoom varies is negligible.Thus,we can make a reasonable assumption of a pinhole model and neglect the depth related perspective distortion due to the thick-lens behavior.We are also assuming that there is no rotation about the optical axis between the observed images taken at different zooms.However we do allow lateral shift of the optical center as explained in section4.4.Since different zoom settings give rise to different resolutions,the least zoomed scene corresponding to entire scene needs to be upsam-pled to the size of q1q2q p1M1M2N1N2pixels,where q1q2q p1are1Y Y2Y3Figure3.1:Illustration of observations at different zoom levels,Y1corresponds to the least zoomed and Y3to the most zoomed images.Here z is the high-resolution image of the same scene.the zoom factors between observed images of the scene Y1Y2Y2Y3Y p1Y p,respectively. Given Y p,the remaining p1observed images are then modeled as decimated and noisy versions of this single high-resolution image of the appropriate region in the scene.With this the most zoomed observed image will have no decimation.If ym D m z m m1p(3.1)y 1(k,l)y (k,l)y 32(k,l)Figure 3.2:Low resolution image formation model is illustrated for three different zoom lev-els.View fixation block just crops a small part of the high-resolution image z .where D is the decimation matrix,size of which depends on the zoom factor.For an integer zoom factor of q ,decimation matrix D consists of 1q 21110111...0111(3.2)Here p is the number of observations,n m 12exp1T m ngiven yChapter4Super-Resolution RestorationIn order to obtain a regularized estimate of the high resolution image zprovides the necessary prior.4.1Image Field ModelingThe MRF provides a convenient and consistent way of modeling context dependent entities such as pixel intensities,depth of the object and other spatially correlated features.This is achieved through characterizing mutual influence among such entities using conditional probabilities for a given neighborhood.The practical use of MRF models is largely ascribed to the equivalence between the MRF and the Gibbs distributions(GRF).We assume that the high resolution image can be represented by an MRF.Let Z be a randomfield over an arbitrary N N lattice of sites L i j1i j N.For the GRF,we have P Z z Ze U zpis a realization of Z,Z p is the partition function given by∑zθ,θis the parameter that defines the MRF model and U zθ∑c C V c z θdenotes the potential function associated with a clique c and C is the set of all cliques. The clique c consists of either a single pixel or a group of pixels belonging to a particular neighborhood system.In this paper we consider only the symmetricfirst order neighborhoods consisting of the four nearest neighbors of each pixel and the second order neighborhoods consisting of the eight nearest neighbors of each pixel.In particular,we use the following twoβ12β2(a)(b)Figure4.1:Cliques used in modeling the image.(a)First order,and(b)Second order neigh-borhood.and four types of cliques shown in Figure4.1.In thefigure,βi is the parameter specified for clique c i.The Gibbs energy prior for zθZ pexp U zθN2∑k1N2∑l1β1z k l z k l12z k l z k l12β2z k l z k1l2z k l z k1l2for two parametersβ1β2,orU z4.2Parameter LearningWe realize that in order to enforce the MRF priors while estimating the high resolution image zθ(4.2) The probability in equation(4.2)can be expressed asP Z zθP Z k l z k l Z m n z m nθ(4.4)θ∆∏k lwhere m nηk l form the given neighborhood model(thefirst order or the second order neighborhood as chosen in this study).Further it can be shown that equation(4.4)can bewritten asˆP Z z∑zk l G exp∑C:k l C V c z k lθ(4.5)where G is the set of intensity levels used.Considering the fact that thefield zpθ(4.6) We maximize the log likelihood of the above probability by using Metropolis-Hastings algorithm as discussed in[49]and obtain the parameters.4.3MAP RestorationHaving learnt the model parameters,we now try to super-resolve the entire scene.We use the MAP estimator to restore the high resolutionfield zis given byˆz arg maxz y2yP y2y P zm’s are independent,one can show that the high resolutionfield zp ∑m1y2θ(4.9)Since the model parameterθhas already been estimated,a solution to the above equation is,indeed,possible.The above cost function is convex and is minimized using the gradient descent technique.The initial estimate zincreasing zoom factors.Finally the most zoomed observed image with the highest resolution is copied with no interpolation.In order to preserve discontinuities we modify the cost for prior probability term as dis-cussed in section4.1.The cost function to be minimized then becomesˆz argminzmD m z2σ2ηV z∑i jµe zsγe zp(4.11)On inclusion of binary linefields in the cost function,the gradient descent technique cannot be used since it involves a differentiation of the cost function.Hence,we minimize the cost by using simulated annealing which leads to a global minima.However,in order to provide a good initial guess and to speed up the computation,the result obtained using the gradient descent method is used as the initial estimate for simulated annealing.The computational time is greatly reduced upon using mean-field annealing,which leads to a near optimal solution.4.4Zoom EstimationWe now extend the proposed algorithm to a more realistic situation in which the successive observations vary by an unknown rational valued zoom factor.Further,considering a real lens system for the imaging process,the numerical image center can no longer be assumed to be fixed.The zoom factor between the successive observations needs to be estimated during the process of forming an initial guess(as discussed in the chapter3)for the proposed super-resolution algorithm.We,however,assume that there is no rotation about the optical axis between the successive observations though we allow a small amount of lateral shift in the optical axis.The image centers move as lens parameters such as focus or zoom are varied[55, 56].Naturally,the accuracy of the image center estimation is an important factor in obtaining the initial guess for our super resolution algorithm.Generally,the rotation of a lens system will cause a rotational drift in the position of the optical axis,while sliding action of a lens group in the process of zooming will cause a translation motion of the image center[55].Theserotational and translational shifts in the position of the optical axis cause a corresponding shifting of the camera’sfield of view.In variable focal length zoom lenses,the focal length is changed by moving groups of lens elements relative to one another.Typically this is done by using a translational type of mechanism on one or more internal groups.These arguments validate our assumption that there is no rotation of the optical axis in the zooming process and at the same time stress the necessity of accounting for the lateral shift in the image centers of the input observations obtained at different zoom settings.We estimate the relative zoom and shift parameters between two observations by minimiz-ing the mean squared distance between an appropriate portion of the digitally zoomed image of the wide angle view and the narrower view observation.The method searches for the zoom factor and the lateral shift that minimizes the distance.We do this by heirarchially searching for the global minima byfirst zooming the wide angle observation and then searching for the shift that corresponds to a local minima of the cost function.The lower and upper bounds for the zooming process needs to be appropriately defined.Naturally,the efficiency of the algo-rithm is constrained by the closeness of the bounds to the solution.It can be greatly enhanced byfirst searching for a rough estimate of the zoom factor and slowly approaching the exact zoom factor by redefining the lower and upper bounds as the factors that correspond to the least cost and the next higher cost.We do this byfirst searching for a discrete zoom factor (say1.4to2.3in steps of0.1)At this point,we need to note that the digital zooming of an image by a rational zoom factor q mFigure4.2:Illustration of zoom and alignment estimation.’A’is the wide angle view and’B’is the narrower angle view.shift in the optical axis in the zooming process is usually small(2to3pixels).The above discussed zoom estimation and the alignment procedure is illustrated in the Figure4.2.。