D10K-6C01 Pengolahan Citra PCD-06 Algoritma Pengolahan Citra 3 Geometry Process Program Studi S-1 Teknik Informatika FMIPA Universitas Padjadjaran Semester Genap 2015-2016

GEOMETRIC PROCESS Geometric Processes modify the arrangement of pixels based on some geometric transformation Topik Bahasan Forward Mapping vs Reverse Mapping Transformasi Geometrik Dasar Skala Rotasi Translasi

ILUSTRASI DAN LINKS http://micro.magnet.fsu.edu/primer/java/digitalimaging/processing/geometricaltransformation/ http://www.imageprocessingbasics.com/ http://filters.sourceforge.net/ Simple Image Processing

Ilustrasi Klasik

Algorithms Pixel art scaling algorithms Efficiency EPX/Scale2×/AdvMAME2× Scale3×/AdvMAME3× and ScaleFX Eagle 2×SaI Super 2×SaI and Super Eagle hqnx family xBR family RotSprite Kopf–Lischinski SuperRes EDIUpsizer FastEDIUpsizer eedi3 EEDI2 NEDI NNEDI NNEDI2 ChromaNEDI NNEDI3 SuperChromaRes Waifu2x

TRANSFORMASI GEOMETRIK

FORWARD MAPPING vs REVERSE MAPPING Forward mapping adalah suatu teknik pemetaan piksel yang mentransformasikan piksel input ke piksel output melalui fungsi pemetaan x dan y Problem dalam FM: holes dan overlap Holes merupakan piksel yang tak terdefinisi, dimana piksel output tidak memiliki piksel koresponden pada citra input Overlap timbul pada saat sebuah piksel output memiliki rujukan pada lebih dari satu piksel input Bagiamana meng-eliminasi problem tersebut ? Dengan Reverse Mapping Teknik yang digunakan: Interpolasi Jenis Interpolasi: Nearest Neighbor, Bilinear, Higher Order, Cubic Convolution, B-Spline

ILUSTRASI

CONTOH HASIL FORWARD MAPPING

Istilah Resampling is the mathematical technique used to create a new version of the image with a different width and/or height in pixels. Increasing the size of an image is called upsampling; reducing its size is called downsampling.

INTERPOLASI Interpolasi (secara matematis) Ilustrasi interpolation is a method of constructing new data points within the range of a discrete set of known data points. Metode untuk menentukan titik data baru menggunakan titik data yang diketahui sebelumnya Ilustrasi

INTERPOLASI CITRA Interpolasi Tanpa Interpolasi Pengolahan Citra Dijital

Image Rotation

INTERPOLASI Mengapa diperlukan? We want BIG images When we see a video clip on a PC, we like to see it in the full screen mode We want GOOD images If some block of an image gets damaged during the transmission, we want to repair it We want COOL images Manipulate images digitally can render fancy artistic effects as we often see in movies Metode: Nearest Neighbour, Bilinier, Bicubic Penggunaan Digital zooming (resolution enhancement) Image inpainting (error concealment) Geometric transformations (where your imagination can fly)

INTERPOLASI Resolution Enhancement Image Inpainting Image Warping

ANTI ALIASING Anti-aliasing is a process which attempts to minimize the appearance of aliased or jagged diagonal edges, termed "jaggies." These give text or images a rough digital appearance:

OPTICAL ZOOM vs DIGITAL ZOOM Most of digital cameras can perform both an optical and a digital zoom. A camera performs an optical zoom by moving the zoom lens so that it increases the magnification of light before it even reaches the digital sensor. In contrast, a digital zoom degrades quality by simply interpolating the image — after it has been acquired at the sensor. 10x Digital Zoom 10x Optical Zoom

Types of Interpolation Algorithm Common interpolation algorithms can be grouped into two categories: adaptive and non-adaptive. Adaptive methods change depending on what they are interpolating (sharp edges vs. smooth texture) proprietary algorithms in licensed software : Qimage, PhotoZoom Pro, Genuine Fractals and others. Non-adaptive methods treat all pixels equally. nearest neighbor, bilinear, bicubic, spline, sinc, lanczos and others

JENIS-JENIS INTERPOLASI Pixel replication Bilinear Bicubic Edge-Directed Interpolation Polynomial Interpolation Lagrange Newton Natural Splines Bezier Splines, Cubic Splines

CONTOH INTERPOLASI Pixel Replication low-resolution image (100×100) high-resolution image (400×400)

Bilinear Interpolation CONTOH INTERPOLASI Bilinear Interpolation low-resolution image (100×100) high-resolution image (400×400)

CONTOH INTERPOLASI Bicubic Interpolation low-resolution image (100×100) high-resolution image (400×400)

Edge-Directed Interpolation, (Li&Orchard’2000) CONTOH INTERPOLASI low-resolution image (100×100) high-resolution image (400×400)

CONTOH LAIN

CONTOH LAIN

Pengolahan Citra Dijital CONTOH LAIN Pengolahan Citra Dijital

TRANSLATION

PERHITUNGAN NUMERIS INTERPOLASI Nearest Neighbor Translasi 1.7 piksel

PERHITUNGAN NUMERIS INTERPOLASI Bilinear Translasi 0.5 piksel

PERHITUNGAN NUMERIS INTERPOLASI Bicubic Translasi 0.5 piksel

Error Concealment/Penghilangan Noise interpolated damaged

Image Mosaicing/Penggabungan Citra

Geometric Transformation

SCALING Memperbesar : enlarging, magnification, scaling up, zooming, upsampling, stretching, zoom-in Memperkecil : shrinking, scaling down, decimation, downsampling, minification, zoom-out hal yang perlu diperhatikan pada proses penskalaan: Resolusi citra tidak bisa ditingkatkan Jumlah piksel yang dimiliki tidak lebih daripada jumlah yang ada pada citra asli Selalu ada degradasi citra Dalam memperbesar, holes harus diisi dengan nilai piksel tertentu melalui interpolasi ataupun educated guest Dalam memperkecil, ada piksel-piksel yang dihilangkan melalui cara perataan (averaging)

TEKNIK SCALING Pembesaran Pengecilan Pixel replication Median Representation Average Representation

MINIFIKASI

ILUSTRASI SCALE a=1/2

ILUSTRASI SHEAR

ROTASI TRANSLASI MIRRORING Formula Jika angle kelipatan 90° maka rotasi dapat dilakukan lebih sederhana (tanpa operasi floating-point) dengan cara transposisi Translasi Proses move piksel, bukan copy piksel Mirroring Flip pada sumbu x atau sumbu y Horizontal mirroring ~ flip pada sumbu y Vertical mirroring ~ flip pada sumbu x

ROTASI

CONTOH ROTASI θ=3o

Ilustrasi Program