Arrays and Images. Francesco Vespignani DiSCoF Università degli Studi di Trento. November 19, 2009

Transcription

1 Arrays and Images Francesco Vespignani DiSCoF Università degli Studi di Trento. November 19, 2009

2 Today Arrays Practice on Matrix Basic Files Management Graphic formats Practice on Images

3 Arrays

4 Structures Since usually we need to work with more than one data chunk, languages offers structures for organizing data of the same type or of a mixture of them. Every language has more ways to organize basic types into larger structures, with different ways for accessing a specific part of the structure. For this topic see also the doc and/or the Mastering Matlab chapter. Matlab: Everything is an Array!

5 Arrays The use of arrays allows to perform the same calculation on a sequence of elements. For example if we want to plot a function we have to calculate it on a (finite!) number of data points x=linspace(0,pi,11) y = sin(x) plot(x,y)

6 Array addressing Element 3 of array x: x(3) Elements 2 to 4 of array x: x(2:4) Element 4 to 2 (inverse order) of the array x: x(4:-1:2) A bunch of non contiguous elements of x: x([8,2,1])

7 Array orientation Row array: r = [ ] r = [1, 2, 3, 4] Column array: c = [ ] c = [1; 2; 3; 4] Passing from row to column: Transpose r = c. c = r. all((r. ). == r) Note the difference between. and, only using complex numbers: a = [1+2i, 3-5i]

8 Matrix 2-dim arrays: m = [ 1 2; 3 4] Matrix addressing (rows and columns): m(2,1) The all elements colon symbol: m(1,:) m(:,2) Multidimensional matrix: tm(:,:,1)=m; tm(:,:,2)=2*m; Matrix size: size(tm) size(tm,1) length(tm) numel(tm)

9 Building Matrix ones, zeros, eye: m = ones(3); m = ones(3,4); m = zeros(5); cat (try with different dim values): dim=1; cat(dim, ones(2), zeros(2)) change a row/colmn value, delete a row /column: m(:,1)=22; m(:,2)=[]; Single index addressing: m = magic(5); m(4,3) m(4+(3-1)*5)

10 Building Matrix ones, zeros, eye: m = ones(3); m = ones(3,4); m = zeros(5); Single index addressing: m = magic(5); m(4,3) m(4+(3-1)*5) change a row/colmn value, delete a row /column: m(:,1)=22; m(:,2)=[]; cat (try with different dim values): dim=1; cat(dim, ones(2), zeros(2))

11 Building Matrix repmat: m = repmat(1:2,3) m = repmat(1:2,3,1) m = repmat(1:2,1,3) Example: multiplication table for i=1:9 for j=1:9 a(i,j) =i*j; end end Multiplication table without loops: m=repmat(1:9,9,1); a = m.* m ; cat (try with different dim values): dim=1; cat(dim, ones(2), zeros(2))

12 Reshape a matrix repmat: m = reshape(1:8,4,2) m = reshape(1:8,2,4) v = reshape(m, numel(m)) m = reshape(1:8,2,2,2) See also permute, circshift, flipud, fliplr, rot90, triu, tril... Squeeze: sometimes matrix can have silly dimensions: m = reshape(1:8,4,2) squeeze(m)

13 Scalar Array mathematics when an array (or matrix) is involved in operations with scalars (i.e. 1x1 matrix) the operation is applied to each single element of the array: m = reshape(1:4,2,2) m-10 m* Scalar assigment to a column/row m(2) = 5 When two arrays have same size element-by-element operations (using the dot operations)are possible: a=[1 2; 3 4] b=[3 3; 5 5] a.* b a.* b -b

14 Linear Algebra Matrix operations are implemented in the without-dot form. For example row-by-column multiplication. a = reshape(1:6,3,2) b = [1 1 1; 2 2 2] a * b b * a b * a Number of rows of the first operand must be the same as the columns of the second. Matrix division is a more complex linear algebra function (involving matrix inversion). a = magic(3) b = a a/b b(1,:)=b(3,:) rank(a) rank(b)

15 Logical Matrix Logical operators may be applied in an element-by-element fashion to matrixes: a = -3:3 abs(a)>1 a(abs(a)>1) a(abs(a)>1) = NaN With logical matrix any and all function may be used: a = -3:3 any(a==0) all(a<5) With Matrix any and all work in a column-by-column

16 find Find returns the indexes of an array that are non-zero. If not differently specified it returns the linear index (fast on rows). For 2d matrix a row, column pair may be returned. a = [ ]; find(a) [x y] = find(a)

17 Practice on Matrix

18 Life Game Wikipedia Conway s Game of Life conwaylife.com (see also the wiki pages). We ll develop a simple algorithm to calculate a next generation. There is much more to do in terms of optimization (use of sparse matrix), graphics, graphical user interface... We ll return on this game also in the next lessons.

19 Life Game After solving numerically the problem we can further elaborate on it: Display the game graphically Create a Movie Search long living pattern with random configurations (brute force) Make statistics on mean life as a function of the initial density Create a GUI to allow people to draw a pattern Reading known patterns, by importing files in the standard formats (look at the web!)

20 Basic commands for files management

21 File and directory management As other scripting language Matlab has a set of commands for the interaction with the file system, some commands have multiple names, similar to thats of windows and Unix OSs. cd, chdir, pwd: change the current directory ls, dir, glob: lists the content of the current directory delete: deletes files system: execute another program filesattrib: gets or changes file s attributes mkdir, rmdir: crea, removes directories copyfile, movefile: copies or moves files

22 Basic strings commands Concatenate strings: c = strcat( hallo, world ) Convert numbers to strings: num2str(1, %03d ) See also sprintf and the documentation about formatting strings sequences in C (try the %12.80e ). Specialized functions for filenames: [d,n,e,v] = fileparts( Data/myfile.bmp ) fullfile(d,strcat(n,e)) Note that some matlab functions (e.g. fileparts) may return multiple values (an array). Moreover a function s behavior may change as a function of the number of return values requested (see find). Much more on strings one of the next lessons.

23 Graphics formats

24 Raster and Vector images Images can be represented (stored as files in a disk) in two ways: Raster: a map of pixel color values Vector: instructions where and how to draw specific items Raster images:.bmp.png.jpg.tiff.ppm Vector images:.svg.ps.pdf

25 Image representation An image can be represented on a video display or printed to paper. Vector images are typically rasterized, according to the specific resolution of the specific media. Conventional PC use in fact raster image representation (monitor and printers), however vector display exist(ed): Plotters Oscilloscope (Atari monitors, arcade games of the 70)

26 SVG files SVG is an open standard maintained by the WWW Consortium and it is part of the XML (Extensible Markup Language) that is used to generate web pages. See the documentation. This makes SVG easy to be displayed by any modern web browser. Multiple nesting of elements are done using tags: <atag>... < \atag>. Inkscape is a drawing program with a graphical GUI that produces SVG files.

27 A simple SVG example See simple.svg. It has an header, the dimension definition (in centimeters, not pixels) and two ellipses drawn with different colors. You can write a simple script that writes text files like this with any of the scripting languages we use (R, matlab, Tcl-Tk). SVG standard includes a vector graphic animations. SVG can also include Raster images.

28 Raster images Raster images are composed by pixels organized in a 2D matrix. Each pixel can be represented by multiple value, giving rise to 3d matrix, where the 3rd dimension is the color dimension.

29 Spatial and color resolution Spatial resolution is determined by the dimension of the matrix of pixels. Usually raster graphics files contains also information about linear dimension (dpi: dots per inch). Every pixel contains a color information that may be 0/1 in a black and white image, a scalar value in a grayscale image, three scalar values (RGB: reg, green, blue) and possibly a transparency value for color images. Other color encoding schemes exists (YCbCr, HSV...). The number of bits used to represent each scalar (color) fixes the number of different colors that can be represented (8 bits per pixel, 256 color; 16 bits per pixel, colors...). 24 bit per pixel usually allow to specify each RGB color in a 0 to 255 range.

30 File formats Raster images can either store a matrix with the color values of single pixels or use a colormap. An image with a colormap is called an indexed image: it is composed by a list of colors (color palette) and the matrix contains only the index to the color of that pixel. When the image is composed by a small number of colors indexed image allows for smaller file size. Bitmap file format is a simple raster image format. It is a binary file with an header that specify the type of image (pixel map or indexed), the matrix dimensions, the number of bits per pixels and the number storage format. Simple uncompressed bmp files are easy to read/write using low-level IO functions (fread, fwrite), as the EEG data of last lesson.

31 Data Compression Efficient image storage and transmission is achieved by compression: Lossless data compression allows the original data to be exactly extracted from the compressed data (zip, gz...). A simple lossless compression technique is to use dictionaries to replace sequences of bits that repeats in the files (similarly to indexed images, that can be seen as a lossless compression technique). Lossy data compression uses approximations to reduce data size and the extracted information may be different from the original. Lossy data compression try to remove the details that are less important at perceptual level and it is mainly used for images, music and video.

32 Image file formats BMP see above JPG or JPEG stores only pixel map images (not indexed) and allows for lossy compression. It s the more diffuse compressed raster image format. PNG it is more complex than JPG and support lossless compression (deflate).it allows various color formats and to store an alpha channel (transparency). TIFF similar to PNG is a complex format (e.g. a low resolution preview) GIF mainly used for small animations Some of these formats needs complex encoding/decoding algorithms and are usually written and read from file using libraries. Scripting languages usually provide specialized function for that (see the matlab commands imread, imwrite).

33 Animations Animations are sequences of images presented at a fixed rate (frames per second fps). Video allows to present also a synchronized sound (and subtitles...). Given the high rate of information stream compression and multiplexing of data is usually mandatory. There are many file formats for video (mpg, avi, wmv...). Some of them (avi, wmv) allow for different compression techniques implemented by codecs. A coded (compressor-decompressor, coder-decoder) is a device or a program (usually implemented in a compiled library) that are used by the applications that creates or play a movie file. There are many codex (MPEG-1, -2, -4, WMV, DivX...) that may work or not on different hardware/platforms. Some are opensource, other are not (wmv...). To know more see the mplayer and VLC documentation.

34 Practice on Images

35 Load and write images Reading, displaying and writing simple raster images. Basic interaction with the matlab figures (adding text to images). Convert to a different types (ind, gray, rgb) and formats (png, jpg...). Changing foreground and background, moving, superimposing images, using a complex scene as a background... Repeating automatically an image process on all image files of a given list or directory.

36 frame We will read indexed bmp files (imread). We will apply this to multiple files. Convert to a rbg image (ind2rbg) and save in another format (jpg, imwrite). We will also try to write a function that changes some colors.

37 Images in Matlab Images in matlab can be indexed, as a couple of array: a 2d matrix containing the indexes for each pixel and a colormap, containing the color palette. RGB images (truecolor) are stored in a 3d array of double, going from 0 to 1. The 3rd dimension has size 3 and represent Red Green and Blue values. RGB images does not contain information about the number of colors, they are rendered by the imshow, according to the property of the display. When writing an image file (imwrite) the double values are converted in an opportune binary format, according to the file format we choose (see imwrite documentation).