Alphabet recognition activities

10 Letter Recognition Activities - Days With Grey

The curiosity about how to teach letters to your child is such a hot topic! Learning the alphabet unlocks so many new doors, and letter recognition is the foundation of early literacy.

“How do I teach my child the alphabet,” is one of the most commonly asked questions. What we have learned in more recent studies is that helping our children hear letter sounds and watch our mouths when we form letters is more important than memorizing. Learn why hands-on learning is important for child development and easy ways you can set up ways to practice.

Here are 10 letter recognition activities for toddlers and preschoolers. Recognizing a letter can happen in four forms; uppercase print, lowercase print, uppercase cursive, and lowercase cursive. To better understand reading development, read our article, A Parent’s Guide to Phonemic Awareness.

This article will look closely at alphabet recognition and how you can help your child learn the letters. – All through hands-on play, of course!

RELATED: Here are five ways to incorporate reading readiness into your daily routine with toddlers, preschoolers, and big kids.

What Is Letter Recognition?

Letter recognition is the ability to identify letter names, recognize what a letter looks like, recognize how a letter sounds, and how notes come together to make blended sounds.

The alphabet does not need to be taught in a specific order; however, many believe teaching should begin with the most common letters. For example, T, L, and M will be taught before X and Q.

I like to begin with the letters in my child’s name.

Activities on Demand

Want great ideas without the ads? Download these 20 hands-on learning games for kids.

Why is Letter Recognition Important?

By Kindergarten, children learning under the Common Core will be asked to recognize and remember lowercase letters of the alphabet.

Let’s remember that we have plenty of time to build solid foundations of what letters look like, what they are called, and what sound they make.

In preschool, we want to respect this time and introduce letters with lots of room for learning through play and exploration. Exploring the letter names, what a letter looks like, letter sounds, and letter relationships take time to develop!

RELATED: 101 preschool activities to use throughout the year!

Typical Stages of Letter Recognition:

Letter Names: Understands letters have names.
Identify 10 Letters: Can identify ten letters, including their name. This is when they also begin to recognize their name in print.
Case Differences: Begins to identify lowercase and uppercase letters.
Letter Sounds: Develops a more in-depth understanding that letters stand for sounds.
Mastery: Masters all letter sounds and can identify letter names.

RELATED: Alphabet toys are a great addition to toys toddlers and preschoolers use daily!

How to Teach Letter Recognition:

Start with the letters in your child’s name: These letters will have meaning, and your child will be invested in wanting to remember them. Begin with these 15+ Name Activities.
Show how the letter is formed: Is it a straight line? Curve? Do you recognize a point in your letter?
Read ABC books: Here is an excellent list of ABC books from Happily Ever Elephants.
Use a poster: Write your child’s name on a poster and hang it in their room. Decorate posters with the letters of the alphabet. Hang them at eye level.
Magnetic letter play: Play with magnetic letters so they can be creative and get comfortable with letter recognition.
Songs: Sing songs about the alphabet.
Sound and picture: Match letter sounds with pictures.
Play games: Letter cards are great for recognition learning (and fun!)
Make ABC books: Have your child stamp, and you write the words.
Relate letters to people they know and love: Share and begin to recognize the names of family and friends.
Sound it out: Talk about how the letter sounds. H, hat, /h/.
Write it out: After much practice with fine motor skills, begin to write the letters.

10 Activities to Introduce, Improve, and Practice Letter Recognition.

Now more than ever, parents are stressed about doing too much. According to this survey that shares the impacts of the pandemic on young children and their parents, the frequency of parents reading to children and indoor play has dropped.

Parents are more likely to rely on screens because it is a way to decompress after a long work day. (No judgment, it is impossible to do all the things. I feel it too.)

This letter recognition post is intended to share low-prep activities to bring back hands-on learning through play that will feel as easy to set up as relying on digital devices.

RELATED: If you have a toddler just starting, begin with these quick and easy letter recognition activities that use two letters simultaneously.

Rock Letters Alphabet Activity

This easy alphabet idea comes from our activity cards set one. Gather some black rocks from the dollar store and write a few letters on each one with a white permanent marker. Have your toddler or preschooler practice with the first letter of family members’ names. Next, try playing with all the letters in your child’s name.

Alphabet Sort; Straights and Curves

Did you know that letters have curves, straights, slants, tunnels, and dots? I didn’t either until it was pointed out to me. Seeing and recognizing this is the first step to writing the letters. Let’s pay attention to how a letter looks before putting the pencil in their hand and asking a child to write their name.

Letter Poke and Find

Grab your muffin tin! This alphabet surprise game is a hoot. Put letters in the muffin tin and cover with tissue paper. Your child plays by poking through the tissue paper and recalling the letter name pulled. This is a great risk-free way to ask your child which letters they recognize without the stress of flashcards.

ABC Bean Sensory Bin

Beans are a hit for sensory play. Bury a few plastic lacing letters and invite your child to dig in. Grasping these small letters will help with fine motor development and stimulate the senses for more learning!

RELATED: Does your child enjoy sensory play? Check out these 40 sensory bins for kids.

Letter Recognition Drive and Park

Curious about which letters your child knows but also wants to tread lightly? Good call! I also don’t enjoy being interrogated. Your child drives each car to the correct parking spot as you call out letters for this letter recognition activity. If your child is new to learning letters, use less. We can add on more letters as your child develops.

Find your Name

Cheers to a classic name activity. (you can also find it in this 15+ name activities for kids post). Write the names of family members throughout the paper. Next, invite your child to find their name on the giant poster and circle it. This is an excellent way to prep for writing and hold a steady hand as your child circles each name.

Splash the Alphabet

When the weather warms up, head outside to splash the alphabet. For this idea, I like to take a back seat with a large seltzer and show my child a letter card. We talk about the letter name and the letter sound; then, he is off to splash it with colored water. This is a BIG win – especially for reluctant learners.

Write with Magnets

We made this magnetic board years ago, but never underestimate a cookie sheet! Make a large letter using tape and have your toddler or preschooler follow the lines with transportation magnets or race cars. This letter activity is a fun prewriting activity to practice the lines and curves of letters.

RELATED: Ready to write? Here are the stages of writing development.

Fine Motor Letter Grab

Let’s put those lacing letters to good use with another activity. Here, your child will fish the letters out from the pond and color-sort them when finished. As I sip my hot tea, my preschooler and I chat about the letters he grabbed. Skills practiced are fine motor development, hand-eye coordination, letter recognition, and color sorting. Phew! Can you believe all that in ONE idea? Five stars.

Alphabet Bingo – with a twist!

Remember bingo? Here is how your child can play solo. Grab some letters and place them in a tissue box. Write the letters you picked on the paper. Invite your child to dig in the box and try and get five in a row to win. This makes a fantastic morning activity we like to call Breakfast Invitations.

Kindergarten Word Families

As your child begins to put sounds together, head to this Kindergarten word family post for a list of consonant, vowel, and consonant words. We call these words CVC words or word families. Invite your child to think of words in the -at family by changing the beginning sound. If it is a word, try using it in a sentence. Toss the letter into the nonsense word dish if it makes a nonsense word.

Another great activity for Kindergartners to explore beginning sounds is this picture and sound match-up we played with my five-year-old.

More Letter Activities

Alphabet Ice Sensory Play
Giant Alphabet Dot to Dot
Writing Letters with Race Cars

Frequently Asked Questions

How do you teach the alphabet?

Start with the letters in your child’s name. These letters are familiar to children, which makes them more invested. Children who feel connected to learning are more likely to take risks. Use these 15-name activities to get started.

What if a child struggles with memorizing letter names?

We can take a step back when a child struggles to memorize letter names. Begin talking about the letters you notice in your environment and invite your child to play with the letters in their name. Take learning letters slow to honor your child’s pace. Meet your child at the stage they are by identifying a few letters at a time. Add more letters as your child develops.

My child is ready to read. What next?

When children show reading readiness, we want to model what our mouth looks like when saying the letter sound. Begin talking about how our voice box vibrates (or doesn’t) when making the letter sounds. Bringing attention to these details will help your child decode words as reading becomes more complex over the years.

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Alphabet Letter Identification Activities - PreKinders

Here are 15 fun, active, hands-on alphabet letter identification activities for Pre-K, Preschool, and Kindergarten.

You can find many more Alphabet Activities here.

Letter Basketball

This is one of my prekinders favorite letter identification activities every year. To prepare this game, I cut copy paper or newsprint paper in half, and write letters on several pieces. I make enough papers for each child, plus one or two extra. I make a line with masking tape on the floor and place the trash can about 4 feet away. As each child has a turn, I tell them which letter to find. They pick up the letter, crumble the paper into a ball, and stand on the tape to toss it into the trash can. If they miss, they get as many chances as needed to get the “ball” in the basket and can move closer if needed. We always cheer when they make it in the basket! This game could also be played with alphabet bean bags if you have them.

Candy Letter Match

Write pairs of letters on sticker dots and place them on the bottom of several Hershey’s Kisses. For my Pre-K kids, I usually put out about 5-10 pairs of letters at a time. Children take turns lifting two Kisses at a time. If the letters match, they keep those Kisses. If they do not match, they have to put them back. At the end of the game, all of the Kisses are put in the middle of the table, and children can choose about 3 pieces to eat. We use this game to practice matching uppercase to uppercase letters, lowercase to lowercase, or uppercase to lowercase, depending on what we are working on.

Alpha-Band

Label each rhythm instrument with a letter. An easy way to make instruments is to put rice inside a plastic Easter egg, and hot glue it closed. We sing the traditional Alphabet Song, or another alphabet song, such as Dr. Jean’s “The Alphabet’s in My Mouth” or “Who Let the Letters Out”, or Jack Hartmann’s “Animal Alphabet Cheer”. Children shake their letter shakers only when they hear their letter called out in the song.

Letter Hunt

Children choose any 10 letters from the letter manipulatives (use foam letters, magnetic letters, letter tiles or other letter manipulatives). Go through a stack of shuffled letter cards, calling out each letter to the children. As the letters are called out, children look to see if they have that letter, and if they do, the letter is put back in the letter basket. We see who is first to clear all of their letters. It’s very similar to a bingo game. In Pre-K, we play until everyone has cleared all of their letters because our goal is learning letters, not competition with the little ones.
*To teach letter sounds: Call out a word and have children identify the first letter of the word.

ABC Sorting Tray

I found this divided tray in a kitchen store. I labeled each section by writing a letter on a sticker dot and placing the matching foam letters in each section of the tray. I placed the letters in a bowl and children sorted and matched the letters into the sections of the tray. When I want to change out the letters in the tray, I just remove the sticker dots and add new ones. I usually try to use letters that are similar, so that children are challenged and use visual discrimination skills to find the differences in the letters. For example, I might use Q, O, D, C, and G since those letters are similar in shape, or I, T, J, or W, V, U.

ABC Sorting Box

Label a craft storage box with letter stickers. Children sort letter manipulatives into the sections of the box. These are magnetic letter tiles in the picture.

Letter Matching Uppercase to Uppercase

For this activity, each child chooses a colored letter box. Children work in pairs to match the letters that are the same. These letters came from a set of foam letters that are sadly no longer available from Lakeshore (bring them back, Lakeshore!) However, you could do the same activity by using handmade cards with the letters written in two different colors. You might also consider using paint chips (paint sample cards) in two different colors and making A-Z sets in the two different colors by writing on the cards with a black marker.

Letter Matching Uppercase to Lowercase

Children work in pairs to match the uppercase and lowercase foam or magnetic letters that are the same. You could also use purchased or handmade letter tiles.

Stamping Game

Write about ten letters on a piece of paper for each child. Put the same ten letters in a bowl or bag, and pass it around the table. Each child has a turn to pull a letter out of the bowl or bag, and announce the letter to the group. Children find the letter on their paper and stamp it out with a rubber stamp.
Other ways we play this game:

I put every letter of the alphabet in the bowl or bag and children determine if the letter is on their paper or not.
I place small objects in the bowl and children identify the beginning letter (e.g. B for ball).

Alphabet Bingo

Each child looks for the letter the teacher calls out on their bingo card. If they have it, they cover it. Play until a card is full.

Alphabet Soup

Children take turns scooping up a letter from a bowl with a spoon or soup ladle. The child identifies the letter, and walks around the room searching for the letter somewhere in the classroom.
*To teach letter sounds: Children search for an object in the room that begins with that letter.

Letter Clips

Children squeeze the clothespins and clip them to the sides of the box. I wrote letters on dot stickers and placed the dot stickers around the sides of the boxes. I wrote letters on the clothespins so the children would match the letters on the clothespins to the letters on the boxes. This is similar to activities where children clip clothespins to a paper plate or cardstock circle; however, in my experience, those were flimsy and awkward to use, which is why I like the box better. Any sturdy box could be used (shoe box, postal box). The boxes in this picture were stacking gift boxes that held chocolate covered nuts (a Christmas gift), and they worked out perfectly. (By the way, Sam’s Club has these chocolate covered nuts in the same stacking boxes every year, and they are awesome!)

Memory Game

Place about three letter manipulatives on a tray, cover them with a cloth, and take one away. When the letters are uncovered, children guess which letter is missing. Children find the letter that is missing among their own set of letter manipulatives. If the children are very interested in writing, they can write the letter that is missing on a dry erase lap board. To increase the difficulty of this game, try using 4 or 5 letters. Another options is to place three letters on the tray, cover them, and ask the children to recall all three letters that were on the tray.

Alphabet Path Games

I made these path games using stickers bought in a craft store (scrapbooking section), and I made individual mats with about 10 letters on them. Each child gets a mat, a game piece, and some plastic chips to cover the letters on their mat. They roll the dice and count out the spaces to move their game piece. If their game piece lands on a letter that is on the mat, they cover that letter with a chip. Play continues until they have covered every letter.
Other ways we use the path games:

Children identify the letter they land on, then find that letter somewhere in the classroom.
Children find an object in the classroom that begins with that letter’s sound.

You’ll also like these resources…

from collecting a dataset to creating a GUI / Habr

Hello, Habr! In this article, I would like to tell you how I made a Russian letter recognizer and screwed a small graphical interface to it.

Spoiler: the result should look like this:

Downloading the dataset

So let's get started! The first thing we need is a dataset. As a dataset, I chose CoMNIST. We download the data set, unpack and delete the folder called I, since this letter is not included in the Russian alphabet. nine0003

Data processing

As we can see, the image data has four channels. The fourth channel is the alpha channel, which we do not need and we remove it:

 def make_background(): image=' ' file_without_extension = image.split('.')[0] image = cv2.imread(image, cv2.IMREAD_UNCHANGED) trans_mask = image[:, :, 3] == 0 image[trans_mask] = [255, 255, 255, 255] new_img = cv2. cvtColor(image, cv2.COLOR_BGRA2BGR) cv2.imwrite(file_without_extension + '.jpeg', new_img)

That is, at the input we had an image that is presented on the left, and the output should be an image that is presented on the right:

per class). Therefore, we need to "inflate" our data. For these purposes, I used the following techniques: shifts, this is when we move our letter by some value up / down and left / right along the axes, and rotations, when we rotate our letter by a certain degree. nine0003

Shifts

 def shift(): image = '' img = cv2.imread(image) file_without_extension = image.split('.')[0] arr_translation = [[15, -15], [-15, 15], [-15, -15], [15, 15]] arr_caption=['15-15','-1515','-15-15','1515'] for i in range(4): transform = AffineTransform( translation=tuple(arr_translation[i])) warp_image = warp(img, transform, mode="wrap") img_convert = cv2. convertScaleAbs(warp_image, alpha=(255.0)) cv2.imwrite(file_without_extension + arr_caption[i] + '.jpeg', img_convert)

Rotations

 def rotate(): image = '' img = Image.open(image) file_without_extension = image.split('.')[0] angles = np.ndarray((2,), buffer=np.array([-13, 13]), dtype=int) for angle in angles: transformed_image = transform.rotate(np.array(img), angle, cval=255, preserve_range=True).astype(np.uint8) cv2.imwrite(file_without_extension + str(angle) + '.jpeg', transformed_image)

Data balancing

Next, we can see that the number of images belonging to each class is different, so we need to balance our dataset.

 def balancing(): arr_len_files = [] for path in root_path: name_path = name_root_path+path+'/' files=os. listdir(name_path) arr_len_files.append(len(files)) min_value=min(arr_len_files) for path in root_path: folder = name_root_path+path arr = [] for the_file in os.listdir(folder): arr.append(folder + '/' + the_file) d=0 k = len(arr) for i in arr: os.remove(i) d += 1 if d == k - min_value: break

As a result, for each letter the number of images should be the same. Next, you should independently divide the data into training, test and validation approximately in the ratio of 70%, 20% and 10%, respectively.

Neural network training

Let's move on to the longest stage - network training. As a neural network, I chose CNN, as it is good for classifying objects. The learning process itself takes 2-2.5 hours and the accuracy was approximately 94% which is pretty good. Below is the code for training the network.

 import tensorflow as tf ImageDataGenerator = tf. keras.preprocessing.image.ImageDataGenerator TRAINING_DIR = "path/to/train/dataset" train_datagen = ImageDataGenerator(rescale=1.0 / 255.) train_generator = train_datagen.flow_from_directory(TRAINING_DIR, batch_size=40, class_mode='binary', target_size=(278,278)) VALIDATION_DIR = "path/to/test/dataset" validation_datagen = ImageDataGenerator(rescale=1.0 / 255.) validation_generator = validation_datagen.flow_from_directory(VALIDATION_DIR, batch_size=40, class_mode='binary', target_size=(278,278)) model = tf.keras.models.Sequential([ tf.keras.layers.Conv2D(16, (3, 3), activation='relu', input_shape=(278,278, 3)), tf.keras.layers.MaxPooling2D(2, 2), tf.keras.layers.Conv2D(32, (3, 3), activation='relu'), tf.keras.layers.MaxPooling2D(2, 2), tf.keras. layers.Conv2D(64, (3, 3), activation='relu'), tf.keras.layers.MaxPooling2D(2, 2), tf.keras.layers.Flatten(), tf.keras.layers.Dense(512, activation='relu'), tf.keras.layers.Dense(33, activation='softmax') ]) model.compile(optimizer='adam', loss='sparse_categorical_crossentropy', metrics=['accuracy']) model.summary() history = model.fit_generator(train_generator, epochs=2, verbose=1, validation_data=validation_generator) model.save('model.h5')

Next, we need to test our neural network on the validation images, in order to make sure that the accuracy on the test data corresponds to reality:

prediction.py

 letters = "YABVGDEZHZYKLMNOPRSTUFFHTSCHSHCHJYYYYY" return letters[result] def predicting(path_to_image): image = keras.preprocessing.image model = keras.models.load_model('path/to/model') img = image. load_img(path_to_image, target_size=(278, 278)) x = image.img_to_array(img) x = np.expand_dims(x, axis=0) images = np.vstack([x]) classes = model.predict(images, batch_size=1) result = int(np.argmax(classes)) result = print_letter(result) print(result)

Screwing on the GUI

And the last thing we have to do is to screw on the graphical interface with minimal features: a canvas on which you can draw numbers, a field where the recognized letter will be displayed, a button for recognizing what is on the canvas, a button to clean up the canvas and put it all together.

app.py

 from PyQt5.QtWidgets import QMainWindow, QApplication, QMenu, QMenuBar, QAction, QFileDialog, QPushButton, QTextBrowser from PyQt5.QtGui import QIcon, QImage, QPainter, QPen, QBrush from PyQt5.QtCore import Qt, QPoint import sys from PyQt5.QtWidgets import QMainWindow, QTextEdit, QAction, QApplication from PyQt5. QtWidgets import (QWidget, QLabel, QLineEdit, QTextEdit, QGridLayout, QApplication) import numpy as np from tensorflow import keras classWindow(QMainWindow): def __init__(self): super().__init__() title = "recognition cyrillic letter" top=200 left=200 width=540 height=340 self.drawing = False self.brushSize = 8 self.brushColor = Qt.black self.lastPoint = QPoint() self.image = QImage(278, 278, QImage.Format_RGB32) self.image.fill(Qt.white) self.nameLabel = QLabel(self) self.nameLabel.setText('RES:') self.line = QLineEdit(self) self.line.move(360, 168) self.line.resize(99, 42) self.nameLabel.move(290, 170) prediction_button = QPushButton('RECOGNITION', self) prediction_button.move(290, 30) prediction_button.resize(230, 33) prediction_button.clicked.connect(self.save) prediction_button.clicked.connect(self. predicting) clean_button = QPushButton('CLEAN', self) clean_button.move(290, 100) clean_button.resize(230, 33) clean_button.clicked.connect(self.clear) self.setWindowTitle(title) self.setGeometry(top, left, width, height) def print_letter(self,result): letters = "YABVGDEZHZYKLMNOPRSTUFFHTSCHSHCHJYYYYY" self.line.setText(letters[result]) return letters[result] def predicting(self): image = keras.preprocessing.image model = keras.models.load_model('model/cyrillic_model.h5') img = image.load_img('res.jpeg', target_size=(278, 278)) x = image.img_to_array(img) x = np.expand_dims(x, axis=0) images = np.vstack([x]) classes = model.predict(images, batch_size=1) result = int(np.argmax(classes)) self.print_letter(result) def mousePressEvent(self, event): if event.button() == Qt.LeftButton: self.drawing = True self. lastPoint = event.pos() def mouseMoveEvent(self, event): if (event.buttons() & Qt.LeftButton) & self.drawing: painter = QPainter(self.image) painter.setPen(QPen(self.brushColor, self.brushSize, Qt.SolidLine, Qt.RoundCap, Qt.RoundJoin)) painter.drawLine(self.lastPoint, event.pos()) self.lastPoint = event.pos() self.update() def mouseReleaseEvent(self, event): if event.button() == Qt.LeftButton: self.drawing = False def paintEvent(self, event): canvasPainter = QPainter(self) canvasPainter.drawImage(0, 0, self.image) def save(self): self.image.save('res.jpeg') def clear(self): self.image.fill(Qt.white) self.update() if __name__ == "__main__": app = QApplication(sys.argv) window = Window() window.show() app.exec() nine0019 
  Conclusion 
  As you can see, what once seemed like “magic” is quite easy to do with the help of modern libraries. 
  Since Python is cross-platform, the code should work everywhere, on Windows, Linux and OSX. I did all this on Ubuntu 18.04. For those who want to experiment on their own, I posted the source code on GitHub. 
  Description of objects and classes in feature spaces. Signs alphabet. 
   
 
  Standard image recognition systems up to present is the system human perception (if we abstract from speed). 
  Usually the purpose of creating recognition systems is to optimize its functioning over a selective set of images. 
  AT general pattern recognition scheme and decision-making (Fig. 5.1) prevailing at labor cost is the operation transformations of the observation space in order to obtain a compact description objects in the feature space. nine0003 
 Systems object recognition - complex dynamic systems with elements artificial intelligence. These systems may include prepared specialists, experts i. e. and be complex man-machine systems. Today they are mostly specialized. 
  
   Fig.   5   .   1   .  Generalized decision scheme for pattern recognition 
  On development stage descriptions of such systems are formed physical and mathematical, chemical, biological, social models characterizing the objects of study. nine0003 
 They should display only those features, values which can be measured, or obtained in follow-up study recognition object. 
  Signs may be deterministic, probabilistic, logical and structural. 
  For the formation zones of existence of signs, characteristics and whose parameters are random character, use the methods of mathematical statistics. 
  Most often - this is the definition of distribution laws and their parameters according to the available samples. nine0003 
 According to the results observations of manifestations of symptoms in different implementations of recognizable objects, situations is formed statistical hypothesis about the species and parameters of the distribution law. 
  However, the main part of the character alphabet, usually constitutes a set of deterministic parameters and characteristics of recognizable classes. 
  Classification image recognition systems allows understand the relationships in such systems and solve the feature selection problem (process heuristic). nine0003 
 Classification also contributes to planning use as a priori information (class description), and a posteriori data (measurements for a given unknown object to be classified). 
  Classification is the distribution of objects, phenomena by class depending on their common properties. The classification is based on certain principles. 
  For classification of recognition systems the following signs can be used: 
    Uniformity information to describe recognizable objects or phenomena. nine0003 
   How to obtain a posteriori information. 
 
   Quantity and the quality of the original a priori information. 
 
   Nature of Information about signs of recognition. 
 
 
  1. Homogeneity of information. Under uniformity we will understand - different or single the physical nature of information (features). According to this principle, recognition systems (SR) images are divided into simple and complex. Simple recognition systems are characterized by a single physical the nature of the signs. For example, only weight - for recognition systems tokens, coins in vending machines such as long-distance telephone, subway turnstile; geometric dimensions - for such recognition systems, as any kind locks. Complex recognition systems characterized by physical heterogeneity signs. nine0003 
 2. Method for obtaining a posteriori information. According to this system principle recognitions are divided into single-level and multilevel. Multi-level complex recognition systems are different from single-level in that not all signs from heterogeneous physical meters used directly for solution of the recognition problem. Here on based on the combination of features of several meters and related processing secondary signs can be obtained, which can be used in the next step, and themselves in their own turn to serve as the basis for the association. That is, we get the 2nd, 3rd and other levels features that determine the hierarchy recognition systems. Moreover, the subsystems who bring together signs, in turn, can also be devices recognition (local systems recognition). In one-level SR information about the features of the recognized object (a posteriori information) formed directly on the basis processing of direct measurements; nine0003 
 AT multilevel SR information about features formed on the basis of indirect measurements as a result of functioning auxiliary recognition devices (for example, when measuring range time delay radar emitted impulse, changing it forms). 
  Table 5.1. 
  nine0175        Systems recognition by the nature of information 
    characteristic features 
 
   method solving the problem of recognition 
    method a priori description of classes 
  
    Deterministic 
    usage geometric proximity measures 
    coordinates reference vectors for each of the classes or coordinates of all objects, belonging to classes 
  
    Probabilistic 
    probabilistic, based on probability measure proximity 
    probabilistic dependencies between features and classes 
  
    Logic 
    logical, based on discrete analysis and propositional calculus 
    brain teaser connections expressed through a system of Boolean equations, where signs are variables, classes - unknown quantities 
  
    Structural 
    grammatical parsing a sentence describing object in non-derivative language structural elements in order to determining its correctness 
    subsets sentences describing objects each class 
  
    Combined 
    special methods for calculating grades 
 nine0170   tabular, involving the use of tables, containing classified objects and their signs (deterministic, probabilistic, logical) 
  
 
  3. Quantity and quality of initial a priori information. Enough or not enough a priori information to definitions of a priori alphabet of classes, building an a priori feature dictionary and descriptions of each class in the language of these signs as a result of direct processing of initial data. Respectively this recognition systems are divided on systems without training, learning (SSR) and self-learning systems (SSR). nine0003 
 Many recognition system is clearly impossible divided into the specified classes, since each of the local recognition systems, included in their composition, itself can present as a system without learning, and the system learning or self-learning. To build a system without training it is necessary to have complete initial a priori information. 
  For learning systems need to deal with a situation where a priori information not enough to describe recognizable classes in feature language. nine0003 
 Initial information for learning systems recognition (OSR) is represented in as a set of objects , , , , where, as a first approximation, one can imagine the presence of three types of weakly correlated among themselves data - deterministic, random and linguistic ( - the number of axes of the outcome space by types of data). Their distribution over  m  classes formation and definition separating functions is the goal of the learning process. It should be noted that the assignment specific transmitter signal to a particular group, for example, does not exclude its inclusion in the group . This signal, for example, is used as deterministic at difference objects of several classes, and how random when working with other classes. nine0003 
 Definition this function is carried out by repeated presentation to the system specified objects (from the set  w1,w2,....,wl  ) indicating which class they are belong. 
  That yes, they are working at the stage of formation with the "teacher" carrying out the instruction about the belonging of the presented for object learning. And before the system will apply, must pass the stage learning. 
  AT unlike systems without training and systems students with a teacher, for self-taught systems are characterized by insufficiency information to form not only class descriptions, but even the alphabet classes. That is, only defined dictionary of recognition features. nine0003 
 However to organize the learning process given a set of rules, according to which the system itself generates a classification. 
  For SSR is characterized by the presence of a period self-learning as well as for OSR there is a learning period. SSR teaching objects are presented sequences. Only while not indicate their belonging to to any classes. 
    Character information about recognition features. In line with its distinctive features of the tasks of creating a system recognition can be divided into deterministic, probabilistic, logical, structural (linguistic), combined. System characteristics on this basis of classification are given in table 5.1. nine0003 
 
  
   Fig.5.2.  Classification with two features and five classes. 
  An example can also serve as a recognition option air targets along two trajectory features (heights and speeds movement) (Fig. 5.2). Grades Assigned: 1- large aircraft; 2- planes medium size; 3 - missiles; - cruise missiles of the ALKM type; 4 - helicopters. It can be seen from the figure that two signs not enough for object recognition by assigned classes. Additionally effective target areas are introduced, polarizing features reflected in signals with narrow-band sounding. nine0003 
 Reduced the scheme is one-sided and only complements many classifications of SR. But she stresses the importance of the procedure compiling an alphabet of features and primary transformations performed wherein. Features are usually chosen an iterative procedure based on a priori information about objects, background, and overlap comparison results class descriptions. The comparison is being made with no correlation between signs in their complex hyperspace. 
  Mathematical models - the goals of the initial (starting) stage of compiling the alphabet of features. nine0003 
 First mathematical models have been used for solving practical problems in the 30s years in the UK when creating air defense systems. For the development of this system were involved scientists of various specialties. System created in the face of uncertainty on possible actions enemy, so research were carried out on adequate mathematical models. In subsequent years, operating research develops as a science, the results of which apply to selection of optimal solutions for management real processes and systems. nine0003 
 good the model is not so easy. Mathematician Bellman R. said "If we try include too much in our model hell of reality, then choke in complex equations; if too simplify it, then it will cease to satisfy our requirements." For execution successful simulation must be satisfied three rules that apply to problems of mathematical modeling and are formulated as follows: 
    Required take into account the main properties of the modeled object; nine0003 
   Follow ignore its minor properties; 
 
   Required be able to separate the main properties from secondary. 
 
 
  Mathematical model is a system of mathematical relations approximately in the abstract form describing the process under study or a system, in our case it is an estimate ratio type and parameter vector, allowing to attribute the object under study to a known class, or at least facilitate classification. nine0003 
 Building and calculation of the mathematical model allow analyze the situation and choose optimal management solutions or justify the proposed solutions. Application of mathematical models necessary in cases where the problem complex and dependent on a large number factors that affect it in different ways decision. 
  Mathematical models can carry out preliminary selection of optimal solutions according to certain criteria. They scientifically justified, and the employee taking decision, can be guided by them when making a final decision. By number of performance criteria mathematical models are divided into single-criteria and multi-criteria. Multicriteria math models contain two or more criteria. "Good" model. Should be: 
    focused; 
 
   reliable in the sense of a guarantee against absurd decisions; 
 
   comfortable in calculations; 
 
   complete, in terms of solution possibilities assigned tasks; 
 
   adaptive, i.e. allowing easy transition to other modifications or update data; 
 
   tolerant gradual changes i.e. at subsequent research is becoming more and more accurate. nine0003 
 
  By accounting for unknown factors mathematical models are divided into deterministic, stochastic and models with elements uncertainty. 
  AT stochastic models unknown factors are random variables, for whose distribution functions are known and various statistical characteristics. And in deterministic models, the unknowns factors are not taken into account. In spite of the apparent simplicity of these models, to them many practical problems are reduced. By the form of the objective function and restrictions deterministic models are divided into: linear, non-linear, dynamic and graphic. In linear models, the target function and constraints are linear in control variables. Construction and calculation of linear models are the most promising section mathematical modeling, so often others try to reduce them tasks either at the stage of setting, or in the process of solving. For linear models any kind and large enough dimension known standard methods solutions. Nonlinear models are models in which either the objective function or any of the restrictions (or all constraints) non-linear in the control variables. Graphic data is usually receive in test results, they difficult to explain and often bad are represented by known equations. nine0003 
 Building models. When building any model management process is desirable stick to the next plan actions: 
    Formulate the goals of studying the system; 
 
   Install most essential for this task factors, components and variables; 
 
   Take into account in one way or another outsiders, not factors included in the model; 
 
   Make an assessment results, model validation, evaluation completeness of the model. nine0003 
 
  Types of models. Models can be classified as: 
    Functional models - express direct dependencies between endogenous and exogenous variables; 
 
   models, expressed using systems of equations relative to endogenous values; 
 
   Models optimization type. Main part models - a system of equations obtained with respect to endogenous variables. The goal is to find the best solution for some indicator; nine0003 
   simulation models - very accurate display process or phenomenon. Mathematical equations may contain complex, nonlinear, stochastic dependencies. 
 
 
  simulation systems occupy a special place in modeling place. Basically, any model imitation because it imitates reality. The simulation system is set of models that simulate the course of the process under study, integrated with the information base and a special system of auxiliary programs that make it easy and promptly implement options calculations. So under imitation in simulators understand the results calculations adequate to the parameters simulated objects. nine0003 
 Decision problems for multidimensional systems is conjugated with great difficulties that wear both mathematical and operational character, because it often requires costs unacceptable amounts of machine time. Approaches to the problem of order reduction The complexity of the models may vary. Of course, a complex nonlinear system can be equivalent to a linear system under certain conditions. Essential properties of controlled systems, such as controllability, stability, optimality solutions are preserved when passing to equivalent system. nine0003 
 Methodology modeling. Process Modeling management involves consistent implementation of three stages of research: 
  The first stage - from the original practical problem to theoretical purely mathematical tasks; 
  Second phase - mathematical study and solution of this tasks; 
  Third stage - transition from mathematical deductions back. 
  Mathematical the model is related to the functioning object and solution oriented assigned task. technological objects, for example, have purposefulness. This circumstance requires, when modeling technological object, draw the closest focus on the goals and objectives to be solve this technological object. nine0003 
 Building complex mathematical models, describing the processes of recognition, really possible only within the framework of the theory complex systems. most suitable apparatus for describing processes and output signals, messages, in this case, is the mathematical theory of systems and especially the apparatus of mathematical structures. 
  Mathematical systems theory suggests that above all a common goal in functioning system components. The system is considered given if its model exists. Initially, not uncommon, this is design documentation, mathematical, physical models, describing signals in components systems. The mathematical model is systems today is represented by a set connected base sets. Binder link between the components of the system we will consider signals carrying information about recognizable images or situations. nine0003 
 Often mathematical the structure is represented by a set objects of various nature 
  , 
  where elements of the structure, including virtual, in the general case with unknown fragments of descriptions (signals, components etc.). 
  Attitude is a term for space in which there are all combinations elements, their mutual arrangement and relationships. In radiophysics, signals are often are given at the nodes of the spatial lattice, it simplifies, structures the analysis. nine0003 
 Such phrases when describing relationships - an arbitrary subset of all tuples elements traditional. On the set-theoretic language the concept of relationships connections between objects. For example, - description of the structure of set No. 12 (tuple) in five-dimensional parameter space (e.g. 3D coordinates, radiation wavelength and time). Many elements included at least one tuple is called a field this relationship. 
  Display - law, graph, fuzzy dependence, showing the connection of signals at the input and the output of an element or a set of them. nine0003 
 described approach allows you to work with known laws, drawings, graphs, fuzzy information within one system, supplementing and refining it over time existence. 
  Description systems are maintained within the framework of external (example black box) and internal models various levels and depths of presentation. Structural, functional, circuit diagrams. For signals make extensive use of reaction independence elements of the system from the presence of other signals, signal values. That is the initial stage of the analysis is linear, isoplanar, diffraction-limited reactions of system elements to input signals. Aberration-free optical the system depicts a luminous dot in monochromatic light in the form diffraction figure, consisting of central bright spot (Erie circle), and a number of light concentric rings, separated by dark spaces, where the illumination drops to zero. nine0003 
 AT these limitations, lens response systems can be expressed as the sum of convolutions from weighted inputs (usually elementary - ) point spread signals lens. 
  , where - magnification factor, - lens transmittance, - input signals, often specified in nodes square grid, - point spread function characterizing lens. 
  Expression for aberrations can also be simplified 
  Equivalent radius of spherical aberration , coma , astigmatism , increasing the size of the Erie circle, you can get from expressions: 
  , , , where , , - corresponding coefficients, characterizing the quality of the optical systems and adjustments - angular field in the space of objects. 
  Everybody models complement each other in different stages of analysis and synthesis of optical-electronic systems. 
  Transition from elements of the same nature to elements the other is carried out through the appropriate relationship. For example, spatial frequencies in the image on the CCD - matrix move to temporal frequencies electrical signals , where - scan line length, - line scan time interval (does not take into account the clock signal), , - spatial and temporal frequencies on the object in the plane of objects and in signal. Optical transfer function where - transfer functions of the components aberrations along the axes , , , . nine0003 
 For completeness of the picture we add "aberration", due to image blurring at frame registration by a matrix photodetector. , where - the speed of the rotating Images, - charge integration time in one frame, - the number of accumulated frames (under conditions low light use summation successive frames without offset), - spatial frequency in direction offset. 
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Systems recognition by the nature of information	characteristic features
Systems recognition by the nature of information	method solving the problem of recognition	method a priori description of classes
Deterministic	usage geometric proximity measures	coordinates reference vectors for each of the classes or coordinates of all objects, belonging to classes
Probabilistic	probabilistic, based on probability measure proximity	probabilistic dependencies between features and classes
Logic	logical, based on discrete analysis and propositional calculus	brain teaser connections expressed through a system of Boolean equations, where signs are variables, classes - unknown quantities
Structural	grammatical parsing a sentence describing object in non-derivative language structural elements in order to determining its correctness	subsets sentences describing objects each class
Combined	special methods for calculating grades nine0170	tabular, involving the use of tables, containing classified objects and their signs (deterministic, probabilistic, logical)