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ANALYSIS AND COMPRESSION

OF REFLECTANCE DATA 

USING AN EVOLVED 

SPECTRAL CORRELATION PROFILE
Peter Morovič*, Ján Morovič*, Michael Brillº, Eric Walowit
*Hewlett Packard Company, ºDatacolor Inc
OUTLINE
• Motivation
• How far did we get for last year’s CIC21?
• Spectral analysis using neighborhood profiles
• Relative/Absolute Spectral Neighborhood Range (R/ASN)
• Spectral Neighborhood Distribution (SND)
• Spectral Neighborhood Correlation (SNC)
• Spectral compression using SNC profile
• Evaluating spectral compression
• Conclusions
2
MOTIVATION
• Spectral data is the basis of all color and imaging research and applications
• Variety of data processed, but stimuli have spectral properties among their causes
• Needed to provide solutions (e.g. multiple illuminants, observers (human/machine),
materials)
• Challenge: spectral data is higher dimensional than colorimetric data → requires more
storage, may also require more computation and operating memory
• But: spectra don’t have dimensionality matching number of samples
• linear combinations of 3-8 basic “spectra” give very close approximations of measurements
taken at 16 or even 31 wavelengths
• PCA typically used to reduce dimensionality and compress spectral data, but:
• PCA weights strip data of range
• PCA weights have no physical meaning → not suitable for physical analysis or computation
3
MEANINGS OF “PHYSICAL MEANING”
• Allows a wavelength-by-wavelength analysis such as
Kubelka-Munk, in coded-and-decoded (codec) state:
Compression will save storage but not cpu time.
• Example: wavelength-derivative encoding, but not PCA
• Allows a wavelength-by-wavelength analysis such as
Kubelka-Munk, in coded state: saves storage and cpu time.
• Example: Neither wavelength-derivative nor PCA
• An option allowing both “physical meanings”—our way—is
to drop certain wavelengths with redundant information.
4
CIC21 INSIGHT
5
High correlation, BUT, not all (neighbouring) wavelengths created equal.
ANALYZING SPECTRA
6
SPECTRAL NEIGHBORHOOD PROFILES
• CIC21 “spectral correlation profile” - intuitive, first attempt
• Now: formal exposition + new domains:
• Relative Spectral Neighborhood Range (same as CIC21)
• Absolute Spectral Neighborhood Range
• Spectral Neighborhood Distribution
• Spectral Neighborhood Correlation
7
RELATIVE SPECTRAL NEIGHBORHOOD RANGE PROFILE
• M reflectances S, with N equal-interval spectral samples (i.e., S is an M x N
matrix)
• Relative Spectral Neighborhood Range Profile defined as pair of (N-1) –
vectors cmin and cmax where at each wavelength λi:
cmin(i) = MINj=1:M S(j, i) - S(j, i+1)
cmax(i) = MAXj=1:M S(j, i) - S(j, i+1)
• I.e., cmin & cmax are lower and upper bounds of neighboring wavelength sample
differences
• if negative → at least one case where reflectance is increasing
• if positive → all reflectances are decreasing between λi and λi+1
8
CHECKING & GENERATING REFLECTANCES
• 1 x N reflectance vector s satisfies rSNR profile, if for all neighboring wavelengths λi and λi+1
following inequalities hold:
• cmin(i) ≤ s(i) - s(i+1) ≤ cmax(i)
• Synthetic reflectances can be generated from an rSNR profile progressively (where superscript
1 refers to the upper and 2 to the lower limit branch at each step):
• Note, following scheme samples extremes of spectral “envelope” - any value within its limits
can be samples by weighting cmax(i) or cmin(i)
• Generated spectra are clipped to valid range [0,1]
9
ABSOLUTE SPECTRAL NEIGHBORHOOD RANGE PROFILE
• rSNR does not consider the offset of actual values at any one wavelength
• Range of data represented by two (N-1)-vectors vmin and vmax
• For rSNR these are implicitly at 0 and 1 respectively
• They are the minimum and maximum reflectance values at any
wavelength λi over the whole S:
vmin(i) = MINj=1:M S(j, i)
vmax(i) = MAXj=1:M S(j, i)
• Generating reflectances: vmin and vmax used as starting point and limit for
progressive process described for rSNR
10
SPECTRAL NEIGHBORHOOD DISTRIBUTION PROFILE
• Distributions, instead of only ranges, of absolute differences across
wavelengths
• N-1 distributions computed from S - e.g., approximated by normal
distribution
• At each wavelength: mean & standard deviation of pair of wavelengths
under scrutiny:
dμ(i) = MEANj=1:M S(j, i) - S(j, i+1)
dσ(i) = STDDj=1:M S(j, i) - S(j, i+1)
• Statistical synthesis: new data consistent in probability of values at λ.
11
SPECTRAL NEIGHBORHOOD DISTRIBUTION PROFILE
12
SPECTRAL NEIGHBORHOOD CORRELATION PROFILE
• Small per-neighboring-wavelength ranges yield high correlation coefficients
• BUT: converse not true for large ranges:
• correlation coefficients can be small if distribution is narrow and the range
is wide due to outliers, or
• large if distribution has spread in the data
• (N-1)-vector r computed to express degree to which sets A and B of m
neighboring wavelengths are correlated:
13
SPECTRAL NEIGHBORHOOD CORRELATION PROFILE
14
COMPRESSING SPECTRA
15
WISHLIST
A compressed representation of spectra that:
Preserves ranges
&
Retains physical meaning of values
16
APPLICATION: OPTIMAL SPECTRAL SAMPLING
• Aim: how to select the optimal set of non-uniform spectral bands for
representing a data set → SNCP
• Given a data set with N equidistant wavelength samples:
• Compute Spectral Neighborhood Correlation Profile (SNCP)
• For i=1:N-1, progressively pick i wavelengths with lowest correlation
• For each of N-1 sets of i wavelengths
• Interpolate values at wavelengths i from full data set
• Compare against original spectral data using MIPE metric (∆E00s under
173 illuminants)
17
SNCP CODEC SUMMARY
• Code: drop samples where the correlation between
wavelengths is greatest
• Decode: interpolate among remaining samples
• Properties: physically-meaningful, compressed
representation that can also be suitable for further
computation performed in same way as on canonical,
equidistant wavelength sample representations (e.g.,
Kubelka-Munk).
18
SNCPs
19
Munsell SOCS
SNCPs
20
Munsell SOCS
Progressive adding of wavelengths

in order from lowest to highest correlation coefficient
MIPE
21
Munsell SOCS
10 samples
discardable with
minimal impact
EVALUATING REDUCED-SAMPLING DATA
22
16-sampleSOCS
11-sampleSOCS
EVALUATING REDUCED-SAMPLING DATA
23
16-sampleSOCS
11-sampleSOCS
CONCLUSIONS
• The relationships between neighboring wavelength intervals are an inherent
characteristic of single reflectance or their sets
• New approaches presented for their characterization that allow for:
• gamut-aware synthesis
• synthesis that preserves original data set’s difference distributions
• dimensionality reduction that takes advantage of highly correlated neighbors
• SNCP enabled physically-meaningful, compressed representation that can also be
suitable for further computation
• Spectral neighborhood based techniques are a useful extension to existing methods of
spectral analysis and processing
• Good starting point to revisiting various applications in the future: e.g., choice of spectral
data used for camera characterization, which authors will explore next
24
THANK YOU!
25

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Analysis and Compression of Reflectance Data Using An Evolved Spectral Correlation Profile

  • 1. ANALYSIS AND COMPRESSION
 OF REFLECTANCE DATA 
 USING AN EVOLVED 
 SPECTRAL CORRELATION PROFILE Peter Morovič*, Ján Morovič*, Michael Brillº, Eric Walowit *Hewlett Packard Company, ºDatacolor Inc
  • 2. OUTLINE • Motivation • How far did we get for last year’s CIC21? • Spectral analysis using neighborhood profiles • Relative/Absolute Spectral Neighborhood Range (R/ASN) • Spectral Neighborhood Distribution (SND) • Spectral Neighborhood Correlation (SNC) • Spectral compression using SNC profile • Evaluating spectral compression • Conclusions 2
  • 3. MOTIVATION • Spectral data is the basis of all color and imaging research and applications • Variety of data processed, but stimuli have spectral properties among their causes • Needed to provide solutions (e.g. multiple illuminants, observers (human/machine), materials) • Challenge: spectral data is higher dimensional than colorimetric data → requires more storage, may also require more computation and operating memory • But: spectra don’t have dimensionality matching number of samples • linear combinations of 3-8 basic “spectra” give very close approximations of measurements taken at 16 or even 31 wavelengths • PCA typically used to reduce dimensionality and compress spectral data, but: • PCA weights strip data of range • PCA weights have no physical meaning → not suitable for physical analysis or computation 3
  • 4. MEANINGS OF “PHYSICAL MEANING” • Allows a wavelength-by-wavelength analysis such as Kubelka-Munk, in coded-and-decoded (codec) state: Compression will save storage but not cpu time. • Example: wavelength-derivative encoding, but not PCA • Allows a wavelength-by-wavelength analysis such as Kubelka-Munk, in coded state: saves storage and cpu time. • Example: Neither wavelength-derivative nor PCA • An option allowing both “physical meanings”—our way—is to drop certain wavelengths with redundant information. 4
  • 5. CIC21 INSIGHT 5 High correlation, BUT, not all (neighbouring) wavelengths created equal.
  • 7. SPECTRAL NEIGHBORHOOD PROFILES • CIC21 “spectral correlation profile” - intuitive, first attempt • Now: formal exposition + new domains: • Relative Spectral Neighborhood Range (same as CIC21) • Absolute Spectral Neighborhood Range • Spectral Neighborhood Distribution • Spectral Neighborhood Correlation 7
  • 8. RELATIVE SPECTRAL NEIGHBORHOOD RANGE PROFILE • M reflectances S, with N equal-interval spectral samples (i.e., S is an M x N matrix) • Relative Spectral Neighborhood Range Profile defined as pair of (N-1) – vectors cmin and cmax where at each wavelength λi: cmin(i) = MINj=1:M S(j, i) - S(j, i+1) cmax(i) = MAXj=1:M S(j, i) - S(j, i+1) • I.e., cmin & cmax are lower and upper bounds of neighboring wavelength sample differences • if negative → at least one case where reflectance is increasing • if positive → all reflectances are decreasing between λi and λi+1 8
  • 9. CHECKING & GENERATING REFLECTANCES • 1 x N reflectance vector s satisfies rSNR profile, if for all neighboring wavelengths λi and λi+1 following inequalities hold: • cmin(i) ≤ s(i) - s(i+1) ≤ cmax(i) • Synthetic reflectances can be generated from an rSNR profile progressively (where superscript 1 refers to the upper and 2 to the lower limit branch at each step): • Note, following scheme samples extremes of spectral “envelope” - any value within its limits can be samples by weighting cmax(i) or cmin(i) • Generated spectra are clipped to valid range [0,1] 9
  • 10. ABSOLUTE SPECTRAL NEIGHBORHOOD RANGE PROFILE • rSNR does not consider the offset of actual values at any one wavelength • Range of data represented by two (N-1)-vectors vmin and vmax • For rSNR these are implicitly at 0 and 1 respectively • They are the minimum and maximum reflectance values at any wavelength λi over the whole S: vmin(i) = MINj=1:M S(j, i) vmax(i) = MAXj=1:M S(j, i) • Generating reflectances: vmin and vmax used as starting point and limit for progressive process described for rSNR 10
  • 11. SPECTRAL NEIGHBORHOOD DISTRIBUTION PROFILE • Distributions, instead of only ranges, of absolute differences across wavelengths • N-1 distributions computed from S - e.g., approximated by normal distribution • At each wavelength: mean & standard deviation of pair of wavelengths under scrutiny: dμ(i) = MEANj=1:M S(j, i) - S(j, i+1) dσ(i) = STDDj=1:M S(j, i) - S(j, i+1) • Statistical synthesis: new data consistent in probability of values at λ. 11
  • 13. SPECTRAL NEIGHBORHOOD CORRELATION PROFILE • Small per-neighboring-wavelength ranges yield high correlation coefficients • BUT: converse not true for large ranges: • correlation coefficients can be small if distribution is narrow and the range is wide due to outliers, or • large if distribution has spread in the data • (N-1)-vector r computed to express degree to which sets A and B of m neighboring wavelengths are correlated: 13
  • 16. WISHLIST A compressed representation of spectra that: Preserves ranges & Retains physical meaning of values 16
  • 17. APPLICATION: OPTIMAL SPECTRAL SAMPLING • Aim: how to select the optimal set of non-uniform spectral bands for representing a data set → SNCP • Given a data set with N equidistant wavelength samples: • Compute Spectral Neighborhood Correlation Profile (SNCP) • For i=1:N-1, progressively pick i wavelengths with lowest correlation • For each of N-1 sets of i wavelengths • Interpolate values at wavelengths i from full data set • Compare against original spectral data using MIPE metric (∆E00s under 173 illuminants) 17
  • 18. SNCP CODEC SUMMARY • Code: drop samples where the correlation between wavelengths is greatest • Decode: interpolate among remaining samples • Properties: physically-meaningful, compressed representation that can also be suitable for further computation performed in same way as on canonical, equidistant wavelength sample representations (e.g., Kubelka-Munk). 18
  • 20. SNCPs 20 Munsell SOCS Progressive adding of wavelengths
 in order from lowest to highest correlation coefficient
  • 24. CONCLUSIONS • The relationships between neighboring wavelength intervals are an inherent characteristic of single reflectance or their sets • New approaches presented for their characterization that allow for: • gamut-aware synthesis • synthesis that preserves original data set’s difference distributions • dimensionality reduction that takes advantage of highly correlated neighbors • SNCP enabled physically-meaningful, compressed representation that can also be suitable for further computation • Spectral neighborhood based techniques are a useful extension to existing methods of spectral analysis and processing • Good starting point to revisiting various applications in the future: e.g., choice of spectral data used for camera characterization, which authors will explore next 24