Image Processing and Camera Geometry

• The following notes cover fundamentals of image processing, camera geometry and stereo geometry

Fundamentals of Image Processing

• Edge detection is an example of image processing
• The number of pixels per unit area defines image resolution
• A binary image comprises only black and white pixels
• A pixel represents a single color value, a small square, and the smallest unit of an image
• Gaussian filter is most effective for removing Gaussian noise
• Spatial domain filtering operates directly on pixel values, while frequency domain filtering modifies frequency components
• High-pass filtering sharpens an image by emphasizing high-frequency components
• Histogram equalization improves image contrast
• Applying histogram equalization to a low-contrast image improves the image contrast
• Image blurring isn't a contrast enhancement technique
• Image interpretation is not a fundamental step in image processing
• JPEG supports both lossless and lossy compression
• RGB, CMYK and HSV are color models used for image processing
• AVI is not an image file format
• Salt-and-pepper noise is caused by sudden disturbances in image acquisition, like faulty sensors
• Sobel filter is best for edge detection
• Gaussian filter is a low-pass filter
• The primary function of a median filter is noise reduction
• All of the following operations improve image brightness: Power-law (gamma) transformation, Logarithmic transformation, and Contrast stretching
• Histogram matching modifies an image to match a given histogram
• Contrast stretching enhances the difference between bright and dark areas
• Gamma correction adjusts brightness non-linearly

Image Analysis: Numerical Questions

• An image with a resolution of 1024 x 768 = 786,432 total pixels
• An 8-bit grayscale image has intensity values ranging from 0 to 255
• Storing an 800 x 600 pixel image with 24-bit color depth requires 14,400,000 bits
• An uncompressed 512 x 512 grayscale image with 8-bit depth requires 256 KB of storage space
• A true-color image with a depth of 24 bits per pixel can represent 16,777,216 colors
• When a 3 x 3 mean filter is applied to an image, 8 neighboring pixels are used in the filtering process (excluding the center pixel)
• A Gaussian filter with a kernel size of 5 x 5 has 25 coefficients
• An image with dimensions 256 x 256 undergoing a Fourier Transform will have a frequency domain size of 256 x 256
• A grayscale image with an intensity range of 50 to 200, after histogram equalization is applied, the new intensity range will be 0 to 255
• Applying a 3 x 3 Laplacian filter to a 256 x 256 image performs 589,824 convolution operations
• A gamma correction function is applied with γ = 2; If the input pixel intensity = 0.5, the new intensity value = 0.25

Camera Geometry

• Light rays pass through a single point before forming an image, a foundational assumption of the pinhole camera model
• The intrinsic camera matrix is defined by 5 parameters
• A major drawback of a pinhole camera is that it requires a very small aperture, which leads to low brightness
• In a pinhole camera, image size is inversely proportional to object distance Z
• Adding a lens to a pinhole camera increases brightness and focus
• Convex lenses reduce image distortion in camera systems
• The focal length of a lens: distance between the camera lens and the image plane when focused at infinity
• CCD cameras convert light into electrical charges
• Low power consumption is NOT an advantage of CCD sensors
• CCD sensors have better low-light performance than CMOS sensors
• A general projective camera transforms a 3D point into a 2D image using perspective projection
• Affine cameras assume that parallel lines remain parallel in the image
• Shear transformation approximates perspective effects in affine cameras
• Camera calibration estimates the focal length and intrinsic parameters
• Checkerboard pattern calibration is commonly used for camera calibration
• In 2D projective geometry, 3 homogeneous coordinates are required to represent a point
• Collinearity is preserved by a projective transformation
• A point at infinity in homogeneous coordinates is represented by (x, y, 0)
• A homography is a transformation that maps points from one 2D plane to another 2D plane
• 9 parameters are needed to define a homography matrix
• A homography matrix uses 4 corresponding points for computation
• Image stitching uses homography estimation
• Perspective correction converts a perspective image into a front-facing view
• Homography transformation is commonly used for rectifying images
• A camera has a focal length of 50 mm and a sensor width of 36 mm, the field of view is 39.6°
• A homography matrix has a determinant value of 0, indicating the transformation is singular and non-invertible
• An affine transformation has 6 degrees of freedom: scaling, translation, rotation, and shear

Stereo Geometry

• Epipolar geometry describes the relationship between two different images of the same scene
• An epipole in stereo vision is a point where the baseline intersects the image plane
• Epipolar lines are parallel in rectified stereo images
• If two cameras are aligned and rectified, the orientation of epipolar lines is horizontal
• The fundamental matrix represents the relationship between corresponding points in two views
• The fundamental matrix is a 3x3 matrix of rank 2
• Eight-point correspondences are used to compute the fundamental matrix using the 8-point algorithm
• In stereo images, the constraint x'T F x = 0 holds for all corresponding points
• The normalized 8-point algorithm reduces numerical instability by normalizing coordinates
• Scaling and translation is applied to points in the normalized 8-point algorithm to make compuation more stable
• The output of the 8-point algorithm is a fundamental matrix
• Algebraic minimization in fundamental matrix estimation minimizes algebraic error based on a linear equation
• Geometric distance computation in stereo vision aims to minimize the squared Euclidean distance
• Perspective transformation is not a type of camera motion model
• In camera motion, the rotation matrix must be orthogonal
• The main constraint of a rigid-body transformation in 3D motion: it preserves distances and angles
• The Euclidean motion model assumes both rotation and translation
• The affine motion model is commonly used in optical flow estimation because it allows translation and scaling
• Optical flow describes the motion of pixels in an image sequence
• The Lucas-Kanade method assumes constant brightness for optical flow
• The brightness constancy equation is fundamental in optical flow computation
• Triangulation in 3D vision estimates the 3D position of a point from multiple images
• Linear triangulation requires two or more calibrated camera views
• SVD decomposition is commonly used for linear triangulation
• Two cameras are placed 10 cm apart. An object's disparity doubles from 5 to 10 pixels, indicating the object is half as far
• A stereo system with a baseline of 50 mm, focal length of 35 mm; for an object at 500 mm distance, the expected disparity is 7 pixels
• A 3D point observed in two images at (120,80) and (110,85) suggests the point is closer to the camera, because greater disparity means the point is nearer