Angular Embedding: from Jarring Intensity Differences to Perceived Luminance Stella X. Yu Computer Science Boston College Acknowledgements: Edward H. Adelson Clare Boothe Luce Professorship NSF CAREER IIS-0644204 IEEE Conference on Computer Vision and Pattern Recognition, 2009 1 / 15
Distinction: Intensity, Brightness, and Lightness 1 4 .7 .3 5 .3 3 .4 6 .2 2 .4 intensity = measured luminance: I 1 > I 2 = I 3 > I 4 = I 5 > I 6 brightness = perceived luminance: B 1 > B 2 > B 3 > B 4 > B 6 > B 5 lightness = perceived reflectance: L 1 = L 2 > L 3 = L 4 = L 6 > L 5 2 / 15
Helmholtz and Hering Debate 1. Helmholtz: byproduct of high-level cognitive cause – recover reflectance from luminance with unknown illumination – Land & McCann, Retinex, 1971 – Barrow & Tenenbaum, intrinsic images, 1978 2. in-between – Ross & Pessoa, selective integration model, 2000 – Kelly & Grossberg, Form-And-Color-And-DEpth, 2000 3. Hering: manifestation of low-level physiological cause – lateral inhibition, center-surround filtering – Blakeslee et al, multiscale filtering, 2005 3 / 15
Basic Brightness Illusions L D Simultaneous Contrast S L D L S D White Anti-snake Snake 4 / 15
Textbook Explanation: Center-Surround Filtering + D L scale too large scale just right L + D L D scale too small S + S center-surround filter = difference of Gaussians 5 / 15
Selective Enhancement is a Must but not by Size 0.4 0.9 0.2 0.7 L D 0 0.5 −0.2 0.3 L ✔ D −0.4 0.1 increment-decrement derivative modified and integrated double-decrement 0.4 0.9 0.2 0.7 L D 0 0.5 −0.2 0.3 D ✘ L −0.4 0.1 Enhancing small edges only explains one of the two illusions! 6 / 15
b b Insight: Selective Enhancement by Edge Geometry 2 1 edge difference intensified around a corner! pixel a pixel b Coarse-scale differences provide Brightness differences across an the right selective enhancement. edge increase with its curvature. 7 / 15
b b b b b b b b Brightness is Analogous to Motion Perception short-range cue long-range cue fine-scale interior cue integration measured intensity perceived brightness 1. Feature → enable brightness with short-range cues fine-scale for interiors, and coarser-scale across edges 2. Aperture → reinforce brightness with long-range cues paths of higher confidence, originating from corners, dominate 3. Integration → realize brightness from pairwise local cues maximally fulfill local orderings in accordance with confidence levels 8 / 15
Brightness Modeling is Global Brightness Ordering 1. edge detection 2. brightness ordering 3. angular embedding intensity pairwise edges pairwise differences brightness I E ( O , C ) B difference B − I 9 / 15
b b b b b New Integration Method: Angular Embedding input: local ordering output: global ordering O = pairwise differences x = positions on a line, or C = confidence in O z = positions on the unit circle old: linear space x ( a ) − x ( b ) = O ( a , b ) ? x ( c ) x ( a ) x ( b ) j b z ( a ) = e j θ ( a ) new: angular space θ ( a ) − θ ( b ) = O ( a , b ) ? z ( c ) b z ( b ) θ ( a ) θ ( c ) θ ( b ) 0 1 10 / 15
b b b b Criterion: Minimize Distance to Local Average j z ( a ) z ( c ) e jO ( a , c ) b z ( b ) e jO ( a , b ) z ( a ) b ˜ z ( c ) O ( a , b ) O ( a , c ) b z ( b ) C ( a , b ) C ( a , c ) θ ( b ) 0 1 � z ( a ) | 2 minimize: ǫ ( z ; O , C ) = D ( a , a ) · | z ( a ) − ˜ a C ( a , b ) � D ( a , a ) z ( b ) e jO ( a , b ) local average: ˜ z ( a ) = b � total confidence: D ( a , a ) = C ( a , b ) b 11 / 15
Optimum: Angles of the Smallest Eigenvector angular embedding ǫ ( z ; O , C ) = z ′ Wz minimize: z = e j θ representation: W = ( I − D − 1 M ) ′ D ( I − D − 1 M ) error: M = C • e jO measurement: D = Diag ( C 1 ) degree: θ ∗ = ∡ z ∗ = ∡ smallest-eigenvector-of ( W , D ) optimum: least squares � C ( a , b )( x ( a ) − x ( b ) − O ( a , b )) 2 minimize: ǫ ( x ; O , C ) = M = C • O + ( C • O ) ′ measurement: D = Diag (( C + C ′ ) 1 ) degree: P = D − 1 ( C + C ′ ) transition: x ∗ = ( I − P ) − 1 · ( D − 1 M 1 ) optimum: 12 / 15
An Efficient and More Robust Integration Method 3 × 6 measurement outliers LS optimum x ∗ original image neighbourhood radius = 2 AE optimum z ∗ AE optimum θ ∗ 13 / 15
Brightness as Intensity Deviating along Gradient Adelson, 1999: X junctions & atmospheres transparency haze clear paint deviation by scene interpretation deviation by intensity context itself n-rev-T rev-T n-rev-X s-rev-X d-rev-X intensity brightness difference 14 / 15
Brightness as Gestalt from Scale-Mixed Differences input: objective intensity ⇓ output: subjective brightness brightness − intensity Simultaneous Contrast Anti-Snake Snake Koffka Ring Benary Cross 15 / 15
Recommend
More recommend
